Given the following transfer function:

H(z): 1.7/1 + 3.6 z^-1 - 0.5/1-0.9z^-1

a. Calculate its right-sided (causal) inverse z-transform h(n).
b. Plot its poles/zeros and determine its region of convergence (ROC).
c. Is the system stable?

Answers

Answer 1

a). u(n) is the unit step function, b). the ROC includes the entire z-plane except for the pole at z = 0.9 , c). the pole at z = 0.9 lies outside the unit circle, so the system is unstable.

a. To calculate the right-sided (causal) inverse z-transform h(n) of the given transfer function H(z), we can use partial fraction decomposition. First, let's rewrite H(z) as follows:

H(z) = 1.7/(1 + 3.6z^-1) - 0.5/(1 - 0.9z^-1)

By using the method of partial fractions, we can rewrite the above expression as:

H(z) = (1.7/3.6)/(1 - (-1/3.6)z^-1) - (0.5/0.9)/(1 - (0.9)z^-1)

Now, we can identify the inverse z-transforms of the individual terms as:

h(n) = (1.7/3.6)(-1/3.6)^n u(n) - (0.5/0.9)(0.9)^n u(n)

Where u(n) is the unit step function.

b. To plot the poles and zeros of the transfer function, we examine the denominator and numerator of H(z):

Denominator: 1 + 3.6z^-1 Numerator: 1.7

Since the denominator is a first-order polynomial, it has one zero at z = -3.6. The numerator doesn't have any zeros.

The region of convergence (ROC) is determined by the location of the poles. In this case, the ROC includes the entire z-plane except for the pole at z = 0.9.

c. To determine the stability of the system, we need to examine the location of the poles. If all the poles lie within the unit circle in the z-plane, the system is stable. In this case, the pole at z = 0.9 lies outside the unit circle, so the system is unstable.

Learn more about unit step function

https://brainly.com/question/32543758

#SPJ11


Related Questions

Determine whether the three points
P = (–6, –9, −7), Q = (–7, −11, −10), R = (−8, –12, —13) are colinear by computing the distances between pairs of points. Distance from P to Q: ______
Distance from Q to R: ______
Distance from P to R: ______
Are the three points colinear (y/n)? _____

Answers

Distance from P to Q: sqrt[14]

Distance from Q to R: sqrt[11]

Distance from P to R: 7

Are the three points collinear? No.

Given the points P = (–6, –9, −7), Q = (–7, −11, −10), and R = (−8, –12, —13), we need to determine if these points are collinear by checking if the distances between any two pairs of points are equal.

To calculate the distance between P and Q, we can use the distance formula:

d(P, Q) = sqrt[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²], where (x1, y1, z1) and (x2, y2, z2) are the coordinates of points P and Q, respectively.

Substituting the values, we have:

d(P, Q) = sqrt[(-7 + 6)² + (-11 + 9)² + (-10 + 7)²]

       = sqrt[1² + 2² + 3²]

       = sqrt[14]

Therefore, the distance from P to Q is sqrt[14].

Next, let's calculate the distance between Q and R:

d(Q, R) = sqrt[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²]

Substituting the values, we have:

d(Q, R) = sqrt[(-8 + 7)² + (-12 + 11)² + (-13 + 10)²]

       = sqrt[(-1)² + (-1)² + (-3)²]

       = sqrt[11]

Therefore, the distance from Q to R is sqrt[11].

Finally, let's calculate the distance between P and R:

d(P, R) = sqrt[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²]

Substituting the values, we have:

d(P, R) = sqrt[(-8 + 6)² + (-12 + 9)² + (-13 + 7)²]

       = sqrt[(-2)² + (-3)² + (-6)²]

       = sqrt[49]

       = 7

Therefore, the distance from P to R is 7.

To determine if the three points are collinear, we need to check if the sum of the distances from P to Q and from Q to R is equal to the distance from P to R.

Distance from P to Q + Distance from Q to R = sqrt[14] + sqrt[11]

                                           ≠ 7 (Distance from P to R)

Therefore, the three points P, Q, and R are not collinear.

In summary:

Distance from P to Q: sqrt[14]

Distance from Q to R: sqrt[11]

Distance from P to R: 7

Are the three points collinear? No.

Learn more about Equation from the link:

brainly.com/question/29538993

#SPJ11

Suppose h(t)=5+200t-t^2 describes the height, in feet, of a ball thrown upwards on an alien planet t seconds after the releasd from the alien's three fingered hand.
(a) Find the equation for velocity of the ball.
h' (t) = _______
(b) Find the equation for acceleration of the ball.
h" (t) = ________
(c) calculate the velocity 30 seconds after release
h' (30) = ________
(d) calculate the acceleration 30 seconds after
h" (30) = ________

Answers

a) the equation for velocity of the ball is h'(t) = 200 - 2t

b) the equation for acceleration of the ball is h''(t) = -2

c) the velocity 30 seconds after release is 140 ft/s.

d) the acceleration 30 seconds after release is -2 ft/s².

(a) To find the equation for velocity of the ball, we need to take the first derivative of the given equation h(t).

h(t) = 5 + 200t - t²

Differentiating h(t) w.r.t t, we get

dh(t) / dt = 0 + 200 - 2tdh(t) / dt = 200 - 2t

Therefore, the equation for velocity of the ball is h'(t) = 200 - 2t

(b) To find the equation for acceleration of the ball, we need to take the second derivative of the given equation h(t).

h(t) = 5 + 200t - t²

Differentiating h(t) twice w.r.t t, we get

d²h(t) / dt² = 0 - 2dt

dh(t) / dt² = - 2

Therefore, the equation for acceleration of the ball is h''(t) = -2

(c) To calculate the velocity 30 seconds after release, we substitute t = 30 in h'(t) = 200 - 2t.

h'(30) = 200 - 2(30)h'(30) = 140

Therefore, the velocity 30 seconds after release is 140 ft/s.

(d) To calculate the acceleration 30 seconds after, we substitute t = 30 in h''(t) = -2h''(30) = -2

Therefore, the acceleration 30 seconds after release is -2 ft/s².

To know more about velocity, visit:

https://brainly.com/question/30559316

#SPJ11

A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function 8(t)=44+8e−0.02t, where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first six years. The average price of the stock is 5 (Round to the nearest cent as needed).

Answers

The average price of the stock over the first six years is $52.

The given function is [tex]S(t)=44+8e^{0.02t}[/tex].

Where, t is the time (in years) since the stock was purchased

We want to find the average price of the stock over the first six years.

To find the average price we will need to find the 6-year sum of the stock price and divide it by 6.

To find the 6-year sum of the stock price, we will need to evaluate the function at t = 0, t = 1, t = 2, t = 3, t = 4, and t = 5 and sum up the results.

Therefore,

S(0)=44+[tex]8e^{-0.02(0)}[/tex] = 44+8 = 52

S(1)=44+[tex]8e^{-0.02(1)}[/tex]= 44+7.982 = 51.982

S(2)=44+[tex]8e^{-0.02(2)}[/tex] = 44+7.965 = 51.965

S(3)=44+[tex]8e^{-0.02(3)}[/tex] = 44+7.949 = 51.949

S(4)=44+8[tex]e^{-0.02(4)}[/tex] = 44+7.933 = 51.933

S(5)=44+[tex]8e^{-0.02(5)}[/tex] = 44+7.916 = 51.916

The 6-year sum of the stock price is 51 + 51.982 + 51.965 + 51.949 + 51.933 + 51.916 = 309.715.

The average price of the stock over the first six years is 309.715/6 = 51.619167 ≈ 52

Therefore, the average price of the stock over the first six years is $52.

To learn more about an average visit:

https://brainly.com/question/11195029.

#SPJ4

the graph of y = - square root x is shifted two units up and five units left

Answers

The final transformed function, after shifting two units up and five units left, is y = -√(x + 5) + 2.

To shift the graph of the function y = -√x, two units up and five units left, we can apply transformations to the original function.

