Given cos 8= 9 41' find sin 8 and cot 0.

Answers

Answer 1

The calculations were performed using the Pythagorean identity sin²θ + cos²θ = 1 to determine sin 8

sin 8 = √(1 - cos² 8) ≈ -0.019

cot 0 = 1/tan 0 = 1/0 = undefined

To find sin 8, we can use the Pythagorean identity sin²θ + cos²θ = 1. Rearranging this equation, we have sin²θ = 1 - cos²θ. Substituting the given value of cos 8 into the equation, we get sin² 8 = 1 - (9 41')². Calculating this, we find sin² 8 ≈ 0.9996. Taking the square root of this value, we get sin 8 ≈ ±√(0.9996) ≈ ±0.0316. Since the angle 8 is given as cos 8 = 9 41', it means 8 is in the fourth quadrant where sin is negative. Therefore, sin 8 ≈ -0.0316.

To find cot 0, we need the value of tan 0. However, tan 0 is undefined because tangent is the ratio of sin to cos, and at 0 degrees, cos 0 is 1 and sin 0 is 0. Therefore, cot 0 = 1/tan 0 = 1/0, which is undefined.

Given cos 8 = 9 41', we found that sin 8 ≈ -0.019 and cot 0 is undefined. The calculations were performed using the Pythagorean identity sin²θ + cos²θ = 1 to determine sin 8, and the definition of cotangent to calculate cot 0.

To know more about Pythagorean identity follow the link:

https://brainly.com/question/24287773

#SPJ11


Related Questions

Transcribed image text:
An orthogonal basis for A, ⎣


−10
2
−6
16
2

−4
8
−12
16
8

−1
5
−3
22
5

−1
10
−3
22
0




, is ⎩






−10
2
−6
16
2




, ⎣


3
3
−3
0
3




, ⎣


6
0
6
6
0




, ⎣


0
5
0
0
−5








. Find the QR factorization of A with the given orthogonal basis. The QR factorization of A is A=QR, where Q= and R=

Answers

To find the QR factorization of matrix A using the given orthogonal basis, we can use the formula:

A = QR

where Q is an orthogonal matrix and R is an upper triangular matrix.

The orthogonal basis for A is given as:

Q = ⎡

−10 2 −6 16 2

3 3 −3 0 3

6 0 6 6 0

0 5 0 0 −5

To find matrix R, we can use the formula:

R = Q^T * A

where Q^T is the transpose of matrix Q.

Calculating the transpose of Q:

Q^T = ⎡

−10 3 6 0

2 3 0 5

−6 −3 6 0

16 0 6 0

2 3 0 −5

Calculating R:

R = Q^T * A = ⎡

−10 3 6 0

2 3 0 5

−6 −3 6 0

16 0 6 0

2 3 0 −5

⎦ * ⎡

−10 2 −6 16 2

−4 8 −12 16 8

−1 5 −3 22 5

−1 10 −3 22 0

Performing the matrix multiplication:

R = ⎡

446 -139 189 100

0 14 0 -42

0 0 0 0

0 0 0 0

Therefore, the QR factorization of matrix A is:

A = QR, where

Q = ⎡

−10 2 −6 16 2

3 3 −3 0 3

6 0 6 6 0

0 5 0 0 −5

R = ⎡

446 -139 189 100

0 14 0 -42

0 0 0 0

0 0 0

Find the demand function x = f(p) that satisfies the initial conditions. 800 (0.04p - 1)³' X = dx dp x = 10,000 when p = $50

Answers

The demand function x = f(p) is x = 8(p - 25)⁴ - 5110000.

Given, the demand function: x = f(p) which satisfies the initial conditions.

800(0.04p-1)³' x = dx/dp And

x = 10,000 when

p = $50

To find the demand function x = f(p),

we need to integrate the derivative function of x with respect to p.

We have: dx/dp = 800(0.04p-1)³dx/dp

= 800(0.04p-1)(0.04)dx/dp

= 32(p - 25)³

Using initial condition x = 10,000

when p = $50

Integrating both sides,

we get x = ∫dx

= ∫32(p - 25)³dp

x = [8(p - 25)⁴] + C

Now, at p = $50,

x = 10,000Putting these values in the demand function, we get 10000 = [8(50 - 25)⁴] + C10000

= 5120000 + C C

= -5110000

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

Which Of The Following Series Converge To 2? 1. ∑N=1[infinity]N+32n 11. ∑N=1[infinity](−3)N−8 11. ∑N=0[infinity]2n1

Answers

Let's find out which of the given series converges to 2.1. ∑N=1∞N+32nNow, we need to find the sum of this series to know whether it converges to 2 or not.

So, we will use the formula of the sum of the series of n terms for this one. Sum of first n terms, S = n/2[2a + (n - 1)d], where a is the first term and d is the common difference. Hence, it is evident that the given series diverges to infinity because the terms are increasing with an increasing value of n and there is no common difference, which can neutralize the increasing terms.

So, the first series does not converge to 2.2. ∑N=1∞(−3)N−8In this series, the common ratio r is -3. If r > 1, then the series will diverge to infinity, and if -1 < r < 1, then the series will converge to a finite number.Now, let's check the common ratio: r = -3 < 1Therefore, this series will converge to a finite number.Let's calculate the sum of the given series Therefore, the given series diverges to infinity and does not converge to 2. Hence, the third series does not converge to 2.Therefore, none of the given series converges to 2.

To know more about series visit :

https://brainly.com/question/31583448

#SPJ11

A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car. Find P(X ≤ 2) A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car. Find P(X > 3) A. 0.05 B. 0.15 C. None of the Choices D. 0.03 E. 0.02

Answers

The probability that a randomly chosen car has at most two occupants is 0.85 and the probability that a randomly chosen car has more than three occupants is 0.05. Thus, the correct option is A. 0.05.

Let X be the number of occupants in a randomly chosen car.

The probabilities are given as:

P(X = 1) = 0.7

P(X = 2) = 0.15

P(X = 3) = 0.10

P(X = 4) = 0.03

P(X = 5) = 0.02

Find P(X ≤ 2): P(X ≤ 2) = P(X = 1) + P(X = 2) = 0.7 + 0.15 = 0.85

Find P(X > 3): P(X > 3) = P(X = 4) + P(X = 5) = 0.03 + 0.02 = 0.05

The probability that a randomly chosen car has at most two occupants is 0.85 and the probability that a randomly chosen car has more than three occupants is 0.05. Thus, the correct option is A. 0.05.

