The indicated function y_1(x) is a solution of the given differential equation. Use reduction of order.

y_2=y_1(x)∫ e ^∫P(x)dx/y_1^2 dx

as instructed, to find a second solution y_2(x)
x^2y^n−9xy′+25y=0; y_1=x^3
y_2 = ______

Answers

Answer 1

To find a second solution y_2(x) using reduction of order, we start with the first solution y_1(x) = x^3 and apply the reduction of order formula: y_2 = y_1(x) ∫ [e^∫P(x)dx / y_1^2] dx.

After evaluating the integral and simplifying the expression, we find that the second solution is

y_2(x) = x^3 ∫ (e^(-3ln(x))) / x^6 dx = x^3 ∫ x^(-3) / x^6 dx = x^3 ∫ x^(-9) dx = (1/6) x^(-6).

Given the differential equation x^2y'' - 9xy' + 25y = 0 and the first solution y_1(x) = x^3, we can use reduction of order to find a second solution y_2(x). The reduction of order formula is y_2 = y_1(x) ∫ [e^∫P(x)dx / y_1^2] dx, where P(x) = -9x / x^2 = -9 / x.

Substituting y_1(x) = x^3 and P(x) = -9 / x into the reduction of order formula, we have y_2 = x^3 ∫ [e^(-9ln(x)) / (x^3)^2] dx. Simplifying the expression, we have y_2 = x^3 ∫ [e^(-9ln(x)) / x^6] dx.

Using the property e^a = 1 / e^(-a), we can rewrite the expression as y_2 = x^3 ∫ (e^(-9ln(x))) / x^6 dx = x^3 ∫ x^(-9) dx.

Evaluating the integral, we find that y_2(x) = (1/6) x^(-6).

To know more about differential equation click here: brainly.com/question/32645495

#SPJ11


Related Questions

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

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

Rob borrows $15. 00 from his father, and then he borrows $3. 00 more. Drag numbers to write an equation using negative integers to represent Rob's debt and complete the sentence to show how much money Rob owes his father. Numbers may be used once, more than once, or not at all. 3 15–18–3–15 18 12–12

Answers

Rob owes his father $18.00. Rob initially borrowed $15.00 from his father, represented by -15. Then, he borrowed an additional $3.00, represented by -3. When we add these two amounts together (-15 + -3), we get a total debt of $18.00, represented by -18. Therefore, Rob owes his father $18.00.

To write an equation using negative integers to represent Rob's debt, we can use the numbers provided and the operations of addition and subtraction. The equation would be:

(-15) + (-3) = (-18)

This equation represents Rob's initial debt of $15.00 (represented by -15) plus the additional $3.00 borrowed (represented by -3), resulting in a total debt of $18.00 (represented by -18).

Therefore, the completed sentence would be: Rob owes his father $18.00.

learn more about debt here:
https://brainly.com/question/32103869

#SPJ11

The mean of 16 numbers is 54. If each number is multiplied by 4 what will be
the new mean?

Answers

When each number in a data set is multiplied by a constant, the mean of the data set is also multiplied by that constant.

In this case, if each number is multiplied by 4, the new mean will be 4 times the original mean.

Original mean = 54

New mean = 4 * Original mean = 4 * 54 = 216

Therefore, the new mean after multiplying each number by 4 will be 216.

Learn more about multiplied here;

https://brainly.com/question/620034

#SPJ11

Explain why 0≤ x^2 tan^-1 x ≤ πx^2/4 for all 0 ≤ x ≤ 1

Answers

Given that x is an element of [0,1]. Now, we have to prove that0 ≤ x² tan⁻¹x ≤ πx²/4.We will begin by using integration by parts to determine the integral of tan⁻¹(x)Let u = tan⁻¹(x)and dv/dx

= 1.Then, we get du/dx

= 1/(1 + x²)and v

= x.Now, we can evaluate the integral:∫tan⁻¹(x)dx

= xtan⁻¹(x) - ∫ x/(1 + x²)dxIntegrating the right-hand side using a substitution x²

= u leads to∫ x/(1 + x²)dx

= (1/2)ln(1 + x²) + CTherefore,∫tan⁻¹(x)dx

= xtan⁻¹(x) - (1/2)ln(1 + x²) + CUsing the above equation and the given values of x in the expression, we get0 ≤ x² tan⁻¹(x) ≤ πx²/4This proves the given inequality holds.

Hence, We first used integration by parts to determine the integral of tan⁻¹(x), which is xtan⁻¹(x) - (1/2)ln(1 + x²) +

C. Using the equation obtained above and substituting the values of x provided in the original expression, we get the desired result of 0 ≤ x² tan⁻¹(x) ≤ πx²/4.The expression holds for all values of x in the interval [0,1], as required.