Starting with the function y = -√x, let's consider the effect of each transformation:

1. Shifting two units up: Adding a positive constant value to the function moves the entire graph vertically upward. In this case, adding two to the function shifts it two units up. The new function becomes y = -√x + 2.

2. Shifting five units left: Subtracting a positive constant value from the variable inside the function shifts the graph horizontally to the right. In this case, subtracting five from x shifts the graph five units left. The new function becomes y = -√(x + 5) + 2.

The final transformed function, after shifting two units up and five units left, is y = -√(x + 5) + 2.

This transformation affects every point on the original graph. Each x-value is shifted five units to the left, and each y-value is shifted two units up. The graph will appear as a reflection of the original graph across the y-axis, translated five units to the left and two units up.

It's important to note that these transformations preserve the shape of the graph, but change its position in the coordinate plane. By applying these shifts, we have effectively moved the graph of y = -√x two units up and five units left, resulting in the transformed function y = -√(x + 5) + 2.

for more such question on function visit

https://brainly.com/question/11624077

#SPJ8

Find the indicated derivative or antiderivative (a) dxd​x2+4x−x1​ (b) ∫x2+4x−x1​dx (c) d/dx​(x+5)(x−2) (d) ∫(x+5)(x−2)dx

Answers

The derivative or antiderivative of the given functions are obtained using quotient rule of differentiation.

a) To find the derivative of the given function dx/ (x^2 + 4x - 1), apply the quotient rule of differentiation.

[tex]df/dx = (g(x)f'(x) - f(x)g'(x)) / (g(x))^2[/tex]

Here, g(x) = x^2 + 4x - 1 and f(x) = 1.

Using the product rule,dg/dx = 2x + 4 and hence g'(x) = 2x + 4

Using the quotient rule,

[tex]d/dx (1/g(x)) = -g'(x) / (g(x))^2\\df/dx = [(x^2 + 4x - 1)(0) - 1(2x + 4)] / (x^2 + 4x - 1)^2\\= -(2x + 4) / (x^2 + 4x - 1)^2[/tex]

b) To find the antiderivative of the given function ∫dx/ (x^2 + 4x - 1), apply the substitution method.

Substituting

[tex]u = x^2 + 4x - 1 \\du = (2x + 4)dx.[/tex]

Now, the integral becomes ∫du / u²

Taking the antiderivative, we get

[tex]-1/u + C = -1 / (x^2 + 4x - 1) + C,[/tex]

where C is the constant of integration.

c) To find the derivative of the given function d/dx (x+5)(x-2),

apply the product rule of differentiation.

[tex]d/dx [(x+5)(x-2)] = (x+5)d/dx (x-2) + (x-2)d/dx (x+5)\\= (x+5)(1) + (x-2)(1)\\= 2x + 3[/tex]

d) To find the antiderivative of the given function ∫(x+5)(x-2)dx, apply the distributive property of integration.

[tex]∫(x+5)(x-2)dx= ∫(x^2 + 3x - 10)dx\\= (x^3/3) + (3x^2/2) - 10x + C,[/tex]

where C is the constant of integration.

Know more about the quotient rule

https://brainly.com/question/32942724

#SPJ11

A company sells x whiteboard markers each year at a price of Sp per parker. The price-demand equation is p = 15-0.003x.
a. What price should the company charge for the markers to maximize revenue?
b. What is the maximum revenue?

Answers

The maximum revenue that the company will obtain is $18,750.

To determine the price at which the company should charge for the markers to maximize revenue, we start by finding the derivative of the price-demand equation and setting it equal to zero. This is because the maximum revenue occurs when the derivative of the revenue function is zero.

The price-demand equation is given as p = 15 - 0.003x, where p represents the price per marker and x represents the quantity sold.

Recall that the revenue equation is R = xp, where R represents revenue. Substituting the given price-demand equation into the revenue equation, we get:

R = x(15 - 0.003x)

R = 15x - 0.003x²

Next, we differentiate the revenue equation with respect to x:

dR/dx = 15 - 0.006x

Setting the derivative equal to zero, we have:

15 - 0.006x = 0

-0.006x = -15

x = 2500

Therefore, the value of x that maximizes the revenue is 2500. Since x represents the quantity sold, we substitute x = 2500 back into the demand equation:

p = 15 - 0.003(2500)

p = 7.50

Hence, the price that the company should charge for the markers to maximize revenue is $7.50 per marker.

Moving on to part (b), to calculate the maximum revenue, we substitute x = 2500 into the revenue equation:

R = (2500)(7.5)

R = $18,750

Therefore, the maximum revenue that the company will obtain is $18,750.

Learn more about Company from the given link:

brainly.com/question/30532251

#SPJ11

Use a calculator to find the following approximations with the given partitions:
a. f(x)=−(x−2)^2+4 from [0,4] with n=4. Left End Approximation
b. f(x)=−(x−2)^2+4 from [0,4] with n=16. Left End Approximation
c. f(x)=−(x−2)^2+4 from [0,4] with n=4. Right End Approximation
d. f(x)=−(x−2)^2+4 from [0,4] with n=16. Right End Approximatio

Answers

a. For f(x) = −(x - 2)² + 4 from [0, 4] with n = 4, Left End Approximation = 2.7031.
b. For f(x) = −(x - 2)² + 4 from [0, 4] with n = 16, Left End Approximation = 2.7201.
c. For f(x) = −(x - 2)² + 4 from [0, 4] with n = 4, Right End Approximation = 3.5938.
d. For f(x) = −(x - 2)² + 4 from [0, 4] with n = 16, Right End Approximation = 3.6454.

Solution: Given functions are: f(x) = −(x - 2)² + 4, a = 0 and b = 4n = 4,

for left end approximation Using the formula of Left End Approximation for 4 intervals= (width/3) [f(0) + f(1) + f(2) + f(3)]

Where, width = (b - a) / n= 4 / 4= 1

f(0) = f(a) = −(0 - 2)² + 4= -4

f(1) = −(1 - 2)² + 4= 1

f(2) = −(2 - 2)² + 4= 4

f(3) = −(3 - 2)² + 4= 1

Put all values in the above formula.= (1/3)[-4 + 1 + 4 + 1]= 2.7031

Therefore, left end approximation for n = 4 is 2.7031n = 16, for left end approximation

Using the formula of Left End Approximation for 16 intervals= (width/3) [f(0) + f(1/16) + f(2/16) + f(3/16) + ... + f(15/16)]

Where, width = (b - a) / n= 4 / 16= 0.25

f(0) = f(a) = −(0 - 2)² + 4= -4

f(1/16) = −(1/16 - 2)² + 4= 3.9419

f(2/16) = −(2/16 - 2)² + 4= 3.5

f(3/16) = −(3/16 - 2)² + 4= 2.9419 and so on....

f(15/16) = −(15/16 - 2)² + 4= -2.9419

Put all values in the above formula.= (0.25/3) [-4 + 3.9419 + 3.5 + 2.9419 + ... - 2.9419]= 2.7201

Therefore, left end approximation for n = 16 is 2.7201n = 4, for right end approximation

Using the formula of Right End Approximation for 4 intervals= (width/3) [f(1) + f(2) + f(3) + f(4)]

Where, width = (b - a) / n= 4 / 4= 1

f(1) = −(1 - 2)² + 4= 1

f(2) = −(2 - 2)² + 4= 4

f(3) = −(3 - 2)² + 4= 1

f(4) = −(4 - 2)² + 4= -4

Put all values in the above formula.= (1/3)[1 + 4 + 1 - 4]= 3.5938

Therefore, right end approximation for n = 4 is 3.5938n = 16, for right end approximation

Using the formula of Right End Approximation for 16 intervals= (width/3) [f(1/16) + f(2/16) + f(3/16) + f(4/16) + ... + f(16/16)]

Where, width = (b - a) / n= 4 / 16= 0.25

f(1/16) = −(1/16 - 2)² + 4= 3.9419

f(2/16) = −(2/16 - 2)² + 4= 3.5

f(3/16) = −(3/16 - 2)² + 4= 2.9419and so on....

f(16/16) = −(16/16 - 2)² + 4= -4

Put all values in the above formula.= (0.25/3)[3.9419 + 3.5 + 2.9419 + ... - 4]= 3.6454

Therefore, right end approximation for n = 16 is 3.6454

Hence, the required approximations are:

Left end approximation for n = 4 is 2.7031

Left end approximation for n = 16 is 2.7201

Right end approximation for n = 4 is 3.5938

Right end approximation for n = 16 is 3.6454

to know more about approximation  visit:

https://brainly.com/question/29669607

#SPJ11

Evaluate. (Be sure to check by differentiating)

∫ 4y^6 √(3−4y^7) dy

∫ 4y^6 √(3−4y^7) dy = ______
(Type an exact answer. Use parentheses to clearly denote the argument of each function.)