Learn more about probability visit:

brainly.com/question/31828911

#SPJ11

Given that \( \phi(x, y, z)=x e^{z} \sin y . \) Find \( \bar{\nabla} \cdot(\bar{\nabla} \phi) \)

Answers

The value of [tex]\bar{\nabla} \cdot(\bar{\nabla} \phi)[/tex] is [tex]e^z\cos y[/tex].

The gradient is a vector operation that transforms a scalar function into a vector with a magnitude equal to the highest rate of change of the function at the gradient's point and a direction pointing in the same direction.

To find [tex]\bar{\nabla} \cdot(\bar{\nabla} \phi)[/tex], we need to calculate the divergence of the gradient of the function ϕ.

The gradient of ϕ is given by:

[tex]\bar{\nabla} \phi[/tex] = (∂x/∂ϕ​, ∂y/∂ϕ, ∂z/∂ϕ)

Let's calculate the partial derivatives of ϕ with respect to each variable:

[tex]\frac{\partial \phi}{\partial x}=e^{z}\sin y[/tex]

[tex]\frac{\partial \phi}{\partial y}=xe^{z}\cos y[/tex]

[tex]\frac{\partial \phi}{\partial z}=xe^{z}\sin y[/tex]

Now, we can find the divergence of [tex]\bar{\nabla} \phi[/tex] by taking the sum of the partial derivatives:

[tex]\bar{\nabla} \cdot(\bar{\nabla} \phi)[/tex] =  [tex]\frac{\partial}{\partial x}(e^z\sin y)+\frac{\partial}{\partial y}(xe^z\cos y)+\frac{\partial}{\partial z}(xe^z\sin y)[/tex]

Simplifying each partial derivative:

[tex]\bar{\nabla} \cdot(\bar{\nabla} \phi)[/tex] = [tex]e^z\cos y[/tex] + [tex](-xe^z\sin y)[/tex] + [tex](xe^z\sin y)[/tex]

Combining like terms, we find:

[tex]\bar{\nabla} \cdot(\bar{\nabla} \phi)[/tex] = [tex]e^z\cos y[/tex]

To learn more about partial derivatives link is here

brainly.com/question/28750217

#SPJ4

The complete question is:

Given that [tex]\phi(x, y, z)=x e^{z} \sin y[/tex] Find [tex]\bar{\nabla} \cdot(\bar{\nabla} \phi)[/tex].

Find only the rational zeros of the following function. \[ f(x)=x^{4}+2 x^{3}-5 x^{2}-4 x+6 \] Select the correct choice below, if necessary, fill in the answer box to complete your choice. A. The rat

Answers

The correct choice is A. The rational zeros of the function are -2. The possible rational zeros of the function are \(x = \pm 1, \pm 2, \pm 3, \pm 6\).

To find the rational zeros of the function \(f(x) = x^4 + 2x^3 - 5x^2 - 4x + 6\), we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number \(r\) is a zero of a polynomial with integer coefficients, then \(r\) must be of the form \(r = \frac{p}{q}\), where \(p\) is a factor of the constant term (in this case, 6) and \(q\) is a factor of the leading coefficient (in this case, 1).

The factors of 6 are \(\pm 1, \pm 2, \pm 3, \pm 6\), and the factors of 1 are \(\pm 1\).

Therefore, the possible rational zeros of the function are:

\(x = \pm 1, \pm 2, \pm 3, \pm 6\).

To determine which of these are actual zeros of the function, we can substitute each value into the function and check if the result is zero.

For \(x = -6\):

\(f(-6) = (-6)^4 + 2(-6)^3 - 5(-6)^2 - 4(-6) + 6 = 1\), not zero.

For \(x = -3\):

\(f(-3) = (-3)^4 + 2(-3)^3 - 5(-3)^2 - 4(-3) + 6 = -72\), not zero.

For \(x = -2\):

\(f(-2) = (-2)^4 + 2(-2)^3 - 5(-2)^2 - 4(-2) + 6 = 0\), zero.

Therefore, \(x = -2\) is a rational zero of the function \(f(x)\).

None of the other possible rational zeros, \(x = \pm 1, \pm 3, \pm 6\), are actual zeros of the function.

Hence, the correct choice is:

A. The rational zeros of the function are -2.

Learn more about rational zeros here

https://brainly.com/question/32719134

#SPJ11

Water is boiled at 120 oC in a mechanically polished stainless steel pressure
cooker placed on top of a heating unit. The inner surface of the bottom of the cooker
is maintained at 130 oC. The cooker has a diameter of 20 cm and a height of 30 cm is
half filled with water. Determine the time it will take for the tank to empty.

Answers

To determine the time it will take for the pressure cooker to empty, we need to consider the rate of evaporation and the volume of water in the cooker. Given the temperatures and dimensions provided, we can calculate the rate of evaporation and use it to estimate the time required for the tank to empty.

The rate of evaporation depends on factors such as the temperature difference between the boiling water and the surrounding surface, as well as the exposed surface area. In this case, the water is boiling at 120°C, while the inner surface of the bottom of the cooker is maintained at 130°C. This temperature difference creates a favorable condition for evaporation.

To calculate the rate of evaporation, we need to determine the surface area of the water exposed to the air. The cooker has a diameter of 20 cm and a height of 30 cm, so the surface area of the water can be calculated using the formula for the lateral surface area of a cylinder, which is 2πrh. Considering that the cooker is half-filled with water, the exposed surface area would be half of the calculated lateral surface area.

Once we have the exposed surface area, we can estimate the rate of evaporation using known empirical formulas or experimental data. By multiplying the rate of evaporation by the volume of water in the cooker, we can determine how much water is evaporating per unit of time. Dividing the initial volume of water in the cooker by this rate will provide an estimate of the time required for the tank to empty.

Learn more about lateral surface area here:

https://brainly.com/question/15476307

#SPJ11

Find the first partial derivatives of the function. f(x,y)=y 5
−6xy f x
(x,y)= f y
(x,y)= Find the first partial derivatives of the function. f(x,t)=e −4t
cosπx f x
(x,t)=
f t
(x,t)=
Find the first partial derivatives of the function. z=(4x+9y) 6
∂x
∂z
=
∂y
∂z
=
Find the first partial derivatives of the function. f(x,y)= x+y
x−y
f x
(x,y)= f y
(x,y)=

Answers

For the function [tex]f(x, y) = y^5 - 6xy: f_x(x, y) = -6y, f_y(x, y) = 5y^4 - 6x[/tex]. For the function [tex]f(x, t) = e^{(-4t)} * cos(πx): f_x(x, t) = -πe^{(-4t)} * sin(πx), f_t(x, t) = -4e^{(-4t)} * cos(πx)[/tex]. For the function z [tex]= (4x + 9y)^6: ∂z/∂x = 24(4x + 9y)^5, ∂z/∂y = 54(4x + 9y)^5[/tex]. For the function [tex]f(x, y) = (x + y)/(x - y): f_x(x, y) = -2y / (x - y)^2, f_y(x, y) = 2x / (x - y)^2[/tex].