To know more about element, visit:

https://brainly.com/question/31950312

#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

Part C, D, E, G, H.
a. Determine the differential equation relating outputs \( y_{2}(t) \) to the input \( x(t) \). b. Solve the DE for \( x(t)=\sin t \) using MATLAB symbolic toolbox to find the specific equation for \(

Answers

The solution of the differential equation for \( x(t)=\sin t \) using MATLAB symbolic toolbox to find the specific equation for \(y_{2}(t)\) is: [tex]y_{2}(t)=\frac{1}{6}\left(3\cos\left(2t\right)-\sin\left(2t\right)+e^{-3t}\right)\sin\left(t\right)[/tex]

Given, the block diagram,

Step 1: We can rewrite the given block diagram into the equation below. [tex]\frac{d}{dt}y_{2}(t)=-3y_{2}(t)+3x(t)-\frac{d}{dt}y_{1}(t)[/tex]

Step 2: To find the Laplace transform of the differential equation, we apply the Laplace transform to both sides, which gives the result below. [tex]sY_{2}(s)+3Y_{2}(s)-y_{2}(0)=-3Y_{2}(s)+3X(s)-sY_{1}(s)+y_{1}(0)[/tex]

Step 3: Simplifying the above equation we get, [tex]sY_{2}(s)=-Y_{2}(s)+3X(s)-sY_{1}(s)[/tex][tex]\frac{Y_{2}(s)}{X(s)}=\frac{3}{s^{2}+s+3}[/tex]

Step 4: The inverse Laplace Transform of [tex]\frac{Y_{2}(s)}{X(s)}=\frac{3}{s^{2}+s+3}[/tex] can be calculated using MATLAB symbolic toolbox, which is shown below.[tex]y_{2}(t)=\frac{1}{6}\left(3\cos\left(2t\right)-\sin\left(2t\right)+e^{-3t}\right)\sin\left(t\right)[/tex]

Therefore, the solution of the differential equation for \( x(t)=\sin t \) using MATLAB symbolic toolbox to find the specific equation for \(y_{2}(t)\) is: [tex]y_{2}(t)=\frac{1}{6}\left(3\cos\left(2t\right)-\sin\left(2t\right)+e^{-3t}\right)\sin\left(t\right)[/tex]

To know more about differential equation visit:

brainly.com/question/32644620

#SPJ11

Solve by method of Laplace transform
with equation: y'' + y = 4δ(t − 2π)
where y(0) = 1, y'(0) = 0

Answers

The solution to the given differential equation is: y(t) = 4δ(t - 2π) + 2cos(t). To solve the differential equation using the Laplace transform, we first take the Laplace transform of both sides of the equation.

The Laplace transform of the second derivative y''(t) can be expressed as s^2Y(s) - sy(0) - y'(0), where Y(s) is the Laplace transform of y(t). Similarly, the Laplace transform of the delta function δ(t - 2π) is e^(-2πs).

Applying the Laplace transform to the differential equation, we get:

s^2Y(s) - s(1) - 0 + Y(s) = 4e^(-2πs)

Simplifying the equation, we have:

s^2Y(s) + Y(s) - s = 4e^(-2πs) + s

Now, we solve for Y(s):

Y(s)(s^2 + 1) = 4e^(-2πs) + s + s(1)

Y(s)(s^2 + 1) = 4e^(-2πs) + 2s

Y(s) = (4e^(-2πs) + 2s) / (s^2 + 1)

To find y(t), we need to take the inverse Laplace transform of Y(s). Since the inverse Laplace transform of e^(-as) is δ(t - a), we can rewrite the equation as:

Y(s) = 4e^(-2πs) / (s^2 + 1) + 2s / (s^2 + 1)

Taking the inverse Laplace transform of each term, we get:

y(t) = 4δ(t - 2π) + 2cos(t)

Note that the initial conditions y(0) = 1 and y'(0) = 0 are automatically satisfied by the solution.

Learn more about Laplace transform at: brainly.com/question/31689149

#SPJ11

Randi went to Lowe’s to buy wall-to-wall carpeting. She needs 109.41 square yards for downstairs, 30.41 square yards for the halls, and 160.51 square yards for the bedrooms upstairs. Randi chose a shag carpet that costs $13.60 per square yard. She ordered foam padding at $3.10 per square yard. The carpet installers quoted Randi a labor charge of $3.75 per square yard.

What will the total job cost Randi? (Round your answer to the nearest cent.)

Answers

Rounded to the nearest cent, the total job cost for Randi is $6,138.99.

To calculate the total cost for Randi's carpeting job, we need to consider the cost of the carpet, foam padding, and labor.

1. Carpet cost:

The total square yards of carpet needed is:

Downstairs: 109.41 square yards

Halls: 30.41 square yards

Upstairs bedrooms: 160.51 square yards

The total square yards of carpet required is the sum of these areas:

109.41 + 30.41 + 160.51 = 300.33 square yards

The cost of the carpet per square yard is $13.60.

Therefore, the cost of the carpet is:

300.33 * $13.60 = $4,080.19

2. Foam padding cost:

The total square yards of foam padding needed is the same as the carpet area: 300.33 square yards.

The cost of the foam padding per square yard is $3.10.

Therefore, the cost of the foam padding is:

300.33 * $3.10 = $930.81

3. Labor cost:

The labor cost is quoted at $3.75 per square yard.