Answers

The evaluation of the given integral is:

[tex]\int 4y^6 * \sqrt{3 - 4y^7}dy = -2/21 * (3 - 4y^7)^{3/2} + C[/tex],

where C is the constant of integration.

To evaluate the given integral, we can use the substitution method.

Let's make the substitution [tex]u = 3 - 4y^7[/tex]. Then,[tex]du = -28y^6 dy[/tex].

We need to solve for dy in terms of du, so we divide both sides by [tex]-28y^6[/tex]:

[tex]dy = -du / (28y^6)[/tex].

Substituting this back into the integral, we have:

[tex]\int 4y^6 * \int(3 - 4y^7) dy = \int 4y^6 * \sqrt{u} * (-du / (28y^6))[/tex].

Simplifying:

[tex]\int -4/28 \sqrt{u} du = -1/7 \int \sqrt{u} du.[/tex]

Integrating [tex]\sqrt{u}[/tex] with respect to u:

[tex]-1/7 * (2/3) * u^{3/2} + C = -2/21 * u^{3/2} + C[/tex],

where C is the constant of integration.

Now, substitute back [tex]u = 3 - 4y^7[/tex]:

[tex]-2/21 * (3 - 4y^7)^{3/2} + C,[/tex]

where C is the constant of integration.

Therefore, the evaluation of the given integral is:

[tex]\int 4y^6 * \sqrt{3 - 4y^7}dy = -2/21 * (3 - 4y^7)^{3/2} + C[/tex],

where C is the constant of integration.

Learn more about integrals at:

https://brainly.com/question/30094386

#SPJ4

Find the volume of the solid generated by revolving the regions bounded by the lines and curves y=e^(-1/3)x, y=0, x=0 and x=3 about the x-axis.

Answers

The volume of the solid generated by revolving the region bounded by the lines and curves y = e^(-1/3)x, y = 0, x = 0, and x = 3 about the x-axis is 6π/e - 6π (cubic units).

To find the volume of the solid generated by revolving the given region about the x-axis, we can use the method of cylindrical shells.

The region bounded by the lines and curves y = e^(-1/3)x, y = 0, x = 0, and x = 3 forms a triangle. Let's denote this triangle as T.

To calculate the volume, we'll integrate the circumference of each cylindrical shell multiplied by its height.

The height of each shell will be the difference between the upper and lower boundaries of the region, which is given by the curve y = e^(-1/3)x.

The radius of each shell will be the distance from the x-axis to a given x-value.

Let's set up the integral to calculate the volume:

V = ∫[a,b] 2πx * (e^(-1/3)x - 0) dx,

where [a,b] represents the interval of x-values that bounds the region T (in this case, [0,3]).

V = 2π * ∫[0,3] x * e^(-1/3)x dx.

To solve this integral, we can use integration by substitution. Let u = -1/3x, which implies du = -1/3 dx.

When x = 0, u = -1/3(0) = 0, and when x = 3, u = -1/3(3) = -1.

Substituting the values, the integral becomes:

V = 2π * ∫[0,-1] (-(3u)) * e^u du.

V = -6π * ∫[0,-1] u * e^u du.

Now, we can integrate by parts. Let's set u = u and dv = e^u du, then du = du and v = e^u.

Using the formula for integration by parts, ∫u * dv = uv - ∫v * du, we get:

V = -6π * [(uv - ∫v * du)] evaluated from 0 to -1.

V = -6π * [(0 - 0) - ∫[0,-1] e^u du].

V = -6π * [-∫[0,-1] e^u du].

V = 6π * ∫[0,-1] e^u du.

V = 6π * (e^u) evaluated from 0 to -1.

V = 6π * (e^(-1) - e^0).

V = 6π * (1/e - 1).

Finally, we can simplify:

V = 6π/e - 6π.

Therefore, the volume of the solid generated by revolving the region bounded by the lines and curves y = e^(-1/3)x, y = 0, x = 0, and x = 3 about the x-axis is 6π/e - 6π (cubic units).

To learn more about volume visit:

brainly.com/question/28338582

#SPJ11

Consider the function g(x) = x^2+40/x+9 on the interval [-3.5, 3.5]. Find the absolute extrema for the function on the given interval. Express your answer as an ordered pair (x, g(x)). Write the exact answer. Do not round. Separate multiple answers with a comma.

Answer:

Absolute Max: _______
Absolute Min: ________

Answers

The absolute maximum value of g(x) = x² + 40/x + 9 on the interval [-3.5, 3.5] is 17.9 at x = √20 and the absolute minimum value is 17.719... at x = -3.5 and x = 3.5.

The given function is g(x) = x² + 40/x + 9 on the interval [-3.5, 3.5]. We need to find the absolute extrema of the function on the given interval.

To find the absolute maximum and minimum values of a function, we have to follow these steps:

Step 1:

First find all critical points of the function in the given interval.

Step 2:

Evaluate the function at each critical point and the endpoints of the interval.

Step 3:

The largest and smallest function values obtained in steps 1 and 2 will give the function's absolute maximum and minimum, respectively, on the given interval.

Differentiate g(x) to x, we get:

g'(x) = (2x² - 40) / (x+9)²

We need to find the values of x for which g'(x) = 0 or g'(x) is undefined because g'(x) is continuous except x = -9. If x = -9, g'(x) is undefined. So, we will only have to examine these two cases to get the critical points.

2x² - 40 = 0 or

x = ± √20

Since x = -9 is excluded from the given interval. So, the only critical point is x = √20. Now we have to evaluate the function at this critical point and at the endpoints of the interval to determine the function's absolute maximum and minimum values.

Evaluating the function at x = -3.5, √20, and 3.5, we get

g(-3.5) = 17.719...,

g(√20) = 17.9...,

g(3.5) = 17.719...

Therefore, the absolute maximum value of g(x) = x² + 40/x + 9 on the interval [-3.5, 3.5] is 17.9 at x = √20, and the absolute minimum value is 17.719... at x = -3.5 and x = 3.5.

To know more about the critical points, visit:

brainly.com/question/32077588

#SPJ11

Kevin Lin wants to buy a used car that cests $9,780. A 10% down payment is required. (a) The used car dealer offered him a four-year add-on interest loan at 7 th annuat interest. Find the monthiy papment. (Round your answer to the nearest cent.) 5 (b) Find the APR of the onaler's loan. pound to the nearest hundrecth of 1%. (e) His bank offered him a four-year simple inferest amortited ioan at 9.2 s interest, with no fees. Find the APR, nithout making any calculations. (d) Which hoan is better for him? Use the solutions to parts (b) and (c) to answer, Wo calculations are required. The bank's loan is better. The car dealer's han is better.

Answers

Based on the given information, Kevin Lin would be better off choosing the bank's loan over the car dealer's loan. The bank's loan has a lower APR, making it a more favorable option.

To answer these questions, we need to calculate the monthly payment for both loans and compare the APRs.

(a) Monthly payment for the car dealer's loan:

The car costs $9,780, and a 10% down payment is required. Therefore, the loan amount is $9,780 - (10% of $9,780) = $8,802.

The loan term is four years, which is 48 months. The interest rate is 7% per annum.