Let's find the first partial derivatives for each given function:

For the function [tex]f(x, y) = y^5 - 6xy[/tex]:

f_x(x, y) = ∂f/∂x

= -6y

f_y(x, y) = ∂f/∂y

[tex]= 5y^4 - 6x[/tex]

For the function [tex]f(x, t) = e^{(-4t)} * cos(πx)[/tex]:

f_x(x, t) = ∂f/∂x

[tex]= -πe^(-4t) * sin(πx)[/tex]

f_t(x, t) = ∂f/∂t

[tex]= -4e^{(-4t)} * cos(πx)[/tex]

For the function [tex]z = (4x + 9y)^6[/tex]:

∂z/∂x [tex]= 6(4x + 9y)^5 * 4[/tex]

[tex]= 24(4x + 9y)^5[/tex]

∂z/∂y [tex]= 6(4x + 9y)^5 * 9[/tex]

[tex]= 54(4x + 9y)^5[/tex]

For the function f(x, y) = (x + y)/(x - y):

f_x(x, y) = ∂f/∂x

= [tex][(x - y) - (x + y)] / (x - y)^2[/tex]

[tex]= -2y / (x - y)^2[/tex]

f_y(x, y) = ∂f/∂y

[tex]= [(x - y) + (x + y)] / (x - y)^2[/tex]

[tex]= 2x / (x - y)^2[/tex]

To know more about function,

https://brainly.com/question/30721594

#SPJ11

The mean number of goals a water polo team scores per match in the first 9 matches of a competition is 7. a) How many goals does the team score in total in the first 9 matches of the competition? b) If the team scores 2 goals in their next match, what would their mean number of goals after 10 matches be?​

Answers

Answer:

a) 36

b) 3.9

Step-by-step explanation:

I really hope this helps

Consider the following system of equations: fi(x, y): x² - 2x - y = -0.6 f2(x, y): x² + 4y² = 8 Using the Gauss-Jacobi method, set up the equations as in the following: x = 91 (x, y) y = 92(x, y) Find the approximate values of x and y when allowable error is 0.005. Round off to four decimal places. x = 2, y = 0.25 X= y = error =

Answers

Using the Gauss-Jacobi method with initial values x = 2 and y = 0.25, and an allowable error of 0.005, we find that the approximate values of x and y are 2.0000 and 0.2500, respectively.

The Gauss-Jacobi method is an iterative numerical method used to solve systems of linear equations. In this case, we have two equations: f1(x, y) = x² - 2x - y + 0.6 = 0 and f2(x, y) = x² + 4y² - 8 = 0.

To apply the Gauss-Jacobi method, we rearrange the equations to solve for x and y:

For f1(x, y):

x = √(2x + y - 0.6)

For f2(x, y):

y = √((8 - x²)/4)

We start with initial values x = 2 and y = 0.25 and iterate using the formulas above. After each iteration, we compute the error using the formulas:

error_x = |new_x - old_x|

error_y = |new_y - old_y|

We continue iterating until both errors are less than or equal to the allowable error of 0.005. In this case, after several iterations, we find that the approximate values of x and y converge to 2.0000 and 0.2500, respectively.

Therefore, the solution to the system of equations using the Gauss-Jacobi method with the given initial values and allowable error is x = 2.0000 and y = 0.2500.

Learn more about Gauss-Jacobi method here:

https://brainly.com/question/30763804

#SPJ11

Complete the statement 8 ounces is to 1 cup as ounces is 10 cups

Answers

Answer:

80

Step-by-step explanation:

8 x 10 = 80

8 ounces is to 1 cup as 1.25 ounces are for 10 cups.


1—>8
x—>10
10•1=10
10/8=1.25

Evaluate the integral. 6) ∫−3xsin7xdx You may use the formula: ∫udv=uv−∫vdu

Answers

The resultant integral is: ∫ −3xsin 7x dx = 3xcos 7x/7 - 3/49 sin 7x + C'

To evaluate the integral ∫ −3xsin 7x dx using the integration by parts formula, we will first define u and dv, apply the formula and solve the resulting integral using integration by substitution.

Let us begin by defining u and dv as:

u = -3xdv = sin 7x dx

Applying the integration by parts formula, we have

∫ −3xsin 7x dx = ∫u

dv = uv - ∫v du= -3x (-cos 7x/7) - ∫-cos 7x/7 d(-3x)= 3xcos 7x/7 - 3/7 ∫cos 7x dx

We can now solve the integral ∫cos 7x dx by applying the substitution method.

Let z = 7x, then dz/dx = 7

⇒ dx = dz/7

Substituting into the integral, we get

∫cos 7x dx

= (1/7) ∫cos z dz

= (1/7) sin z + C

= (1/7) sin 7x + C'

where C' is the constant of integration.

We can now substitute back into the integration by parts formula to obtain the final solution of the integral as:

∫ −3xsin 7x dx = 3xcos 7x/7 - 3/7 (1/7) sin 7x + C'

= 3xcos 7x/7 - 3/49 sin 7x + C'

Therefore, ∫ −3xsin 7x dx = 3xcos 7x/7 - 3/49 sin 7x + C'

Know more about integral here:

https://brainly.com/question/30094386

#SPJ11

If a point is reflected over a line, then the given line must be _________ the line formed by the point and its prime.

Answers

If a point is reflected over a line, the given line must be perpendicular to the line formed by the point and its prime.

When a point is reflected over a line, the resulting image appears on the opposite side of the line, maintaining the same distance from the line. In this reflection process, the line of reflection acts as the perpendicular bisector of the line segment connecting the point and its reflected image, also known as its prime.

The perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle. It intersects the line segment at its midpoint, forming right angles with both the line segment and the line of reflection.

Since the line of reflection is the perpendicular bisector of the line segment connecting the point and its prime, it must be perpendicular to that line. The perpendicularity ensures that the angle between the line of reflection and the line segment is 90 degrees, maintaining the equality of distances between the point and its prime on either side of the line of reflection.

Therefore, when a point is reflected over a line, the given line must be perpendicular to the line formed by the point and its prime.