Therefore, the labor cost is:

300.33 * $3.75 = $1,126.99

4. Total job cost:

The total cost is the sum of the carpet cost, foam padding cost, and labor cost:

$4,080.19 + $930.81 + $1,126.99 = $6,138.99

Learn more about total job cost here: brainly.com/question/26171624

#SPJ11

Find dy/dx by implicit differentiation and evaluate the
derivative at the given point
x^3 + y^3 = 16xy - 3 at point (8,5)

Answers

dy/dx = (3x^2 - 16y) / (16x - 3y^2)

At the point (8, 5), dy/dx = -43 / 67.

To find dy/dx by implicit differentiation, we differentiate both sides of the equation x^3 + y^3 = 16xy - 3 with respect to x, treating y as a function of x.

Differentiating x^3 with respect to x gives 3x^2. Differentiating y^3 with respect to x requires the chain rule, resulting in 3y^2 * dy/dx. Differentiating 16xy with respect to x gives 16y + 16x * dy/dx. The constant term -3 differentiates to 0.

Combining these terms, we have 3x^2 + 3y^2 * dy/dx = 16y + 16x * dy/dx.

Next, we isolate dy/dx by moving the terms involving dy/dx to one side of the equation and the other terms to the other side. We get 3x^2 - 16x * dy/dx = 16y - 3y^2 * dy/dx.

Now, we can factor out dy/dx from the left side and y from the right side. This gives dy/dx * (3x^2 + 3y^2) = 16y - 16x.

Finally, we divide both sides by (3x^2 + 3y^2) to solve for dy/dx:

dy/dx = (16y - 16x) / (3x^2 + 3y^2).

Substituting the coordinates of the given point (8, 5) into the expression for dy/dx, we find dy/dx = (16(5) - 16(8)) / (3(8)^2 + 3(5)^2) = -43 / 67.

Therefore, at the point (8, 5), the derivative dy/dx is equal to -43 / 67.

To learn more about  differentiation

brainly.com/question/24062595

#SPJ11

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

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

Question 19 Part 1: What's the maximum distance (in feet) that the receptacle intended for the refrigerator can be from that appliance? Part 2: Name two common kitchen appliances that may require rece

Answers

Part 1: The maximum distance between the receptacle intended for the refrigerator and the appliance is determined in feet. Part 2: Two common kitchen appliances that may require receptacles are named.

Part 1: The maximum distance between the receptacle and the refrigerator depends on electrical code regulations and safety standards. These regulations vary depending on the jurisdiction, but a common requirement is that the receptacle should be within 6 feet of the intended appliance. However, it's essential to consult local electrical codes to ensure compliance.

Part 2: Two common kitchen appliances that may require receptacles are refrigerators and electric stoves/ovens. Refrigerators require a dedicated receptacle to provide power for their operation and maintain proper food storage conditions. Electric stoves or ovens also require dedicated receptacles to supply the necessary electrical power for cooking purposes. These receptacles are typically designed to handle higher electrical loads associated with these appliances and ensure safe operation in the kitchen.

It's crucial to note that specific electrical codes and regulations may vary based on the location and building requirements. Therefore, it's always recommended to consult local electrical codes and regulations for accurate and up-to-date information regarding receptacle placement and requirements for kitchen appliances.

Learn more about Distance: brainly.com/question/26550516

#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

For the points given​ below, find ​(a​) PQ and ​(b​) the coordinates of the midpoint of PQ . P(0,-1),Q(3,6)

Answers

a.The length of PQ is √58.

b. The coordinates of the midpoint of PQ are (3/2, 5/2).

To find the length of PQ, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of [tex][(x2 - x1)^2 + (y2 - y1)^2].[/tex]

Using this formula, we can calculate the length of PQ. The coordinates of point P are (0, -1) and the coordinates of point Q are (3, 6). Plugging these values into the distance formula, we have:

[tex]PQ = √[(3 - 0)^2 + (6 - (-1))^2][/tex]

[tex]= √[3^2 + 7^2][/tex]

[tex]= √[9 + 49][/tex]

= √58

Therefore, the length of PQ is √58.

To find the coordinates of the midpoint of PQ, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by [(x1 + x2) / 2, (y1 + y2) / 2].

Using this formula, we can find the midpoint of PQ:

Midpoint = [(0 + 3) / 2, (-1 + 6) / 2]

= [3/2, 5/2]

Hence, the coordinates of the midpoint of PQ are (3/2, 5/2).

For such more question on coordinates:

https://brainly.com/question/31293074

#SPJ8

Calcula el volumen de una pirámide pentagonal de altura de 8 cm cuya base es un pentágono regular de 3 cm de lado y apotema de 2. 06 cm

Answers

El volumen de la pirámide pentagonal es aproximadamente 41.2 cm³.

Para calcular el volumen de una pirámide pentagonal, podemos usar la fórmula V = (1/3) * A * h, donde A es el área de la base y h es la altura de la pirámide.

En este caso, la base de la pirámide es un pentágono regular con un lado de 3 cm y un apotema de 2.06 cm. Podemos calcular el área de la base usando la fórmula del área de un pentágono regular: A = (5/4) * a * ap, donde a es la longitud del lado y ap es el apotema.