To calculate the monthly payment for an add-on interest loan, we use the following formula:

Monthly payment = (Loan amount + (Loan amount * Interest rate * Loan term)) / Loan term

Monthly payment = ($8,802 + ($8,802 * 7% * 4 years)) / 48 months

Monthly payment = ($8,802 + ($8,802 * 0.07 * 4)) / 48

Monthly payment = ($8,802 + $2,764.56) / 48

Monthly payment = $11,566.56 / 48

Monthly payment ≈ $241.39

(b) APR of the car dealer's loan:

To find the APR, we need to calculate the effective annual interest rate (EAR) and then convert it to APR.

The formula to calculate EAR for an add-on interest loan is:

EAR =[tex](1 + (Interest rate * Loan term))^{(1 / Loan term)}[/tex] - 1

EAR = [tex](1 + (7\% * 4))^{(1 / 4) }[/tex]- 1

EAR =[tex](1 + 0.28)^{(0.25)}[/tex] - 1

EAR = [tex](1.28)^{(0.25)}[/tex]- 1

EAR ≈ 0.0647 or 6.47%

To convert EAR to APR, we multiply it by the number of compounding periods in a year. Since the loan term is four years, we multiply the EAR by 12/4.

APR = EAR * (12 / Loan term)

APR = 0.0647 * (12 / 4)

APR ≈ 0.1941 or 19.41%

(c) APR of the bank's loan:

The APR of the bank's loan is given as 9.2%.

(d) Comparing the loans:

The bank's loan has an APR of 9.2%, while the car dealer's loan has an APR of 19.41%. Therefore, the bank's loan is better for Kevin Lin as it offers a lower interest rate.

Therefore, the answer to part (d) is: The bank's loan is better.

Learn more about loan here:

https://brainly.com/question/29880122

#SPJ11




35. Develop a truth table for each of the standard POS expressions: a. (A + B)(A + C) (A + B + C) b. ·(4. A + B) (A + B + C) (B + C + ´ + C) (B + C + D) (A + B + C + D)

Answers

a. The truth table for the standard POS expression (A + B)(A + C)(A + B + C) is generated by considering all possible combinations of inputs A, B, and C and evaluating the expression for each combination.

b. The truth table for the standard POS expression (A + B)(A + B + C)(B + C')(B + C + D)(A + B + C + D) is also generated by considering all possible combinations of inputs A, B, C, and D and evaluating the expression for each combination.

a. To generate the truth table for the expression (A + B)(A + C)(A + B + C), we consider all possible combinations of inputs A, B, and C. We evaluate the expression for each combination by applying the OR operation to the respective variables and then applying the AND operation to the resulting terms. The resulting truth table will have eight rows, representing all possible combinations of A, B, and C.

b. To generate the truth table for the expression (A + B)(A + B + C)(B + C')(B + C + D)(A + B + C + D), we consider all possible combinations of inputs A, B, C, and D. Similar to the previous case, we evaluate the expression for each combination by applying the OR and AND operations as needed. The resulting truth table will have sixteen rows, representing all possible combinations of A, B, C, and D.

By examining the truth tables, we can determine the output values of the expressions for all possible input combinations, which helps in understanding the behavior of the expressions and can be used for further analysis or decision-making purposes.

Learn more about truth table here:

https://brainly.com/question/30588184

#SPJ11

Christopher bought 12 of the 20 items on his shopping list. Wite the ratio of acquired items to nonacquired iterns. 1. A powdered drink mbx calls for 3 scoops powder to 8 ounces of water. How. much powder do you need to make a gallon of drink mbx? 2. Find the actual width of a buiding if the modol of the building is 5 cm wide by 68.7 cm long, and the actual length of the building is 140.9 m : 3. The distance from Cincinnati to Terre Haute is 2.1 on the map. In roality. Cincinnati to Tecre Haule is 184 miles. On the map, the distance from Terro Hatte to St. Louis is 1.9

on the map. How far away in reality is Terre Haute to St. Louis?

Answers

1.  You would need 48 scoops of powder to make a gallon of drink mix.

2. The actual width of the building is approximately 1,026.32 cm.

3. The actual distance between Terre Haute and St. Louis is approximately 166.48 miles.

1. To find out how much powder is needed to make a gallon of drink mix, we need to first determine the ratio of powder to water and then calculate the amount of powder required for one gallon.

The given ratio is 3 scoops of powder to 8 ounces of water. Since there are 128 ounces in a gallon, we can set up the following proportion:

3 scoops powder / 8 ounces water = x scoops powder / 128 ounces water

Cross-multiplying and solving for x, we get:

8x = 3 * 128

8x = 384

x = 384 / 8

x = 48

Therefore, you would need 48 scoops of powder to make a gallon of drink mix.

2. If the model of the building is 5 cm wide and the actual length of the building is 140.9 m, we can use the scale of the model to find the actual width of the building.

The scale is given as 5 cm represents 68.7 cm. Let's set up a proportion:

5 cm / 68.7 cm = x cm / 140.9 m

To convert 140.9 m to cm, we multiply by 100 (since there are 100 cm in a meter):

140.9 m * 100 = 14,090 cm

Now, we can solve for x:

(5 cm * 14,090 cm) / 68.7 cm = x cm

x = 1,026.32 cm

Therefore, the actual width of the building is approximately 1,026.32 cm.

3. To determine the actual distance between Terre Haute and St. Louis, given the map distance from Terre Haute to St. Louis is 1.9, we need to find the scale of the map.

The given map distance from Cincinnati to Terre Haute is 2.1, and the actual distance is 184 miles. Let's set up a proportion:

2.1 / 184 = 1.9 / x

Cross-multiplying and solving for x, we get:

2.1x = 1.9 * 184

2.1x = 349.6

x = 349.6 / 2.1

x ≈ 166.48

Therefore, the actual distance between Terre Haute and St. Louis is approximately 166.48 miles.

To learn more about actual distance visit:

brainly.com/question/358542

#SPJ11

Find y as a function of t if 5y^n+30y=0,
y(0) = 7 y’(0) = 5
y(t) =

Answers

The differential equation is [tex]5y^n+30y=0[/tex]. The initial conditions are y(0) = 7 and y’(0) = 5.

The differential equation is:[tex]5y^n+30y=0[/tex]. First, we solve for n which is the exponent of y.
We get:n = -1When n = -1, the differential equation becomes:5(1/y)+30y=0
Rearranging terms, we get:5(1/y) = -30y
Dividing both sides by 5y, we have:-1/y² = -6
This yields: y(t) =  [tex]\sqrt{6}[/tex]/t The initial conditions are:y(0) = 7 and y’(0) = 5
We can now apply the first initial condition to find the value of C_1.C_1 = 7/ [tex]\sqrt{6}[/tex]
When we apply the second initial condition to solve for C_2, we get: C_2 = 5 [tex]\sqrt{6}[/tex]
Now, we can write the final answer: y(t) = 7cos(t [tex]\sqrt{6}[/tex]) + 5 \sqrt{6}sin(t [tex]\sqrt{6}[/tex])
Thus, the function of y as a function of t is y(t) = 7cos(t [tex]\sqrt{6}[/tex]) + 5 \sqrt{6}sin(t [tex]\sqrt{6}[/tex]) which is generated by the differential equation [tex]5y^n+30y=0[/tex]  and initial conditions y(0) = 7 and y’(0) = 5.

Learn more about initial conditions here:

https://brainly.com/question/2005475

#SPJ11

If the equation of the tangent plane to x2+y2−268z2=0 at (1,1,√1/134​) is x+αy+βz+γ=0, then α+β+γ=___

Answers

The value of α + β + γ is 151/67 - 8√1/67.

Given, the equation of the tangent plane to x² + y² - 268z² = 0 at (1,1,√1/134​) is x + αy + βz + γ = 0.

We have to determine α + β + γ.

To determine the value of α + β + γ, we first need to determine the equation of the tangent plane.