For more questions on the perpendicular, click on:

https://brainly.com/question/17565270

#SPJ8

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and in the United Kingdom. Suppose that independent rando samples of television ads are taken in the two countries. A random sample of 400 television ads in
the United Kingdom reveals that 142 use humor, while a random sample of 500 television ads in the United States reveals that 122 use humor.
a) Set up the null and alternative hypotheses needed to determine whether the proportion of ads using humor in the United Kingdom differs from the proportion of ads using humor in the United States.
b) Test the hypotheses you set up in part a by using critical values and by setting a equal to .10, .05, .01, and .001. How much evidence is there that the proportions of U.K. and U.S. ads
using humor are different?
c) Set up the hypotheses needed to attempt to establish that the difference between the proportions of U.K. and U.S. ads using humor is more than .05 (five percentage points). Test these hypotheses by using a p-value and by setting a equal to .10, .05, .01, and .001. How much evidence is there that the difference between the proportions exceeds .05?
d) Calculate a 95 percent confidence interval for the difference between the proportion of U.K. ads using humor and the proportion of U.S. ads using humor. Interpret this interval. Can we be 95 percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor?

Answers

a) The proportion of ads using humor in the United Kingdom is different from the proportion. b) The Critical value is ±3.291. c) The chosen significance level (a), we reject the null hypothesis in favor of the alternative hypothesis. d) We cannot be 95 percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor.

a) The null hypothesis (H₀) and alternative hypothesis (H₁) for determining whether the proportion of ads using humor in the United Kingdom differs from the proportion of ads using humor in the United States are:

H₀: The proportion of ads using humor in the United Kingdom is equal to the proportion of ads using humor in the United States.

H₁: The proportion of ads using humor in the United Kingdom is different from the proportion of ads using humor in the United States.

b) To test the hypotheses, we can use the two-sample z-test for proportions. The test statistic is calculated as:

z = (p₁ - p₂) / √(p*(1-p)*((1/n₁) + (1/n₂)))

where p1 and p2 are the sample proportions, n₁ and n₂ are the sample sizes, and p is the pooled sample proportion.

Let's calculate the test statistic and compare it to the critical values for different significance levels (a):

For a = 0.10:

Critical value = ±1.645

For a = 0.05:

Critical value = ±1.96

For a = 0.01:

Critical value = ±2.576

For a = 0.001:

Critical value = ±3.291

c) The hypotheses needed to establish that the difference between the proportions of U.K. and U.S. ads using humor is more than 0.05 are:

H0: The difference between the proportions of U.K. and U.S. ads using humor is less than or equal to 0.05.

H1: The difference between the proportions of U.K. and U.S. ads using humor is greater than 0.05.

To test these hypotheses, we can calculate the p-value associated with the test statistic. If the p-value is less than the chosen significance level (a), we reject the null hypothesis in favor of the alternative hypothesis.

d) To calculate a 95 percent confidence interval for the difference between the proportion of U.K. ads using humor and the proportion of U.S. ads using humor, we can use the formula:

CI = (p₁ - p₂) ± z*(√((p₁*(1-p₁)/n₁) + (p₂*(1-p₂)/n₂)))

where CI is the confidence interval, p₁ and p₂ are the sample proportions, n₁ and n₂ are the sample sizes, and z is the critical value corresponding to the desired confidence level.

Interpreting the confidence interval, if the interval is entirely above 0.05, it suggests that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor. However, if the interval includes 0.05, we cannot be 95 percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor.

To know more about proportion:

https://brainly.com/question/31548894


#SPJ4

Jacob is going on a road trip across the country. He covers 10 miles in
15 minutes. He then spends 10 minutes buying gas and some snacks at the
gas station. He then continues on his road trip.
Describe the distance traveled between 10 minutes and 15 minutes.

Answers

The distance covered between 10 minutes and 15 minutes is increasing

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Speed is the ratio of total distance travelled to total time taken. It is given by:

Speed = distance / time

From the graph:

The distance covered between 10 minutes and 15 minutes is increasing

Find out more on equation at: https://brainly.com/question/29797709

#SPJ1

Examine the behavior of f(x,y)= x 2
+y 2
4x 2.5

as (x,y) approaches (0,0). (a) Changing to polar coordinates, we find lim (x,y)→(0,0)

( x 2
+y 2
4x 2.5

)=lim r→0 +
,θ= anything ​
( (b) Since f(0,0) is undefined, f has a discontinuity at (x,y)=(0,0). Is it possible to define a function g:R 2
→R such that g(x,y)=f(x,y) for all (x,y)

=(0,0) and g is continuous everywhere? If so, what would the value of g(0,0) be? If there is no continuous function g, enter DNE. g(0,0)=

Answers

a.) f(x,y) is discontinuous at (0,0).

b.) g(0,0) is DNE. Hence, the value of g(0,0) is DNE.

Examine the behavior of

f(x,y)=x²+y² / 4x².5

as (x, y) approaches (0, 0):

(a) Changing to polar coordinates, we find

lim(x, y)→(0, 0)

(x²+y²/4x².5)

= lim r→0

+ (1/4cos⁴θ) (r²sin²θ + r²cos²θ)/r²

= lim r→0

+ (1/4cos⁴θ)(sin²θ + cos²θ)

= lim r→0

+ 1/4cos⁴θ = ∞

Note that the limit does not exist.

Therefore, f(x,y) is discontinuous at (0,0).

(b) It is impossible to define a continuous function

g(x, y) = f(x, y)

for all (x, y) ≠ (0, 0)

and g is continuous everywhere, since

lim (x, y)→(0, 0)

f(x, y) does not exist.

It is due to the reason that f(0,0) is undefined.

Therefore, g(0,0) is DNE. Hence, the value of g(0,0) is DNE.

To know more about discontinuous visit:

https://brainly.com/question/30089265

#SPJ11

In each of these scenarios, a credit card company has violated a federal or state law. Match each act to the scenario that applies.

Answers

Answer:

I'm sorry, but I don't have any information about the scenarios you're referring to. Could you please provide me with more details so I can help you better?

Find the value of the following function at x = 2 and x = 3. Does the Intermediate Value Theorem guarantee that the function has a real zero between these two x- values? Answer f(x)= x³ + 5x² - 8x +

Answers

f(2) = 20, f(3) = 56 .Since the function does not change sign between x = 2 and x = 3 (both values are positive), the Intermediate Value Theorem does not guarantee that the function has a real zero between these two x-values.

To find the value of the function f(x) = x³ + 5x² - 8x + 8 at x = 2 and x = 3, we substitute these values into the function:

f(2) = (2)³ + 5(2)² - 8(2) + 8

     = 8 + 20 - 16 + 8

     = 20

f(3) = (3)³ + 5(3)² - 8(3) + 8

     = 27 + 45 - 24 + 8

     = 56

Therefore, f(2) = 20 and f(3) = 56.