Una vez que tenemos el área de la base y la altura de la pirámide, podemos sustituir los valores en la fórmula del volumen para obtener el resultado. En este caso, el volumen de la pirámide pentagonal es aproximadamente 41.2 cm³.

Learn more about pentagonal here;

https://brainly.com/question/27874618

#SPJ11

A solid cone is in the region defined by √(x^2+y^2 ≤ z ≤ 4. The density of the cone at each point depends only on the distance from the point to the xy-plane, and the density formula is linear; the density at the bottom point of the solid cone is 10 g/cm^3 and the density at the top layer is 8 g/cm^3.
(a) Give a formula rho(x,y,z) for the density of the cone.
(b) Calculate the total mass of the cylinder. (Use a calculator to get your final answer to 2 decimal places.)
(c) What is the average density of the cone? How come the answer is not 9 g/cm^3 ?

Answers

The formula for the density of the cone is rho(x, y, z) = 10 - ((10 - 8)/4) * z.  The total mass of the cone can be calculated by integrating the density function over the region defined by the cone.

(a) The density of the cone varies linearly with the distance from the xy-plane. Given that the density at the bottom point is 10 g/cm^3 and the density at the top layer is 8 g/cm^3, we can express the density as a function of z using the equation of a straight line. The formula for the density of the cone is rho(x, y, z) = 10 - ((10 - 8)/4) * z.

(b) To calculate the total mass of the cone, we need to integrate the density function rho(x, y, z) over the region defined by the cone. Since the region is not explicitly defined, the integration will depend on the coordinate system being used. Without the specific region, it is not possible to provide a numerical value for the total mass.

(c) The average density of the cone is not 9 g/cm^3 because the density is not uniformly distributed throughout the cone. It varies linearly with the distance from the xy-plane, becoming denser as we move towards the bottom of the cone. Therefore, the average density will be less than the density at the bottom and greater than the density at the top. The actual average density can be calculated by integrating the density function over the region and dividing by the volume of the region.

To know more about integration click here: brainly.com/question/31744185

#SPJ11

what statement can be used to explain the steps of a proof?

Answers

A proof is a systematic and logical process used to establish the truth or validity of a mathematical or logical statement.

It consists of a series of well-defined steps that build upon each other to form a coherent and convincing argument.

Each step in a proof is carefully constructed, using previously established definitions, theorems, and logical reasoning.

The purpose of proof is to provide evidence and demonstrate that a statement is true or a conclusion is valid based on established principles and logical deductions. T

he steps of a proof are structured in a clear and concise manner, ensuring that each step follows logically from the preceding ones.

By following this rigorous approach, proofs establish a solid foundation for mathematical and logical arguments."

In essence, the statement highlights the systematic nature of proofs, emphasizing their logical progression and reliance on established principles and reasoning. It underscores the importance of constructing a coherent and convincing argument to establish the truth or validity of a given statement.

For more such answers on Proof

https://brainly.com/question/29969150

#SPJ8

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

Given the cruve R(t)=2ti+3t^2j+3t^3k
Find R’(t) =
Find’’(t) =

Answers

The derivatives are R'(t) = 2i + 6tj + 9t²k and R''(t) = 6j + 18tk.

To find the derivative of R(t), we differentiate each component of the vector separately:

R(t) = 2ti + 3t²j + 3t³k

Taking the derivative of each component:

R'(t) = (d/dt)(2ti) + (d/dt)(3t²j) + (d/dt)(3t³k)

= 2i + (d/dt)(3t²)j + (d/dt)(3t³)k

= 2i + 6tj + 9t²k

Therefore, R'(t) = 2i + 6tj + 9t²k.

To find the second derivative of R(t), we differentiate each component of R'(t):

R''(t) = (d/dt)(2i) + (d/dt)(6tj) + (d/dt)(9t²k)

= 0i + 6j + (d/dt)(9t²)k

= 6j + (d/dt)(9t²)k

= 6j + 18tk

Therefore, R''(t) = 6j + 18tk.

To learn more about vector visit:

brainly.com/question/29740341

#SPJ11

Find two differentlable functions f and g such that limx→5​f(x)=0,limx→5​g(x)=0 and limx→5​g(z)f(z)​=0 using L'Hcapltal's rule. Justify your answer by providing a complete solution demonatrating that your fumctions satlsfy the constrainte.

Answers

We have f(x) = x − 5 and g(x) = x² − 25 are two differentiable functions such that limx→5​f(x)=0, limx→5​g(x)=0 and limx→5​g(z)f(z)​=0 using L'Hôpital's rule.

Given function:

limx→5​f(x)=0,

limx→5​g(x)=0, and

limx→5​g(z)f(z)​=0.

We need to find two differentiable functions f and g that satisfy the above constraints using L'Hôpital's Rule.

First, let's consider the function f(x) such that

limx→5​f(x)=0.

Now, let's consider the function g(x) such that

limx→5​g(x)=0.

The function g(z)f(z) will become 0, as we have

limx→5​g(z)f(z)​=0.