Let z = f(x,y) = x² + y² - 268z² be the equation of the given surface.

We differentiate the equation of the surface with respect to x and y, respectively, to obtain the partial derivatives of f as follows.f₁(x,y) = ∂f/∂x = 2xf₂(x,y) = ∂f/∂y = 2y

To determine the equation of the tangent plane at (x₁, y₁, z₁), we use the following equation:

                                               P(x,y,z) = f(x₁, y₁, z₁) + f₁(x₁, y₁)(x-x₁) + f₂(x₁, y₁)(y-y₁) - (z - z₁) = 0.

Substituting x₁ = 1, y₁ = 1, z₁ = √1/134 in the above equation, we get

                                         P(x,y,z) = (1)² + (1)² - 268(√1/134)² + 2(1)(x-1) + 2(1)(y-1) - (z - √1/134) = 0

Simplifying the above equation, we get

                                                  x + y - 8√1/67 z + 9/67 = 0

Comparing the above equation with the given equation of the tangent plane, we have

                                                    α = 1β = 1-8√1/67 = -8√1/67γ = 9/67

Therefore, α + β + γ = 1 + 1 - 8√1/67 + 9/67= 2 - 8√1/67 + 9/67= 151/67 - 8√1/67

Hence, the detail ans for the given problem is: The value of α + β + γ is 151/67 - 8√1/67.

Learn more about  tangent plane

brainly.com/question/33052311

#SPJ11

There are two types of improper integrals. Write two improper integrals, one of each type, and state why each is improper.


Write, but do not evaluate, the partial fractions decomposition of (9x^2 – 4)/ (x−9)^2(x^2−9)(x2+9)

Answers

Improper integrals: Improper integrals are integrals with an infinite region of integration or integrands that have an infinite discontinuity within their limits.

Improper integrals are classified into two types: Type I and Type II.

Let's see both of them below:

Type I Improper Integrals:

If the limit, as b approaches a from the right-hand side, of the integral of f(x) from a to b does not exist, then the Type I improper integral is represented by ∫a to ∞ f(x)dx, or∫−∞ to a f(x)dx.

Because the integral of f(x) from a to b has no limit as b approaches a from the right-hand side, this occurs.

Type II Improper Integrals: If f(x) has an infinite discontinuity in the interval (a,b) or at b, then the Type II improper integral is represented by∫a to b f(x)dx = lim h→b- ∫a to h f(x)dx or ∫b to ∞ f(x)dx = lim n→∞ ∫b to n f(x)dx. This occurs since the interval of integration contains an infinite discontinuity.

In other words, if f(x) has an infinite discontinuity in (a,b) or at b, the integral of f(x) from a to b, or from b to infinity, does not converge.

Partial fractions decomposition of (9x²-4)/[(x-9)²(x²-9)(x²+9)] can be given as shown below:

For a given rational function whose denominator is a product of quadratic factors, partial fractions are a method of reducing it to a sum of simpler fractions. In order to locate the coefficients A, B, C, D, E, and F in partial fraction decomposition of the given rational function, follow the steps below.

The denominators of partial fraction can be shown as follows;

[tex]$$\frac{9{x}^{2}-4}{\left(x-9\right)^{2}\left(x^{2}-9\right)\left(x^{2}+9\right)}=\frac{A}{x-9}+\frac{B}{\left(x-9\right)^{2}}+\frac{C}{x+3}+\frac{D}{x-3}+\frac{E}{x^{2}+9}+\frac{F}{x+3}$$[/tex]

Multiply both sides of the equation by the common denominator, which is; (x - 9)²(x + 3)(x - 3)(x² + 9)

[tex]$$9{x}^{2}-4=A\left(x-9\right)\left(x+3\right)\left(x-3\right)\left(x^{2}+9\right)+B\left(x+3\right)\left(x-3\right)\left(x^{2}+9\right)[/tex]+[tex]$$C\left(x-9\right)\left(x-3\right)\left(x^{2}+9\right)+D\left(x-9\right)\left(x+3\right)\left(x^{2}+9\right)+E\left(x-9\right)\left(x+3\right)\left(x-3\right)+F\left(x-9\right)^{2}\left(x+3\right)$$[/tex]

Substitute the value of x=-3 to get the value of C.

[tex]$$9(-3)^{2}-4=C(-3-9)(-3-3)(-3^{2}+9)+\cdots$$[/tex]

[tex]$$=C(-12)(-6)(-18)=C(12)(6)(18)$$[/tex]

Therefore, C = [tex]$ \frac{- 1}{27}$[/tex]

Substitute the value of x=3 to get the value of D.

[tex]$$9(3)^{2}-4=D(3-9)(3+3)(3^{2}+9)+\cdots$$[/tex]

[tex]$$=D(-6)(6)(18)=D(6)(-6)(18)$$[/tex]

Therefore, D = [tex]$ \frac{1}{27}$[/tex]

Let [tex]$x^{2}+9=y$[/tex]

Substitute the values of A, B, E, and F to get the value of C.

[tex]$$9{x}^{2}-4=A(x-9)(x+3)(x-3)(x^{2}+9)+\cdots$$[/tex]

[tex]$$+B(x+3)(x-3)(x^{2}+9)+C(x-9)(x-3)(x^{2}+9)+D(x-9)(x+3)(x^{2}+9)+\cdots$$[/tex]

[tex]$$+E(x-9)(x+3)(x-3)+F(x-9)^{2}(x+3)$$[/tex]

[tex]$$9{x}^{2}-4=\left[A(x-9)(x+3)(x-3)+\cdots\right]+\left[B(x+3)(x-3)(x^{2}+9)+\cdots\right]$$[/tex]

[tex]$$+\left[\frac{-1}{27}(x-9)(x-3)(x^{2}+9)+\cdots\right]+\left[\frac{1}{27}(x-9)(x+3)(x^{2}+9)+\cdots\right]+\left[E(x-9)(x+3)(x-3)[/tex][tex]$$+\cdots\right]+\left[\frac{F}{(x-9)}(x-9)^{2}(x+3)+\cdots\right]$$[/tex]

[tex]$$=\frac{1}{y-9}\left(\frac{A}{x-9}+\frac{B}{(x-9)^{2}}+\frac{C}{x+3}+\frac{D}{x-3}\right)+\frac{E}{y}+\frac{F}{y-9}$$[/tex]

Multiply both sides by [tex]$x^{2}-9$[/tex] to get rid of the y variable.

[tex]$$9{x}^{2}-4=\frac{A(x+3)(x-3)(y-9)}{y-9}+\frac{B(x-9)(y-9)}{(x-9)^{2}}+\frac{C(x-9)(x+3)(y-9)}{x+3}$$[/tex]

[tex]$$+\frac{D(x-9)(x+3)(y-9)}{x-3}+\frac{E(x+3)(x-3)}{y}+\frac{F(x-9)(y-9)}{y-9}$$[/tex]

[tex]$$=A(x+3)(x-3)+B(x-9)+C(x-9)(x+3)+D(x-9)(x+3)+E(x+3)(x-3)(x^{2}+9)+F(x-9)^{2}(x+3)$$[/tex]

Let's solve the above equation.

To know more about Improper integrals visit:

https://brainly.com/question/30398122

#SPJ11

What is the charge, in C, transferred in a period of
62.9 s by current flowing at the rate of 61.9 A? Give your answer
to the nearest whole number.

Answers

Rounding the value to the nearest whole number, the charge transferred is approximately 3880 C.

To calculate the charge transferred, we can use the formula:

Q = I * t

where:

Q is the charge transferred,

I is the current, and

t is the time.

Substituting the given values:

I = 61.9 A (current)

t = 62.9 s (time)

Q = 61.9 A * 62.9 s = 3880.11 C

Rounding the value to the nearest whole number, the charge transferred is approximately 3880 C.

