Sketch and set up integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13 rotated about y = -3. Please show steps!

Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

A:

Q: The current population of a small town is 2104 people. It is believed that town's population is…

A:

Q: Find the present value of a continuous stream of income over 5 years when the rate of income is…

A: On solving this we will get

Q: Match each of the following vectors with its magnitude. t=(-7, 1) a. 5√2 u = -21-8j b. 2√√5 a vector…

A:

Q: B. Find the derivative 11. f(x) = 5x³ 12. f(x)=(x²-3) (2x-3) 13. f(x)=(2²+5)(4x-3) of each of the…

A:

Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

Q: 2) dy = y² (1+ex) dx

A:

Q: If f(x)=5x(sinx+cosx), find f′(x) =

A: Product Rule of differentiation : du.vdx=u.dvdx +dudx.v dxndx=n.xn-1 dsin(x)dx=cos(x)  and…

Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

A:

Q: Evaluate efffxv xdv,where D is the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

A: Given problem:- Evaluate  ∫∫∫D xdv ,where D is the tetrahedron with vertices (0,0,0), (2,0,0),…

Q: Given cost and price (demand) functions C(q) = 110q+41,500 and p(q) = -1.9q+870, what is the…

A: Given  Cost function C(q) = 110q + 41,500  price function p(q) = -1.9q +870

Q: Find the 1) Sketch the ii) Determine the ::::.) Set-up iv.) Integrate 2 ²) y = x ²²₁₂ y = 2 = x₁…

A: Given problem:- Find the area bounded by curves y=x2 , y=2-x, x≥ 0

Q: A hotel rents rooms to customers by the night. The hotel determines that if it sets the price of the…

A:

Q: evaluate lim x →0 sin x-x 3 x

A: Given, limx->0 (sin x -x)/x³ SInce we have a indeterminate form, Applying l'Hoptials rule we…

Q: r(x) = 5 log4 (3x + 10)

A:

Q: Solve for the slope of each of the given point of a function

A: Given that,

Q: Use the power series 1 = Σ( Σ(-1)-1-1, x +1 n=1 to find a power series, centered at 0, of the…

A:

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A:

Q: 2. (4x³ - 3x² + 2x) dx

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A: To find the volume of the solid of revolution formed by rotating about the x-axis the region bounded…

Q: Sort St Question 2. Evaluate the following integral region). Show all your work! cos(x²) dx dy. Make…

A:

Q: Let T : R² ⇒ R³ be a linear transformation such that T([ 1 ]) = = 8 [][]) ([ 13 0 What is T -1 and T…

A: Concept: A linear transformation is a feature from one functional area to some other that takes into…

Q: - 6 = ₁6 -X

A:

Q: Evaluate fx² cosh x dx

A:

Q: For the following function, find the equation of the tangent line at the point (1, 2). f(x)=√9x² - 1…

A: We have to find equation of tangent line

Q: Given cost and price (demand) functions C(q) = 110q+40,700 and p(q) = -1.9q + 900, what profit can…

A:

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: topic- quadratic equations and derivatives

Q: Use finite difference approximation to find the values of y(0.25), y(0.5), and y (0.75) for the…

A:

Q: Assume A = 21 2] and B = 1 3 [43] [4 3 11 7 6 show that (AB)' = B' A'

A: Given matrices A and B, To show that AB'=B'A'

Q: Given that sin(0)= TT 3 and 2 <0<π what is the exact value of cos(20)?

A:

Q: Convert the rectangular equation x2 = −2y2 + 5x2 y2 to polar equation

A: The rectangular equation is x2=-2y2+5x2y2

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A:

Q: Q) choose one only 1) If y = (x − a)√2ax − x² + a² sin-¹(*), then y' = 2√/2ax-x² a a is constant. 2)…

A:

Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

A:

Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: This question can be solved using the concept of maxima and minima.

Q: fesch² (1- csch² (1+ 3x) dx

A: Hyperbolic function need to be integrated.

Q: Charles plots the point with the polar coordinates (-5,-). How does he plot this point? Drag a value…

A:

Q: 3. Find f'(x) if f(x)= 3 2x + sin r

A:

Q: Given I(0) = cos (0 + π), (a) Find I(-) analytically. (b) Find I' numerically by using a central…

A: Given: Iθ=cosθ+π. (a) Differentiate with respect to θ, I'θ=-sinθ+π…

Q: Solve using Variation of Parameters (D² + 1) y = tan x O y = c₁ cos x + c₂ sin x − cos x ln(secx +…

A: The objective is to find the general solution using variation of parameter.

Q: You start driving away from Morgantown at 12:00. Your distance away t hours after you left is given…

A:

Q: 1. For each of the following solve the system that is given. a) : (x, y, z]-[5,-1,3]+[4,-5,2] and…

A: Concept: The system of equations in complex form:…

Q: yı y' = 2x +2y +1 3x +y -2

A: We can solve the given differential equation .

Q: family

A: Please refer to the image below

Q: tanx - x x-0 x - sinx 1. lim

A:

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A: We have to find the area of the given region.

Q: Solve for the area bounded by the graphs of y = √√√x + 2, y = x + 2, x = 2, x = 4

A: Graph:

Q: Question 1. Sketch the following regions in the xy-plane. Make sure to shade the region and label…

A: To sketch the given regions in xy plane.

Q: Given that Inx+3 f(x) = 3lnx-1 Find the formula for f−¹(x). State the domain of f−¹(x). Show all…

A:

Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-