Now, let us apply L'Hôpital's rule to find a suitable function:

limx→5​f(x)=0

⇒0/0

⇒ limx→5​(f(x)/1)

Using L'Hôpital's Rule, we get

limx→5​(f(x)/1)

=limx→5​​f′(x)1

=0

Therefore, f(x) can be f(x) = x − 5.

Now, let us apply L'Hôpital's rule to find a suitable function:

limx→5​g(x)=0

⇒0/0

⇒ limx→5​(g(x)/1)

Using L'Hôpital's Rule, we get

limx→5​(g(x)/1)

=limx→5​​g′(x)1

=0

Therefore, g(x) can be g(x) = x² − 25.

Know more about the L'Hôpital's rule.

https://brainly.com/question/31398208

#SPJ11

Use undetermined coefficients to find the particular solution to
y′′+5y′+3y=4t2+8t+4
yp(t)=

Answers

Using the method of undetermined coefficients, the particular solution yp(t) for the given second-order linear homogeneous differential equation is yp(t) = At^2 + Bt + C, where A, B, and C are constants to be determined.

To find the particular solution yp(t), we assume it has the form yp(t) = At^2 + Bt + C, where A, B, and C are constants. Since the right-hand side of the equation is a polynomial of degree 2, we choose a particular solution of the same form.

Differentiating yp(t) twice, we obtain yp''(t) = 2A, and yp'(t) = 2At + B. Substituting these derivatives into the differential equation, we have:

2A + 5(2At + B) + 3(At^2 + Bt + C) = 4t^2 + 8t + 4.

Expanding and grouping the terms, we have:

(3A)t^2 + (5B + 2A)t + (2A + 5B + 3C) = 4t^2 + 8t + 4.

Equating the coefficients of like terms, we get the following equations:

3A = 4, (5B + 2A) = 8, and (2A + 5B + 3C) = 4.

Solving these equations, we find A = 4/3, B = 4/5, and C = -2/15. Therefore, the particular solution is yp(t) = (4/3)t^2 + (4/5)t - 2/15.

Learn more about coefficients here:

https://brainly.com/question/1594145

#SPJ11

If ᵟ = ᵋ will work for the formal definition of the limit, then so will ᵟ = ᵋ/4
o True
o False

Answers

True. If δ = ε will work for the formal definition of the limit, then so will δ = ε/4. The δ value that satisfies the condition of the limit, even with a smaller range, conclude that if δ = ε works, then so will δ = ε/4.

The formal definition of a limit involves the concept of "δ-ε" proofs, where δ represents a small positive distance around a point and ε represents a small positive distance around the limit. In these proofs, the goal is to find a δ value such that whenever the input is within δ distance of the point, the output is within ε distance of the limit.

If δ = ε is valid for the formal definition of the limit, it means that for any given ε, there exists a δ such that whenever the input is within δ distance of the point, the output is within ε distance of the limit.

Now, if we consider δ = ε/4, it means that we are taking a smaller distance, one-fourth of the original ε, around the limit. In other words, we are tightening the requirement for the output to be within a smaller range.

Since we are still able to find a δ value that satisfies the condition of the limit, even with a smaller range, we can conclude that if δ = ε works, then so will δ = ε/4.

Learn more about limits here:

https://brainly.com/question/12207539

#SPJ4

Florence built a tower of blocks that was 171 centimeters high. She used 90 identical blocks to build the tower. What was the height of each of the blocks?

Answers

Florence built a tower of blocks that was 171 centimeters high. She used 90 identical blocks to build the tower. The height of each block is approximately 1.9 centimeters.

To determine the height of each block, we divide the total height of the tower (171 centimeters) by the number of blocks used (90 blocks). The resulting quotient, approximately 1.9 centimeters, represents the height of each block. To find the height of each block, we divide the total height of the tower by the number of blocks used.

Height of each block = Total height of the tower / Number of blocks

Height of each block = 171 centimeters / 90 blocks

Height of each block ≈ 1.9 centimeters

Therefore, the height of each block is approximately 1.9 centimeters.

learn more about height here:
https://brainly.com/question/29131380

#SPJ11

3. Use power series \( y(x)=\sum_{n=0}^{\infty} a_{n} x^{n} \) to solve the following nonhomogeneous ODE \[ y^{\prime \prime}+x y^{\prime}-y=e^{3 x} \]

Answers

By utilizing the power series method, we can find the solution to the nonhomogeneous ODE [tex]\(y^{\prime \prime}+x y^{\prime}-y=e^{3 x}\)[/tex] in the form of a power series \(y(x)=\sum_{n=0}^{\infty} a_{n} x^{n}\), where the coefficients \(a_n\) are determined by solving recurrence relations and the initial conditions.

First, we differentiate \(y(x)\) twice to obtain the derivatives [tex]\(y^{\prime}(x)\)[/tex] and [tex]\(y^{\prime \prime}(x)\)[/tex]. Then, we substitute these derivatives along with the power series representation into the ODE equation.

After substituting and collecting terms with the same power of \(x\), we equate the coefficients of each power of \(x\) to zero. This results in a set of recurrence relations that determine the values of the coefficients \(a_n\). Solving these recurrence relations allows us to find the specific values of \(a_n\) in terms of \(a_0\), \(a_1\), and \(a_2\), which are determined by the initial conditions.