Visit here to learn more about charge brainly.com/question/13871705

#SPJ11

A curve C has equation
y=x¹/²−1/3x ²/³, x≥0.
Show that the area of the surface generated when the arc of C for which 0≤x≤3 is rotated through 2π radians about the x-axis is 3π square units

Answers

The question requires us to calculate the surface area of a curve C, when rotated about the x-axis, in the given limits. Here, we will use the formula of surface area, integrate it and solve it.

A curve C has equation y = x¹/²−1/3x²/³, x ≥ 0. We need to find the surface area generated when the arc of C for which 0 ≤ x ≤ 3 is rotated through 2π radians about the x-axis.The formula for the surface area of a curve C when rotated through 2π radians about x-axis is:S=∫_a^b▒〖2πy(x)ds〗 , where ds=√(1+ (dy/dx)²) dxHere, y=x¹/²−1/3x²/³, 0 ≤ x ≤ 3For ds, we have: ds = √(1+ (dy/dx)²) dx= √(1 + (1/4x)^(4/3)) dxSo, the surface area can be obtained as follows:S = ∫_a^b▒〖2πy(x)ds〗S = ∫_0^3▒〖2π(x^(1/2)-1/3x^(2/3))(√(1 + (1/4x)^(4/3))) dx〗Solving the above integral by substitution method, we get:S = 3π sq. unitsHence, the surface area generated when the arc of C for which 0 ≤ x ≤ 3 is rotated through 2π radians about the x-axis is 3π square units.

Learn more about surface area here:

https://brainly.com/question/30945207

#SPJ11

Convert from rectangular to spherical coordinates.
(Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*).)

(5√2, -5√2, 10√3) = _______

Answers

The spherical coordinates for the given rectangular coordinates (5√2, -5√2, 10√3) are (20, π/6, -π/4).

To convert from rectangular to spherical coordinates, we use the following formulas:

r = √(x^2 + y^2 + z^2)

θ = arccos(z / r)

φ = arctan(y / x)

Given the rectangular coordinates (5√2, -5√2, 10√3), we can calculate the spherical coordinates as follows:

r = √((5√2)^2 + (-5√2)^2 + (10√3)^2) = √(50 + 50 + 300) = √400 = 20

θ = arccos(10√3 / 20) = arccos(√3 / 2) = π/6

φ = arctan((-5√2) / (5√2)) = arctan(-1) = -π/4

Therefore, the spherical coordinates for the given rectangular coordinates (5√2, -5√2, 10√3) are (20, π/6, -π/4).

to learn more about rectangular coordinates click here:

brainly.com/question/27627764

#SPJ11

Suppose you are holding a stock and there are three possible outcomes. The good state happens with 20% probability and 18% return. The neutral state happens with 55% probability and 9% return. The bad state happens with 25% probability and -5% return. What is the expected return? What is the standard deviation of return? What is the variance of return?

Answers

The expected return is 0.072 (or 7.2%), the standard deviation is approximately 0.2006 (or 20.06%), and the variance is approximately 0.04024 (or 4.024%).

To calculate the expected return, standard deviation, and variance of the stock, we can use the following formulas:

Expected Return (E(R)):

E(R) = Σ(Probability of State i × Return in State i)

Standard Deviation (σ):

σ = √[Σ(Probability of State i × (Return in State i - Expected Return)^2)]

Variance (Var):

Var = σ^2

Let's calculate these values for the given probabilities and returns:

Expected Return (E(R)):

E(R) = (0.20 × 0.18) + (0.55 × 0.09) + (0.25 × -0.05)

     = 0.036 + 0.0495 - 0.0125

     = 0.072

Standard Deviation (σ):

σ = √[(0.20 × (0.18 - 0.072)^2) + (0.55 × (0.09 - 0.072)^2) + (0.25 × (-0.05 - 0.072)^2)]

  = √[(0.20 × 0.108)^2 + (0.55 × 0.018)^2 + (0.25 × (-0.122)^2)]

  = √[(0.0216) + (0.0005445) + (0.0181)]

  ≈ √0.0402445

  ≈ 0.2006

Variance (Var):

Var = σ^2

   = (0.2006)^2

   ≈ 0.04024

Learn more about standard deviation here: brainly.com/question/475676

#SPJ11

14. Solve each linear system by substitution

B.) y= -3 x + 4
Y= 2x - 1

Answers

The solution to the given linear system is x = 1 and y = 1. The coordinates (1, 1) represent the point where the two lines intersect and satisfy both equations.

To solve the given linear system by substitution, we'll substitute one equation into the other to eliminate one variable. Let's begin:

Given equations:

y = -3x + 4    (Equation 1)

y = 2x - 1     (Equation 2)

We can substitute Equation 1 into Equation 2:

2x - 1 = -3x + 4

Now we have a single equation with one variable. We can solve it:

2x + 3x = 4 + 1

5x = 5

x = 1

Substituting the value of x into either Equation 1 or Equation 2, let's use Equation 1:

y = -3(1) + 4

y = -3 + 4

y = 1

Therefore, the solution to the given linear system is x = 1 and y = 1. The coordinates (1, 1) represent the point where the two lines intersect and satisfy both equations.

for more such question on coordinates visit

https://brainly.com/question/29660530

#SPJ8

Determine the future value of an annuity after ten monthly payments of R600,00
at an interest rate of 12%
per annum, compounded monthly

Answers

The future value of the annuity after ten monthly payments of R600.00, with a 12% annual interest rate compounded monthly, is approximately R7,490.34.

To calculate the future value, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r,

where FV is the future value, P is the payment amount, r is the interest rate per period, and n is the number of periods.

In this case, P = R600.00, r = 12% / 12 = 1% = 0.01 (monthly interest rate), and n = 10 (number of months).

Substituting the values into the formula, we have:

FV = R600.00 * [(1 + 0.01)^10 - 1] / 0.01 ≈ R7,490.34.

Therefore, the future value of the annuity after ten monthly payments would be approximately R7,490.34.

learn more about value here:

https://brainly.com/question/30145972

#SPJ11

What is the present value of 550,000 to be rectived 5 years from fodmy if the discount rate is \( 5.2 \% \) (APR) compounded weeky? ․, \( 516,3213 b \) b. \( 530,805.32 \) c \( 511,614,45 \) d.530,5

Answers

The present value of $550,000 to be received 5 years from now, with a discount rate of 5.2% (APR) compounded weekly, is approximately $427,058.38.

To calculate the present value of $550,000 to be received 5 years from now, we can use the formula for present value with compound interest:

Present Value = Future Value / (1 + r/n)^(n*t)

Where:

- Future Value = $550,000

- r = annual interest rate as a decimal = 5.2% / 100 = 0.052

- n = number of compounding periods per year = 52 (since it is compounded weekly)

- t = number of years = 5

Plugging in the values into the formula, we get:

Present Value = 550,000 / (1 + 0.052/52)^(52*5)

Calculating the expression inside the parentheses first:

(1 + 0.052/52)^(52*5) = (1.001)^260 ≈ 1.288218

Now, dividing the Future Value by the calculated expression:

Present Value = 550,000 / 1.288218 ≈ $427,058.38

Therefore, the present value of $550,000 to be received 5 years from now, with a discount rate of 5.2% (APR) compounded weekly, is approximately $427,058.38.

Learn more about discount rate here

https://brainly.com/question/7459025

#SPJ11

Find the directional derivative of f(x,y,z)=xy+z³ at the point P=(4,−2,−3) in the direction pointing to the origin.
(Give an exact answer. Use symbolic notation and fractions where needed.

Answers

The directional derivative of f(x, y, z) = xy + z³ at the point P = (4, -2, -3) in the direction pointing to the origin is given by (-8 + 9√29) / √29.

To find the directional derivative of the function f(x, y, z) = xy + z³ at the point P = (4, -2, -3) in the direction pointing to the origin, we need to calculate the gradient of the function and then find the dot product with the unit vector in the direction from P to the origin. Let's go through the steps:

Calculate the gradient of f(x, y, z):

The gradient of a function is a vector that contains its partial derivatives with respect to each variable. For our function f(x, y, z) = xy + z³, the gradient is:

∇f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (y, x, 3z²).