To determine if the Intermediate Value Theorem guarantees that the function has a real zero between x = 2 and x = 3, we need to check if the function changes sign between these two x-values.

Evaluate f(2) = 20 and f(3) = 56:

f(2) = 20 is positive,

f(3) = 56 is positive.

Since the function does not change sign between x = 2 and x = 3 (both values are positive), the Intermediate Value Theorem does not guarantee that the function has a real zero between these two x-values.

Learn more about Intermediate Value Theorem here: https://brainly.com/question/29712240

#SPJ11

The complete question is:

Find the value of the following function at x = 2 and x = 3. Does the Intermediate Value Theorem guarantee that the function has a real zero between these two x- values? Answer f(x)= x³ + 5x² - 8x +8

The differential equation sin(y) y'= (1-y) y' + y²e-5vis: O partial and non-linear Oordinary and first order Onon-linear and ordinary O partial and first order

Answers

the given differential equation can be classified as a non-linear and ordinary first-order differential equation.

The given differential equation sin(y) y' = (1 - y) y' + y²e^(-5) is a non-linear and ordinary differential equation.

It is non-linear because the terms involving y and y' are not of a simple linear form (e.g., y' = a*x + b*y). The presence of sin(y) and y²e^(-5) makes it a non-linear equation.

It is ordinary because it involves only ordinary derivatives, without any partial derivatives. The equation is expressed in terms of a single independent variable (usually denoted as x) and a single dependent variable (usually denoted as y). There are no partial derivatives with respect to multiple variables.

Furthermore, it is a first-order differential equation because it involves only the first derivative of the dependent variable y (y'). There are no higher-order derivatives present in the equation.

To know more about derivatives visit:

brainly.com/question/25324584

#SPJ11

Assume the quarterback and the receiver are in the same place as in the previous example. This time, however, the quarterback throws the ball at velocity of 40 mph and an angle of 45°. Write the initial velocity vector of the ball, v, in component form. 15 =

Answers

The initial velocity vector of the ball, v, in component form, was approximately 28.3i + 28.3j. This tells us the velocity of the ball in the x and y directions, respectively.

To write the initial velocity vector of the ball, v, in component form, we use the following equation:

v = vi + vj, where v is the initial velocity vector of the ball, vi is the velocity vector in the x-direction, and vj is the velocity vector in the y-direction.

We also know that the ball's velocity, v, equals 40 mph, and the angle between the ball's initial velocity and the horizontal, θ, is 45°. We can use trigonometric functions to solve for vi and vj. Specifically, we know that:

sin(θ) = vj / vvj

= v * sin(θ)cos(θ)

= vi / vvi

= v * cos(θ)

Plugging in the values we know, we get:

vj = 40 * sin(45°)

≈ 28.3 mph

vi = 40 * cos(45°)

≈ 28.3 mph

Therefore, the initial velocity vector of the ball, v, in component form is: v = 28.3i + 28.3j. Hence, we can write the initial velocity vector of a ball thrown by a quarterback to a receiver in component form by using the velocity and angle of the ball.

Specifically, we can break up the velocity vector into components in the x and y directions and find the values of these components using trigonometric functions. Once we have these values, we can write the initial velocity vector of the ball in component form.

To know more about the velocity vector, visit:

brainly.com/question/13492374

#SPJ11

A cone with height h and radius r has a lateral surface area (the curved surface only, excluding the base) of S = √√²+h². Complete pa C a. Estimate the change in the surface area when r increases from r= 2.30 to r= 2.35 and h decreases from h = 0.66 to h = 0.64. The estimated change in surface area is (Round to three decimal places as needed.) b. When r = 100 and h = 200, is the surface area more sensitive to a small change in r or a small change in h? Explain. Find dS for r= 100 and h = 200.

Answers

b) By comparing the magnitudes of |∂S/∂r| and |∂S/∂h|, we can determine whether the surface area is more sensitive to a small change in r or a small change in h.

To estimate the change in the surface area of the cone when r increases and h decreases, we'll calculate the partial derivatives of the surface area equation with respect to r and h. Then, we'll use these derivatives to estimate the change in surface area.

Given:

Lateral surface area, S = √([tex]r^2 + h^2[/tex])

a) Estimate the change in surface area:

To estimate the change in surface area, we'll calculate the partial derivatives of S with respect to r and h, and then use these derivatives to estimate the change in surface area when r and h change.

Let's find the partial derivatives:

∂S/∂r = ∂(√([tex]r^2 + h^2[/tex]))/∂r

        = (1/2) * ([tex]r^2 + h^2[/tex])^(-1/2) * 2r

        = r / √([tex]r^2 + h^2[/tex])

∂S/∂h = ∂(√[tex](r^2 + h^2[/tex]))/∂h

        = (1/2) * ([tex]r^2 + h^2)^{(-1/2)}[/tex] * 2h

        = h / √[tex](r^2 + h^2[/tex])

Now, we'll calculate the change in surface area:

ΔS ≈ (∂S/∂r * Δr) + (∂S/∂h * Δh)

Where Δr is the change in r and Δh is the change in h.

Given: Δr = 2.35 - 2.30

= 0.05 and Δh

= 0.64 - 0.66

= -0.02

Substituting these values, we have:

ΔS ≈ (r / √[tex](r^2 + h^2)[/tex]) * Δr + (h / √[tex](r^2 + h^2)[/tex]) * Δh

Let's substitute the given values of r and h:

ΔS ≈ (2.30 / √([tex]2.30^2 + 0.66^2[/tex])) * 0.05 + (0.66 / √([tex]2.30^2 + 0.66^2)[/tex]) * (-0.02)

Calculating this expression will give us the estimated change in surface area.

b) To determine whether the surface area is more sensitive to a small change in r or a small change in h, we'll compare the magnitudes of the partial derivatives ∂S/∂r and ∂S/∂h for r = 100 and h = 200.

Let's calculate the partial derivatives for r = 100 and h = 200:

∂S/∂r = 100 / √([tex]100^2 + 200^2[/tex])

∂S/∂h = 200 / √([tex]100^2 + 200^2[/tex])

By comparing the magnitudes of these partial derivatives, we can determine which factor has a larger impact on the surface area.

Now, let's calculate ∂S/∂r and ∂S/∂h for r = 100 and h = 200:

∂S/∂r = 100 / √([tex]100^2 + 200^2[/tex])

∂S/∂h = 200 / √([tex]100^2 + 200^2[/tex])

Now, let's compare the magnitudes of these partial derivatives:

|∂S/∂r| = 100 / √([tex]100^2 + 200^2)[/tex]

|∂S/∂h| = 200 /

√([tex]100^2 + 200^2)[/tex]

To know more about derivatives visit:

brainly.com/question/25324584

#SPJ11

Final answer:

To estimate the change in surface area, we can use the formula for the lateral surface area of a cone. When r = 100 and h = 200, the surface area is more sensitive to a small change in r than a small change in h.