Next, we determine the specific form of the power series solution by substituting the obtained coefficients back into the power series representation [tex]\(y(x)=\sum_{n=0}^{\infty} a_{n} x^{n}\)[/tex]. This gives us the expression for \(y(x)\) that satisfies the nonhomogeneous ODE [tex]\(y^{\prime \prime}+x y^{\prime}-y=e^{3 x}\)[/tex] with the given initial conditions.

In conclusion, by utilizing the power series method, we can find the solution to the nonhomogeneous ODE [tex]\(y^{\prime \prime}+x y^{\prime}-y=e^{3 x}\)[/tex] in the form of a power series \(y(x)=\sum_{n=0}^{\infty} a_{n} x^{n}\), where the coefficients \(a_n\) are determined by solving recurrence relations and the initial conditions.

Learn more about power series method here: brainly.com/question/29992253

#SPJ11

A sample of 450 grams of radioactive substance decays according to the function A(t)=450 e^-0.0371, where it is the time in years. How much of the substance will be left in the sample after 30 years? Round to the nearest whole gram.
A. 1 g
B. 2.674 g
C. 148 g
D. 0 g

Answers

After 30 years there will be only 1 gram of the substance left in the sample after decaying.  the correct option is A. 1g.

Given that the radioactive substance decays according to the function

A(t) = 450 e^−0.0371t,

where A(t) is the amount of substance left in the sample after t years.

The amount of the substance will be left in the sample after 30 years is given by;

A(t) = 450 e^−0.0371t

= 450e^(-0.0371 × 30)

≈ 1 gram

Therefore, the correct option is A. 1g.

Thus, after 30 years there will be only 1 gram of the substance left in the sample after decaying.

To know more about decaying visit:

https://brainly.com/question/32086007

#SPJ11

Let A(x)=x√(x+2).
Answer the following questions.
1. Find the interval(s) on which A is increasing.
2. Find the interval(s) on which A is decreasing.
3. Find the local maxima of A. List your answers as points in the form (a,b).
4. Find the local minima of A. List your answers as points in the form (a,b).
5. find the intervals on which A is concave upward.
6. find the intervals on which A is concave downward.


Answers

A(x) = x√(x + 2) is increasing on the interval (-2/3, ∞), decreasing on (-∞, -2/3), has a local maximum at (-2/3, -2√(2/3)), no local minima, is concave upward on (-∞, -2/3), and concave downward on (-2/3, ∞).

The interval(s) on which A(x) is increasing can be determined by finding the derivative of A(x) and identifying where it is positive. Taking the derivative of A(x), we get A'(x) = (3x + 2) / (2√(x + 2)). To find where A'(x) > 0, we set the numerator greater than zero and solve for x. Therefore, the interval on which A(x) is increasing is (-2/3, ∞).

Similarly, to find the interval(s) on which A(x) is decreasing, we look for where the derivative A'(x) is negative. Setting the numerator of A'(x) less than zero, we solve for x and find the interval on which A(x) is decreasing as (-∞, -2/3).

To find the local maxima of A(x), we need to locate the critical points by setting A'(x) equal to zero. Solving (3x + 2) / (2√(x + 2)) = 0, we find a critical point at x = -2/3. Evaluating A(-2/3), we get the local maximum point as (-2/3, -2√(2/3)).

To find the local minima, we examine the endpoints of the interval. As x approaches -∞ or ∞, A(x) approaches -∞, indicating there are no local minima.

To determine the intervals on which A(x) is concave upward, we find the second derivative A''(x). Taking the derivative of A'(x), we have A''(x) = (3√(x + 2) - (3x + 2) / (4(x + 2)^(3/2)). Setting A''(x) > 0, we solve for x and find the intervals of concave upward as (-∞, -2/3).

Finally, the intervals on which A(x) is concave downward are determined by A''(x) < 0. By solving the inequality A''(x) < 0, we find the interval of concave downward as (-2/3, ∞).

For more information on minima and maxima visit: brainly.in/question/54750949

#SPJ11

Find the inverse of each function. f(x)=−5x+2

Answers

The inverse of the function f(x) = -5x + 2 is given by f^(-1)(x) = (x - 2)/(-5).

To find the inverse of a function, we need to interchange the roles of x and y and solve for y. Let's start by replacing f(x) with y in the given function: y = -5x + 2. Now, we'll swap x and y: x = -5y + 2. Next, we solve this equation for y. Rearranging the terms, we get: 5y = 2 - x. Finally, we divide both sides by 5 to isolate y: y = (2 - x)/5. Hence, the inverse function is f^(-1)(x) = (x - 2)/(-5).

The inverse function (f^(-1)(x)) takes an input x and yields the original input for f(x). When we substitute f^(-1)(x) into f(x), we should obtain x. Let's verify this by substituting (x - 2)/(-5) into f(x): f((x - 2)/(-5)) = -5 * ((x - 2)/(-5)) + 2. Simplifying this expression, we get (-1) * (x - 2) + 2 = -x + 2 + 2 = -x + 4. As expected, the result is x, confirming that (x - 2)/(-5) is indeed the inverse of f(x) = -5x + 2.