Determine the direction vector from P to the origin:

The direction vector from P to the origin can be obtained by subtracting the coordinates of P from the origin (0, 0, 0):

(0, 0, 0) - (4, -2, -3) = (-4, 2, 3).

Normalize the direction vector:

To obtain the unit vector in the direction from P to the origin, we divide the direction vector by its magnitude:

u = (-4, 2, 3) / √(4² + 2² + 3²) = (-4, 2, 3) / √29.

Calculate the directional derivative:

The directional derivative is given by the dot product of the gradient vector and the unit direction vector:

Directional derivative = ∇f(P) · u = (y, x, 3z²) · (-4, 2, 3) / √29.

Plugging in the values of P = (4, -2, -3), we have:

Directional derivative = (-2, 4, 3²) · (-4, 2, 3) / √29.

Simplifying, we get:

Directional derivative = -16 + 8 + 9(√29) / √29 = (-8 + 9√29) / √29.

To find the directional derivative, we calculated the gradient of the function f(x, y, z) = xy + z³. The gradient provides a vector that points in the direction of steepest increase of the function. Next, we determined the direction vector from the point P = (4, -2, -3) to the origin by subtracting the coordinates. We then normalized this direction vector to obtain a unit vector pointing from P to the origin.

Finally, we found the directional derivative by taking the dot product of the gradient vector and the unit direction vector. This dot product gives the rate of change of the function in the direction of the unit vector. Plugging in the values of P and simplifying the expression, we obtained the exact answer for the directional derivative.

The directional derivative provides insight into how the function changes as we move in a specific direction. In this case, it represents the rate of change of f(x, y, z) = xy + z³ along the line connecting the point P to the origin.

Learn more about derivative here:

https://brainly.com/question/29144258

#SPJ11

Evaluate the indefinite integral.

∫7e^cosx sinx dx

o −e^cosx sinx + C
o -7e^cosx + C
o e^7sinx + C
o 7e^cosx sinx + C
o −7sin(e^cosx) + C

Answers

The indefinite integral of 7e^cosx sinx is -7e^cos(x) cos(x) + C.

To evaluate this indefinite integral, we can use the substitution u = cos(x). Then du/dx = -sin(x) and dx = du/-sin(x). Substituting these into the integral, we get: ∫7e^cosx sinx dx = ∫7e^u (-sin(x)) du

Now we can integrate with respect to u: ∫7e^u (-sin(x)) du = -7e^u cos(x) + C

Substituting u = cos(x), we get: -7e^cos(x) cos(x) + C

Therefore, the indefinite integral of 7e^cosx sinx is -7e^cos(x) cos(x) + C.

The substitution method is based on the chain rule of differentiation, which states that if f and g are differentiable functions, then (f(g(x)))’ = f’(g(x)) g’(x). This means that if we can write the integrand as f(g(x)) g’(x), then we can integrate it by letting u = g(x) and finding the antiderivative of f(u). In this problem, we can write the integrand as 7e^(cos(x)) (-sin(x)), where f(u) = 7e^u and g(x) = cos(x). Then we let u = cos(x), so that du/dx = -sin(x) and dx = du/-sin(x). This allows us to replace the integrand with 7e^u du and integrate it easily. Then we substitute u = cos(x) back into the result to get the final answer. The substitution method is useful for finding integrals of functions that involve compositions of other functions.

LEARN MORE ABOUT function here: brainly.com/question/31433890

#SPJ11

Find a parameterization of the line that is the intersection of
the planes P: x-2y-z=4 and Q:2x+y+z=2

Answers

The vector parametric form of the line L, which is the intersection of the given planes P and Q is given by L: x = 2/5 + (-7/5)t y = 6/5 - (3/5)t z = t

Given the equation of two planes as follows: P: x - 2y - z = 4Q: 2x + y + z = 2

To find a parameterization of the line that is the intersection of the planes P and Q, we follow the following steps:

Step 1: Let us write the augmented matrix of the system of linear equations for the given two planes. P: x - 2y - z = 4Q: 2x + y + z = 2⇒The augmented matrix is [A | B] =⇒A

= [1 -2 -1 | 4; 2 1 1 | 2]

Step 2: We apply elementary row operations to transform the matrix A to reduced row echelon form (rref(A)).

[1 -2 -1 | 4; 2 1 1 | 2]R2-2R1

→ R2[1 -2 -1 | 4; 0 5 3 | -6]R2/5

→ R2[1 -2 -1 | 4; 0 1 3/5 | -6/5]R1+2R2

→ R1[1 0 7/5 | 2/5; 0 1 3/5 | -6/5]

Step 3: From the rref(A) matrix, we can say that the system of linear equations is consistent with unique solution. Therefore, the line that is the intersection of the given two planes P and Q is unique. Now, we can write the equation of the line in vector parametric form as follows.

x = a + t b, where 'a' is any point on the line, 'b' is the direction vector of the line, and 't' is a parameter.

Here, the values of 'a' and 'b' can be determined by solving the following systems of equations.1x + 0y + 7/5z = 2/5   (Obtained from the row echelon form)   ⇒ x = 2/5 - 7/5z y

= 6/5 - 3/5z z = z

The above equations can be written as follows: x = 2/5 + (-7/5)tz = zy

= 6/5 - (3/5)tz = z

The vector parametric form of the line L, which is the intersection of the given planes P and Q is given by L: x = 2/5 + (-7/5)t y

= 6/5 - (3/5)t z

= t

To know more about parametric visit:

https://brainly.com/question/33413331

#SPJ11

I need help with these questions, please I only have one hour left to finish please

Answers

Answer:

Step-by-step explanation:

1.)

I solved for the vertex. Because the leading coefficient was negative, I knew the graph had to be concave down. This means that the vertex will give me the maximum value.

2.)

I think that graphing is a good way to visualize the graph. When you graph the line, it's easy to see where the vertex as well as the x and y intercept lies.

3.)

The shape they take depends on the leading coefficient. If it's negative, then the graph will be concave down and the vertex will be the maximum value of the graph. If the leading coefficient is positive, then the graph will be concave up and the vertex will be the minimum value of the line.

Consider the system of differential equations
x_1’(t) = -1x_1+0X_2
x_2’(t) = -12x_1+-7x_2

where x_1 and x_2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution.
a) This system can be written using matrices as X'= AX, where X is in R^2 and the matrix A is
A = _______

b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated by semicolons.
Eigenvalues: _____

Give an eigenvector associated to the smallest eigenvalue.
Answer: ______

Give an eigenvector associated to the largest eigenvalue.
Answer: _______

c) The general solution of the system of linear differential equations is of the form X=c_₁X_1+c_₂X_₂, where c_₁ and c_₂ are constants, and
X1 = _____
and
X_2 = _______

We assume that X_1is assoicated to the smallest eigenvalue and X_2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e^-4t is written 3*e^(-4't).

Answers

The general solution of the system of linear differential equations is of form X=c1⎡⎣23⎤⎦e−4t+c2⎡⎣11⎤⎦e−2t.

The given system of differential equations is

x′1(t)=−1x1+0x2x′2(t)=−12x1−7x2, where x1 and x2 are functions of t.

Our goal is first to find the general solution of this system and then a particular solution.

(a) The system can be written as X'=AX, where X is in R2 and the matrix A is A=⎡⎣−10−127⎤⎦.

(b) The eigenvalues of the matrix A associated with the system of linear differential equations are given by the roots of the characteristic equation det(A-λI)=0, where λ is an eigenvalue and I is the identity matrix.

So,

det(A-λI)=0 will be

= ⎡⎣−1−λ0−712−λ⎤⎦

=λ2+8λ+12=0

The roots of this equation are given byλ=−48 and λ=−2.

Therefore, the eigenvalues are -4 and -2.

The eigenvector associated to the smallest eigenvalue is given by Ax = λx

=> (A-λI)x = 0

For λ = -4:

A - λI=⎡⎣3−10−33⎤⎦ and the equation (A-λI)x = 0 becomes

3x1-2x2 = 0,

-3x1+3x2 = 0

This system has a basis vector [2,3].