Explanation:

To estimate the change in surface area, we can use the formula for the lateral surface area of a cone, which is S = √(r²+h²). To calculate the change in surface area when the radius increases from 2.30 to 2.35 and the height decreases from 0.66 to 0.64, we can plug in the new values into the formula and subtract the original surface area from the new surface area. The estimated change in surface area is approximately 0.0042.

When r = 100 and h = 200, we can calculate the surface area using the same formula and compare the effect of a small change in r and a small change in h. By finding the derivative of the surface area with respect to r and h, we can determine which has a greater impact on the surface area. The value of the derivative with respect to r is greater than the value with respect to h, indicating that the surface area is more sensitive to a small change in r.

Keywords: cone, lateral surface area, change, radius, height, estimate, derivative

Learn more about Cone surface area here:

https://brainly.com/question/23877107

#SPJ2

An 11.09 mol sample of an ideal gas is heated from 6.64 to
464.34◦C keeping the pressure constant and equal to 1.58 bar.
What is the change in U and H?
C¯p(J mol^−1 K^−1) = 34.45 + (4.98 × 10^−3)T − (1.44 × 105)(T^−2).
Answers:
∆H = 184179.58 J
∆U = 141976.07 J

Answers

The change in U and H for given sample of an ideal gas by keeping the pressure constant is given by ∆H = 184179.58 J and ∆U = 184179.58 J.

To calculate the change in internal energy (∆U) and enthalpy (∆H) of the gas, use the equation,

∆U = ∆H - ∆(PV)

The pressure (P) is constant, the work done (∆(PV)) is zero.

Therefore, we can simplify the equation to,

∆U = ∆H

To find the change in enthalpy (∆H), we can use the equation,

∆H = ∫(Cp dT)

The specific heat capacity of the gas (Cp) as a function of temperature (T),

we can integrate the equation over the temperature range to calculate the change in enthalpy.

∆H = ∫(Cp dT) between the initial temperature (T₁) and final temperature (T₂).

∆H = ∫[(34.45 + (4.98 × 10⁻³)T - (1.44 × 10⁵)(T⁻²)) dT]

between T₁ = 6.64 °C and T₂ = 464.34 °C.

∆H = [34.45T + (4.98 × 10⁻³)(T²)/2 + (1.44 × 10⁵)(T⁻¹)]

between T₁ = 6.64 °C and T₂ = 464.34 °C.

∆H = [34.45(464.34) + (4.98 × 10⁻³)((464.34)²)/2 + (1.44 × 10⁵)((464.34)⁻¹)] - [34.45(6.64) + (4.98 × 10⁻³)((6.64)²)/2 + (1.44 × 10⁵)((6.64)⁻¹)]

∆H ≈ 184179.58 J

Since ∆U = ∆H , the change in internal energy (∆U) is also approximately 184179.58 J.

Therefore, the change in U and H by keeping the pressure constant is equal to ,

∆H = 184179.58 J

∆U = 184179.58 J

Learn more about pressure here

brainly.com/question/31970628

#SPJ4

For each of the following situations, find the critical value(s) for z or t.
a) H0:p=0.8 vs. HA:p=0.8 at α=0.05
b) b) H0:p=0.5 vs. HA:p>0.5 at α=0.10 c) c) H0:μ=40 vs. HA:μ=40 at α=0.10;n=48 d) d) H0:p=0.8 vs. HA:p>0.8 at α=0.05;n=330
e) e) H0:μ=80 vs. HA:μ<80 at α=0.10;n=1000
a) The critical value(s) is(are) = (Use a comma to separate answers as needed. Round to two decimal places as needed.)
b) The critical value(s) is(are) = (Use a comma to separate answers as needed. Round to two decimal places as needed.) c) The critical value(s) is(are) = (Use a comma to separate answers as needed. Round to two decimal places as needed.) d) The critical value(s) is(are) = (Use a comma to separate answers as needed. Round to two decimal places as needed.) e) The critical value(s) is(are) = (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Answers

a) In the given problem H0: p = 0.8 vs. HA: p ≠ 0.8 at α = 0.05The significance level is α = 0.05. Since it is a two-tailed test, we need to split the alpha level in half, α/2 = 0.025.Using the z-table, we find the critical z-value as ±1.96.b) In the given problem H0: p = 0.5 vs. HA: p > 0.5 at α = 0.10

The significance level is α = 0.10. Since it is a right-tailed test, we find the z-score with a right-tailed area of 0.10.Using the z-table, we find the critical z-value as 1.28.c) In the given problem H0:

μ = 40 vs. HA: μ ≠ 40 at

α = 0.10,

n = 48The significance level is

α = 0.10.

Since it is a two-tailed test, we need to split the alpha level in half,

α/2 = 0.05.

Using the t-table with n - 1 = 47 degrees of freedom, we find the critical t-value as ±1.676.d) In the given problem H0:

p = 0.8 vs. HA:

p > 0.8 at

α = 0.05,

n = 330

The significance level is α = 0.05.

To know more about problem visit:

https://brainly.com/question/31611375

#SPJ11

To minimize the staff verticality error in levelling, the staff is rocked fore and back and the reading taken is the; Select one: a. Average of the lowest and highest b. Lowest c. The average minus the lowest d. The difference between the highest and lowest e. Highest f. None of the given answers

Answers

The reading taken to minimize staff verticality error in leveling is the average of the lowest and highest readings.

To minimize staff verticality error in leveling, it is important to account for any rocking or tilting of the staff. This is done by taking readings at different points while rocking the staff forward and backward. The purpose of this is to find the average reading that eliminates the effect of any staff tilting. By taking the average of the lowest and highest readings, we can minimize the impact of any staff verticality error. This approach helps ensure more accurate and reliable leveling measurements.

Know more about average here:

https://brainly.com/question/24057012

#SPJ11

A lamp has two bulbs, each of a type with average lifetime 1,600 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean = 1,600, find the probability that both of the lamp's bulbs fail within 1,500 hours. (Round your answer to four decimal places.)
Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,500 hours. (Round your answer to four decimal places.)

Answers

the probability that the two bulbs fail within a total of 1,500 hours is approximately 0.4312.

For the first part, we can model the lifetime of each bulb using an exponential distribution with mean = 1,600 hours. The probability density function (PDF) of the exponential distribution is given by:

f(x) = (1/mean) *[tex]e^{(-x/mean)}[/tex]

To find the probability that both bulbs fail within 1,500 hours, we need to calculate the probability that a single bulb fails within 1,500 hours and then multiply it by itself since the events are independent.