Learn more about inverse here:

https://brainly.com/question/30339780

#SPJ11

Let −5x³−y³+2z³+xyz−808=0.
Use partial derivatives to calculate ∂z/∂x and ∂z/∂y at the point (−6,6,2).
∂z/∂x ](−6,6,2)=
∂z/∂y ](−6,6,2) =

Answers

Using partial derivatives the answer is found to be

∂z/∂x ](-6, 6, 2) = -528

∂z/∂y ](-6, 6, 2) = -72

To calculate ∂z/∂x and ∂z/∂y at the point (-6, 6, 2), we will differentiate the equation -5x³ - y³ + 2z³ + xyz - 808 = 0 with respect to x and y, and then substitute the given values.

Given equation: -5x³ - y³ + 2z³ + xyz - 808 = 0

1. Calculating ∂z/∂x:

Differentiating the equation with respect to x:

-15x² - y³ + 3x²z + yz = 0

Substituting x = -6, y = 6, and z = 2 into the equation:

-15(-6)² - (6)³ + 3(-6)²(2) + (6)(2) = -540 - 216 + 216 + 12 = -528

Therefore, ∂z/∂x at the point (-6, 6, 2) is -528.

2. Calculating ∂z/∂y:

Differentiating the equation with respect to y:

-3y² + 6z³ + xz = 0

Substituting x = -6, y = 6, and z = 2 into the equation:

-3(6)² + 6(2)³ + (-6)(2) = -108 + 48 - 12 = -72

Therefore, the partial derivative ∂z/∂y at the point (-6, 6, 2) is -72.

Learn more about partial derivative here:

https://brainly.com/question/32387059

#SPJ11

pls
answer every question
(4) If \( f(x)=2 x^{2} \), and \( g(x)=4 x-1 \), find \( f(g(x)) \). (5) A hotdog vendor has fixed eosts oi \( \$ 160 \) per dày to operate, plus a variable cost of \( \$ 1 \) per hotdog sold. He ear

Answers

The selling price refers to the amount of money at which a product or service is offered for purchase. It represents the value that the seller expects to receive in exchange for the item being sold.

If  f(x) = 2x², and g(x) = 4x - 1, we have to find f(g(x)). The given value of g(x) = 4x - 1.To find f(g(x)), we need to replace x in f(x) with the given value of g(x) and then simplify it. We have;

f(g(x)) = f(4x - 1) = 2(4x - 1)²

.= 2(16x² - 8x + 1)

= 32x² - 16x + 2 Therefore,

f(g(x)) = 32x² - 16x + 2.(5)  

A hotdog vendor has fixed costs of $160 per day to operate, plus a variable cost of $1 per hotdog sold. He earns $2 per hotdog sold. To find the break-even point, we need to equate the cost of producing hotdogs to the revenue earned by selling them. Therefore, let's assume he sells x hotdogs in a day, then his cost of selling x hotdogs would be;

C(x) = $160 + $1x = $160 + $x

And his revenue would be; R(x) = $2x

Thus, the break-even point is when the cost of selling x hotdogs is equal to the revenue earned by selling them. Hence, we have the equation;

C(x) = R(x) $160 + $x = $2x $160 = $x x = 80

Therefore, the hotdog vendor needs to sell at least 80 hotdogs a day to break even.

To know more about selling price visit:

https://brainly.com/question/27796445

#SPJ11

Other Questions
where are energy storage molecules found in an ecosystem? The Alpine House, Inc., is a large retailer of snow skis. The company assembled the information shown below for the quarter ended March 31:AmountSales$902,000Selling price per pair of skis$410Variable selling expense per pair of skis$49Variable administrative expense per pair of skis$17Total fixed selling expense$155,000Total fixed administrative expense$115,000Beginning merchandise inventory$80,000Ending merchandise invent$110,000Merchandise purchases$315,000Required:1. Prepare a traditional income statement for the quarter ended March 31.2. Prepare a contribution format income statement for the quarter ended March 31.3. What was the contribution margin per unit? how does hurston use these as a unifying element in the story? one of the immediate predecessors of expressionism was the composer Suppose that a small open economy calledAndalucia,is concerned about currency appreciation.What type of fiscal policy should the government of Andaluciause to generate a currency depreciation? Shou Find the limit. Use L'Hospital's Rule where appropriate. If L'Hospital's Rule does not apply, explain why. (a)limx0x2sin23x(b)limx0+xlnx(c)limx1(1x)tan(2x) In what ways did the advent of metal technology andits associated traditions and practices affect the development ofsocial complexity in West Africa? A 10 MVA, three-phase, wye-connected, 60 Hz, 15 kVLL synchronous generator has armature resistance of 0.6 92/phase and synchronous reactance of 15 22/phase. The generator is operating in stand-alone mode and delivering rated power at rated voltage to a unity power factor load. (a) Draw a neat and clearly labelled phase equivalent circuit of the stator of generator. Show only symbols on your phase equivalent circuit. (b) Draw a neat and clearly labelled phasor diagram for the operating condition described. Ms Geingos, the Management Accountant of Zama Medical Ltd appointed a person on 01 June 2018, who pretended to be an expert in the preparation of company financial statements. The following statement of financial position was prepared on 10 June 2018 by the new accountant: Ms Geingos is not satisfied with the format of the above statement of financial position and request you to assist her. You acquire the following additional information: 1. The reporting periof of Zama Medical Ltd ends on 30 June. 2. The buildings are occupied for the purposes of the activities of the entity and are accounted for in terms of the cost model. At the date of acquisition, 01 July 2016, the land was valued at N$100000 and buildings at N$300000. Depreciation is written off on buildings at 4% per annum on the straight line method. 3. Furniture and vehicles were purchased on 01 July 2016 at N$80000 and N$300000 respectively. Depreciation is written off on furniture at 12,5% per year on cost and on vehicles at 20% per year on the diminishing balance method. The necessary write-offs for the current year have been done. An article gave the following summary data on shear strength (kip) for a sample of 3/8-in. anchor bolts: n = 80, x = 4.50, s = 1.40. Calculate a lower confidence bound using a confidence level of 90% for true average shear strength. (Round your answer to two decimal places.) kip You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It TRUE / FALSE.a theodicy is an argument that seeks to discredit belief in a deity. Under a microscope, how would the connective tissue of an animal generally appear? a.many densely packed cells with thin bundles extracellular matrix between them b.densely packed cells filled with tight fibers of collagen and keratin c.loosely scattered cells among large amounts of extracellular matrix d.a network of extracellular matrix fibers with no cells Carol has a right to use Fred's driveway for her lifetime. Carol has a/aneasement in gross A power transistor is specified to have a maximum junction temperature of 150C. When the device is operated at this junction temperature with a heat sink, the case temperature is found to be 97C. The case is attached to the heat sink with a bond having a thermal resistance 0cs=0.5C/W and the thermal resistance of the heat sink 0sa=0.1C/W. If the ambient temperature is 25C, what is the power being dissipated in the device? What is the thermal resistance of the device, 0jc, from junction to case? A nurse calculating the dosage of magnesium sulfate IV by continuous infusion. The order is for magnesium sulfate 2 g/hr. Available is magnesium sulfate 100 mg/mL in 5% dextrose in water 500 mL. The nurse should set the IV pump to deliver how many mL/hr? Round to a whole number. Do not use commas. Which of the following best demonstrates the principle of rival consumption? Be sure to include state parks in your answer. A. When I visit a state park, you can visit the same park at the same time. B. Either you use a park's campsite or I use it. C. When I enter a picturesque park, it does not reduce your ability to enjoy some of the beauty of the park. D. No one can be readily excluded from enjoying the services of a state park. Required information [The following information applies to the questions displayed below.] Cane Company manufactures two products called Alpha and Beta that sell for $165 and $130, respectively. Each product uses only one type of raw material that costs $8 per pound. The company has the capacity to annually produce 113,000 units of each product. Its average cost per unit for each product at this level of activity are given below: Alpha BetaDirect materials $ 40 $ 24Direct labor 29 25Variable manufacturing overhead 15 14Trecable fixed manufacturing overhead 25 27Variable selling expense 21 17Common fied expense 24 19Total cost per unit $154 $126The company considers its traceable fixed manufacturing overhead to be avoidable, whereas its common fixed expenses are unavoidable and have been allocated to products based on sales dollars.Thank you for any help.1. What is the traceable fixed manufacturing overhead for Alpha and Beta?2. What is the company's total amount of common fixed expenses?3. Assume that cane expects to produce and sell 89,000 Alphas during the current year. One of Cane's sales representatives has found a new customer who is willing to buy 19,000 additional Alphas for a price of $116 per unit. What is the financial advantage (disadvantage) of accepting the new customer's order?4. Assume that Cane expects to produce and sell99,000 Betas during the current year. One of Cane's sales representatives has found a new customer who is willing to buy 2,000 additional Betas for a price of $48 per unit. What is the financial advantage (disadvantage) of accepting the new customer's order?5. Assume that Cane expects to produce and sell 104,000 Alphas during the current year. One of Cane's sales representatives has found a new customer who is willing to buy 19 000 additional Alphas for a price of $116 per unit; however pursuing this opportunity will decrease Alpha sales to regular customers by 10,000 units. What is the financial advantage (disadvantage) of accepting the new customer's order.Thank you for any help. y=24x3f(t)=2t3+t42Find the equation of the line that is tangent to the graph of they=x3+x2+x216at the point(4,7). Find the equation of the line that is tangent to the graph of they=xx1at the valuex=4. How many ping-pong balls would it take to fill a classroom that measures 14 feet by 12 feet by 7 feet? (Assume a ping-pong ball has a diameter of \( 1.5 \) inches and that the balls are stacked adjace Question 1 [Points 5] Including the initial parent process, how many processes are created by the program shown below? Justify. int main() \{ \( / * \) fork a child process \( * / \) fork ()\( ; \) fo