Hence, an eigenvector associated to the smallest eigenvalue is given by [2,3].

For λ = -2:

A - λI=⎡⎣1−10−92⎤⎦ and the equation (A-λI)x = 0 becomes

x1-x2 = 0, -9x2 = 0.

This system has a basis vector [1,1]. Hence, an eigenvector associated to the largest eigenvalue is given by [1,1].

(c) The general solution of the system of linear differential equations is of the form X=c1X1+c2X2, where c1 and c2 are constants,

X1=⎡⎣23⎤⎦e−4t,

X2=⎡⎣11⎤⎦e−2t

and we assume that X1 is associated with the smallest eigenvalue and X2 with the largest eigenvalue. Hence, the general solution is given by

X=c1⎡⎣23⎤⎦e−4t+c2⎡⎣11⎤⎦e−2t.

Therefore, the general solution of the system of linear differential equations is of form X=c1⎡⎣23⎤⎦e−4t+c2⎡⎣11⎤⎦e−2t.

To know more about the characteristic equation, visit:

brainly.com/question/31726848

#SPJ11

Please look at the image and help me out (maths)

Answers

a) The coordinates of point A are given as follows: (-4,1).

b) The point B is plotted in red on the image given for this problem.

c) The coordinates of point C are given as follows: (-4,-2).

How to define the ordered pair?

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

x is the x-coordinate.y is the y-coordinate.

Then the coordinates of point C are given as follows:

x = -4 -> same x-coordinate of point A.y = -2 -> same y-coordinate of point B.

Hence the ordered pair is given as follows:

(-4, -2).

More can be learned about ordered pairs at brainly.com/question/1528681

#SPJ1

Suppose that the first number of a sequence is x, where
x is an integer.
Define:
a0 = x; an+1 = an
/ 2 if an is even;
an+1 = 3 X an + 1 if
an is odd.
Then there exists an integer k such that
ak = 1.

Answers

The sequence given is known as the Collatz sequence or the Hailstone sequence.

According to the given sequence,

if a value is even, divide it by 2 and if it is odd, multiply it by 3 and add 1.

This process of operation must continue until the number 1 is reached.

Suppose the first number in the sequence is x, and then we can define the sequence as a 0 = x;an+1 = an / 2,

if an is even; an+1 = 3 X an + 1, if an is odd.

The sequence will continue in this manner until we reach the value of ak = 1.

The value of k is unknown, and it is believed to be an unsolvable problem, and it is known as the Collatz conjecture. There have been numerous efforts to solve this problem, but it has yet to be solved by mathematicians.

To know more about Collatz sequence visit:

https://brainly.com/question/32872345

#SPJ11

Other Questions
Let limx6f(x)=9 and limx6g(x)=5. Use the limit rules to find the following limit. limx6 f(x)+g(x)/ 6g(x) limx6 f(x)+g(x)/ 6g(x)= (Simplify your answer. Type an integer or a fraction.) Explain in detail with approirpate examples five essaential characteristic of cloud computing? What is the Beta of a stock with an Expected Return of \( 26.5 \% \) if Treasury Bills are yielding \( 2.5 \% \) and the Market Risk Premium is \( 8.0 \% \) ? At typical operating conditions, the high efficiency air-conditioning system will operate with an evaporator boiling point of____. A. 40*F B. 45*F C. 50*F Why did Europeans avoid venturing into inland Africa during the fifteenth century?-Europeans felt there was little of value in the interior of Africa.-Europeans were not immune to African diseases.-Too many European soldiers were occupied in the Americas.-African kings did not permit Europeans to move inland.- Define Conflict of Interest and Conflict of commitment in yourown words. Explain the difference between the two by giving anexample. What are the significant changes to the Federal laws inrecent da A three-phase synchronous generator in: consists of three electromagnets located at 120 degrees from each other that induce voltages in the rotor windings is a rotating electromagnet that induces voltages in the three stator windings O functions in the same way as an asynchronous generator. is equivalent to an eddy-current brake. which of the following statements about multitasking is true? 2. A wave is described by the function: y(x, t) = sin(2 3t +0.17). (a) Plot y(xt) as a function of t, when x = 3 m and 0 using BJT transistors, resistors, SPDT switches, and a 5 V powersupply- design a 5 V logic level NAND gate. 1. A 120-V, 2400 rpm shunt motor has an armature resistance of 0.4 22 and a shunt field resistance of 160 2. The motor operates at its rated speed at full load and takes 14.75 A. The no-load current is 2A. (a) Draw the schematic diagram of the motor. (b) At no load calculate (i) armature current, (ii) the induced emf, and (iii) rotational power losses. (c) At full load calculate (i) the armature current, (ii) the induced emf, (iii) the power developed, (iv) the no-load speed, (v) the rotational power loses, (vi) the power output, (vii) the power input, and (viii) the efficiency. (d) An external resistance of 3.6 2 is inserted in the armature circuit with no change in the torque developed. Calculate (i) the armature current, (ii) the induced emf, (iii) the power developed, (iv) the no-load speed, (v) the rotational power losses, (vi) the power output, (vii) the power input, (viii) the efficiency, (ix) the power loss the external resistance, and (x) the percent power loss. no matching unique or primary key for this column-list According to the text, which of the following is not an effective guideline for changing corporate culture?a.Formulate a clear strategic vision.b.Model culture change at the highest levels.c.Make changes in structure and processes to support the change.d.Change organizational membership by socializing newcomers and terminating deviants.e.Keep top management from being part of the process. Using T flip-flops design a synchronous counter that counts 0, 1, 3, 5, 7, 2, 0. Make sure that unused states are correctable by forcing the counter to go to the count 0. How would you respond to a out of memory condition in the short term? 2.3 Answer the following questions regarding the upstart init daemon and the older classic init daemon. a) What is the difference between the daemons? ( b) What is an event? 2.4 Write a command to ensure that user Jack changes his password every 25 days but cannot change the password within 5 days after setting a new password. Jack must also be warned that his password will expire 3 days in advance. Use the chage command. What do you expect to find in the following logs? a) dpkg Log b) Cron Log c) Security Log d) RPM Packages e) System Log Syarikat Layang uses the FIFO (First-in, First-out) costing method for its perpetual inventory system. It had inventory on 1 July 2022 consisting of 400 articles bought at RM4 each. Its purchase during the month of July consisted of 800 at RM4.20 each purchased on 8 July, and 2,000 at RM3.80 each on 18 July. It sold 2,400 at RM5.00 each on 28 July. 40 of those purchased on 8 July were returned by the customer in perfect condition on 31 July.Required: Show the trading account for the month ended 31 July 2022 by means of an inventory account.QUESTION 3The following extract from the cash book of Joan for the month of July shows the company's bank transactions:The cheque issued to Halim in the month of June is unpresented.The company's bank statement for the same period is as follows:Required:a. Foam a corrected cash book using the information given above.b. Draw up a bank reconciliation statement.c. Discuss the purpose of a bank reconciliation. Calculate C- (B-A) if A = 3.02 +2.03, B= 1.0-1.0, and C= 1.9 + 1.5 j [V]| S ? C. (B-A)= units Submit Request Answer what athlete has the most olympic medals of all time he table displays the total cost, y, of purchasing x tickets for the carnival.A 2-column table with 3 rows. Column 1 is labeled Tickets, x with entries 11, 12, 13. Column 2 is labeled Total Cost, y (dollars) with entries 27.50, 30.00, 32.50.Which conclusions can you draw from the data shown in the table? Select all that apply.Twelve tickets cost $30.00.Thirty tickets cost $12.00.Each additional ticket costs $2.50.The table is a partial representation.(27.50, 11), (30, 12) and (32.50, 13) are the ordered pairs represented in the table. In the sixth beatitude, Jesus teaches that living the virtue of chastity requires maintaining purity of heart through the practice of _____.