P(both bulbs fail within 1,500 hours) = P(bulb 1 fails within 1,500 hours) * P(bulb 2 fails within 1,500 hours)

Let's calculate each probability:

P(bulb 1 fails within 1,500 hours) = ∫[0, 1500] (1/1600) * [tex]e^{(-x/1600)}[/tex] dx

Using integration, we can find that P(bulb 1 fails within 1,500 hours) = 0.5455 (rounded to four decimal places).

Since the two bulbs are independent, the probability that both bulbs fail within 1,500 hours is:

P(both bulbs fail within 1,500 hours) = P(bulb 1 fails within 1,500 hours) * P(bulb 2 fails within 1,500 hours)

                                    = 0.5455 * 0.5455

                                    = 0.2972 (rounded to four decimal places)

Therefore, the probability that both of the lamp's bulbs fail within 1,500 hours is approximately 0.2972.

For the second part, if one bulb burns out and is replaced by a new bulb, the lifetime of the new bulb is independent of the previous bulb's lifetime. So we need to calculate the probability that the first bulb fails within 1,500 hours and the second bulb fails within the remaining time (1,500 hours - the lifetime of the first bulb).

P(first bulb fails within 1,500 hours) = ∫[0, 1500] (1/1600) * [tex]e^{(-x/1600)}[/tex] dx (same as before)

Using the same calculation, we find P(first bulb fails within 1,500 hours) = 0.5455 (rounded to four decimal places).

Now, let T be the lifetime of the first bulb. We know that T follows an exponential distribution with mean 1,600 hours. The remaining time for the second bulb to fail is (1,500 - T). So the probability that the second bulb fails within (1,500 - T) hours is:

P(second bulb fails within (1,500 - T) hours) = ∫[0, 1500-T] (1/1600) *[tex]e^{(-x/1600)}[/tex] dx

Calculating this integral, we find P(second bulb fails within (1,500 - T) hours) = 1 - [tex]e^{(-(1500 - T)}[/tex]/1600)

Finally, the probability that the two bulbs fail within a total of 1,500 hours is:

P(both bulbs fail within 1,500 hours) = P(first bulb fails within 1,500 hours) * P(second bulb fails within (1,500 - T) hours)

                                    = 0.5455 * (1 - [tex]e^{(-(1500 - T)/1600)}[/tex])

Since T follows an exponential distribution with mean 1,600, we can integrate over all possible values of T and multiply by the probability density function of T to find the overall probability:

P(both bulbs fail within 1,500 hours) = ∫[0,

infinity] (1/1600) * 0.5455 * (1 -[tex]e^{(-(1500 - T)/1600)}) * e^{(-T/1600) }[/tex]dT

Performing this integration, we find P(both bulbs fail within 1,500 hours) = 0.4312 (rounded to four decimal places).

To know more about probability visit:

brainly.com/question/31828911

#SPJ11

Find lim P→(−2,−2,0)

( x+1
1

+ y+1
1

+ z−5
2

)

Answers

The given limit is: lim[tex]P → (−2, −2, 0)(x+11+ y+11+ z−52)[/tex]. To solve this limit we will use the following steps:Substitute[tex]x = -2, y = -2, and z = 0[/tex]in the given[limit.tex]lim P → (−2, −2, 0)((-2)+11+ (-2)+11+ (0−5)2) = lim P → (−2, −2, 0)(−4) = −4.[/tex]

Since the value of the limit is finite and is equal to -4, it can be concluded that the given limit exists. Therefore, the required limit of the given expression is -4. The expression is given bylim[tex]P → (−2, −2, 0)(x+11+ y+11+ z−52)[/tex]

which on substituting the values of x, y, and z is equal to [tex]lim P → (−2, −2, 0)((-2)+11+ (-2)+11+ (0−5)2) = lim P → (−2, −2, 0)(−4) = −4.[/tex]Therefore, the required limit of the given expression is -4.

To know more about Substitute visit:

https://brainly.com/question/29383142

#SPJ11

trying to the inverse function f^-1 of the function f
f(x)=10cos(2/5x)

Answers

The inverse function [tex]f^(-1) of f(x) = 10cos(2/5x) is f^(-1)(x) = (5/2)cos^(-1)(x/10)[/tex].

To find the inverse function of f(x) = 10cos(2/5x), we need to follow a few steps. First, let's replace f(x) with y to rewrite the equation as y = 10cos(2/5x).

Interchange x and y

To find the inverse, we need to interchange x and y in the equation. So, the equation becomes x = 10cos(2/5y).

Solve for y

Next, we need to solve the equation for y. Divide both sides by 10: x/10 = cos(2/5y).

Find the inverse function

To isolate y, we need to apply the inverse cosine function (cos^(-1)) to both sides:[tex]cos^(-1)(x/10) = 2/5y[/tex]. Now, multiply both sides by 5/2 to solve for y:[tex]y = (5/2)cos^(-1)(x/10)[/tex].

So, the inverse function f^(-1) of f(x) = 10cos(2/5x) is f^(-1)(x) = (5/2)cos^(-1)(x/10).

Learn more about  inverse function

brainly.com/question/29141206

#SPJ11

If 25 days after a $640.00 loan is charged, it costs $850.00 to pay it off, what is the simple daily interest rate?
a. 2.11%
b. 2.71%
c. 1.01%
d. 1.31%​

Answers

The simple daily Interest rate is approximately 1.31%.The correct answer is d) 1.31%.

To find the simple daily interest rate, we can use the formula:

Interest = Principal × Rate × Time

Given:

Principal (loan amount) = $640.00

Amount to pay off = $850.00

Time = 25 days

We need to find the rate.

First, let's calculate the interest by subtracting the principal from the amount to pay off:

Interest = Amount to pay off - Principal

Interest = $850.00 - $640.00

Interest = $210.00

Now, let's calculate the daily interest rate:

Daily Interest Rate = (Interest / Principal) × (1 / Time)

Daily Interest Rate = ($210.00 / $640.00) × (1 / 25)

Calculating the expression:

Daily Interest Rate = (0.328125) × (0.04)

Daily Interest Rate = 0.013125

To convert the decimal to a percentage, we multiply by 100:

Daily Interest Rate = 0.013125 × 100

Daily Interest Rate = 1.3125%

Therefore, the simple daily interest rate is approximately 1.31%.

The correct answer is d) 1.31%.

For more questions on Interest .

https://brainly.com/question/25720319

#SPJ8

What are the differences between theoretical
probability, subjective probability and experimental probability?
Provide an example for each one with reference to rolling a pair of
dice.

Answers

Probability is the study of random occurrences, with various approaches that quantify the likelihood of occurrence. Here are the differences between theoretical probability, subjective probability, and experimental probability.

Theoretical probability: It is the probability based on mathematical theories that are used to calculate the probability of a certain event occurring. Theoretical probability is used when there are equal outcomes for every event, making the event random, such as flipping a coin or rolling a die.

Example: When rolling a pair of dice, the theoretical probability of getting a sum of 6 would be 5/36.

Because there are only five possible ways to get a sum of 6 in rolling a pair of dice, but there are 36 total combinations possible.

Subjective probability: It is a probability that is based on personal judgment or opinions, and therefore varies from person to person. This type of probability is used when there is insufficient information to establish the probability precisely, and different people may have different opinions.

Example: When rolling a pair of dice, a person who believes that rolling a sum of 6 is more likely than other values might assign a higher probability of 0.2 or 20%.

Experimental probability: It is the probability determined by conducting a series of trials or experiments to determine the likelihood of an event occurring. This type of probability is used when the likelihood of an event cannot be calculated, and empirical evidence is needed to determine the probability of an event.

Example: When rolling a pair of dice, if we roll them 100 times and get a sum of 6 20 times, the experimental probability of rolling a sum of 6 would be 20/100 or 0.2 or 20%.

Know more about the experimental probability.

https://brainly.com/question/8652467

#SPJ11

which value is equivalent to the expression shown? 3(1/4-2) + |-7|

Answers

The value that is equivalent is -7/4. Option C

What is a fraction?

A fraction is simply defined as the part of a whole number, a whole variable or a whole element.

The different types of fractions are;

Mixed fractionsProper fractionsImproper fractionsComplex fractions

From the information given, we have that;

3(1/4-2) + |-7|

find the lowest common multiple, we get;

3(1 - 8 /4) + 7

expand the bracket, we get;

3(-7/4) + 7

-21/4 + 7

-21 + 28/4

-7/4

Learn more about fractions at: https://brainly.com/question/11562149

#SPJ1

The complete question:

Which value is equivalent to the expression shown? 3(1/4-2) + |-7| is:

a. 7/4

b.7/2

c. -7/4

d. -7/2

Other Questions
Discuss the stability of Et2O*BF3, Me3N*BF3, PhH2N*BCl3 and Mes3P*B(C6F5)3 (Mes (mesityl) = 2,4,6-Me3- C6H2) adducts and place them in the order from least stable to most stable. Explain your answer. The average length of a baby sunfish in the east town hatchery is 2.2 inches with a standard deviation of 0.6 inches. Assume the population is bell shaped. Approximately what percentage of fish have z-scores because 2 and -2?Answer:68%75%88.9%95%99.7% **for sociology**Why was homosexuality considered deviant in our society? How did homosexuality go from a status of deviance to normality? How was this change possible based off of society's culture and meaning. How did this progress over the years?Thankyou for your time True or False: One of Aristotle's great virtues is that hescrupulously records his sources for the observations he reports.Explain why you chose that answer. Find the equation for (a) the tangent plane and (b) the normal line at the point Po *Po(1211, e) on (a) Using a coefficient of 5 for y, the equation for the tangent plane is on the surface 8x Iny+yInz Water at 10C (rho = 999.7 kg/m3 and = 1.307 103 kg/ms) is flowing steadily in a 0.12-cm-diameter, 14-m-long pipe at an average velocity of 0.9 m/s.Determine the pressure drop. (You must provide an answer before moving on to the next part.)The pressure drop is ________ kPa. r(t)=2ti+ 21t 2j+t 2k a local television station sent out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. there were 650 responses with the following results: 195 were interested in an interview show and a documentary, but not reruns. 26 were interested in an interview show and reruns but not a documentary. 91 were interested in reruns but not an interview show. 156 were interested in an interview show but not a documentary. 65 were interested in a documentary and reruns. 39 were interested in an interview show and reruns. 52 were interested in none of the three. how many are interested in exactly one kind of show? Find all solutions of the equation in the interval[0,2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)10sinx=10+5cosxx= "The Piper Co purchased a new machine 4 years ago at $10 million.The machine can be sold for $4.75 million today. The firm's currentbalance sheet shows a net fixed assets of $2.65 million, currentli" Identify the definition that applies to the compound in red. F-(aq) HSO4-(aq) HF(aq) SO42-(aq) Arrhenius acid Bronsted-Lowry acid Arrhenius base Bronsted-Lowry base From April through December 2000, the stock price of QRS Company had a roller coaster ride. The chart below indicates th e price of the stock at the beginning of each month during that period. Find the monthly average rate of change in price between May and August.Month. PriceApril (x = 1). 114May 107June 89July 100August 95September 110October 93November 85December 65 a.why is it important to protect biodiversity in urban areas?b. Name three factors that affect biodiversity in urbanecosystems If the H atom in an OH bond is replaced by a deuterium atom (D), would the Raman band for the O-H stretching vibration move to a higher or lower wavenumber position? Briefly explain your answer. How does the payload free worm method differ from the payload method? Obtain the general solution. (D4 - D-3D+D+2)y=0 y= C ex + Ce2x + e-x(C3+ C4x) y=Ce-x+ Cex + ex(C3+ C4x) y=Ce* + Ce-2x + e-x(C3+ C4x) Oy=Ce-x+ Ce-2x + e*(C3+4x) QUESTION 2 Obtain the genral solution. (D +5D+7D+3)y=0 y=eX(C-Cx) + 3e-3x y=eX(C+Cx) 3x + e-x Oy=eX(C+Cx) + 3ex Oy=ex(C+Cx) + e-x QUESTION 3 Find the solution to the given homogeneous linear ODE. (4D5-23D3-33D-17D-3)y=0 O -1 y=eX(C + Cx) + Ce-x + (C+Csx)e x 3x y=eX(C + Cx) + C3ex + (C+C5x)e O y= eX(C + Cx) + Cex + (C+C5x)e x 7x y=ex(C + x) + 3ex + (C4+ 5x)e What is the effective rate of interest on a loan that charges you 8% compounded weekly? 8.32% 8.47% 8.61% 8.17% Firms produce and sell different goods and services. Household purchase these goods from the firms. In return firms receives_ from household.O a. revenue O b. lossO c. expenses O d. None of the option What was the change in Global's book value of equity from 2020 to 2021 according to Table 2.1? Does this imply that the market price of Global's shares increased in 2021? Explain Solve and check the linear equation. 4x+1=5 The solution set is (). (Simplify your answer.) ***