A real estate company owns 120 apartments which are fully occupied when the rent is $700 per month. Analytics indicate that for each $35 increase in rent, 5 apartments will become unoccupied. What rent should be charged in order to obtain the largest gross income?

Q: Suppose that P is a critical point of z = f (x, y). Suppose further that at P, the following hold:…

A: Given that P is a critical point P of

Q: Evaluate the integral. +C 2x + 9 x² + 6x +34 17 -da

A:

Q: List the four smallest elements of the set. (Enter your answers as a comma-separated list.) {y|y =…

A: {y|y = x2 − 3, x  integers}

Q: Find the derivative of the following function. y = -88x²-1 ...

A:

Q: Write the domain of the function f. 6 f(x) = 12x³ + X

A:

Q: (a) Setup an integral to calculate the area between the curves r = 2 + sin 30 and r = 4 - cos 30.

A: As per guidelines we can answer only first question if multiple questions are posted.Please repost…

Q: True or false: If f is a function such that lim f(x) = L and x→a+ lim f(x) = L x-a where a and I are…

A: For a Function f( x ) at If Function is continuous at  then

Q: Consider the following differential equation to be solved by the method of unde y" + 2y = -18x²e2x…

A:

Q: Use the function f(x)=x^2-6x+13 to answer how to algebraically find the vertex.

A:

Q: Calculate the derivative of y with respect to x, if x³/² + y-5/2 = 7. dy dx

A: Given equation, .derivative rules:

Q: For which value of t does the line given by the parametric equations x = t -1, y = 1+ 2t, z = 3 - t…

A:

Q: Find the arc length of the curve on the given interval. Parametric Equations x= 7t + 5, y = 7 - 8t…

A:

Q: The given curve is rotated about the y-axis. Set up, but do not evaluate, an integral for the area…

A: The given curve equation is  ,

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. √13n an =…

A: To determine whether the sequence  converge or diverge.To find the limit if the sequence is…

Q: y = ln(5t³ - 6) y = ln(4- 3x²)

A: y=ln⁡(5t3−6)

Q: Find an equation of the tangent line to the curve at each given point. x=2-3 cos 6, y = 3 + 2 sin 8…

A:

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: The given parametric equations

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. }} dy…

A: To find:-

Q: Find the differ y = √3 dy= = Evaluate dy fc x = 1, G y =

A:

Q: What is the minimum degree of the polynomial function whose graph approximates each given graph?…

A: Consider the graph

Q: The vectors (8,-12, 16) and (8, 12, 5) are orthogonal. Select one: True O False

A:

Q: (a) Find the unit tangent vector on the curve r(t) = [cos (t),2t,3sin(4t)] when t = 0.

A: To find the unit tangent vector on the curve .Note: Since the student has posted multiple questions…

Q: Find the total differential. 8x + y 3z - 2y dw = W = 8 3z-2y dx + 3z- - 4y - 16x (3z-2y)² Jdy + (7…

A:

Q: Find the slope of the line tangent to the graph of the function at the given value of x. == -√x; x =…

A:

Q: Find a possible formula for the graph. Y A 8TT X

A:

Q: Find the first and second derivatives of the following. 1-4√√x+x³ (a) y = (b) y = 3x²e² Y (c) y = x³…

A:

Q: Solve the equation. 3q 9-4 - 1 9-3 1 The solution set is 2q² -5q 2 q-7q+12 3 16 ±0 0.0.. (0) {}

A: Given

Q: Evaluate the following integral using integration by parts. √x20 In x dx

A: I=∫x20ln⁡xdx

Q: Find the exact length of the curve. x = et t₁ y = 4et/2, 0≤t≤4

A: Given, .Formula for length of curve is,

Q: Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: Does the sequence {a} converge or diverge? Find the limit if the sequence is convergent. an =√4n…

A:

Q: The magnitude of the vector (3, -2, 4) is 29. Select one: O True O False

A: The given statement "The magnitude of the vector  is "

Q: A tank contains 90 kg of salt and 2000 L of water. A solution of a concentration 0.0225 kg of salt…

A:

Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

A: To find the parametric equations for the line segment that joins the point .Note: Since the student…

Q: Find the lines that are tangent to the curve y=sin(pi*x/2) at x=1

A:

Q: A company is planning to manufacture snowboards. The fixed costs are $100 per day and total costs…

A: Given that,The company manufactures snowboards. The fixed cost is $100 per day and total cost $5100…

Q: 7.2x dy + y(2 + y²x) dx = 0

A:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A:

Q: Visually estimate the location of the centroid of the region shown. Then find the exact coordinates…

A:

Q: Consider the function f(x) = -2x³ + 36x² - 192x + 1.

A: f(x)=−2x3+36x2−192x+1

Q: Find the derivative of the function. y=e22x

A: Find the derivative of the function.y=e22x

Q: Express 0.132 as a geometric series

A: The given number .The aim is to write the number as a geometric series.

Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

A: Horizontal tangent lines to a curve occur at local extrema of the curve, that is at the peaks or…

Q: Use the quotient rule to find the derivative. x² + 8x +3 y= √x OA. dy 2x+8 dx X B. O C. dy dx dy dx…

A:

Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

A: f(x) = 2x-7

Q: 4. COS V sin v = csc v sin v 5. cot(a) cos(-a) + sin(- α) - csc (α)

A:

Q: dy dx and find the particular solution satisfying the initial condition y(0) = -3. Solve the…

A:

Q: Consider g(x) = -6x³ + 14 - 14x - 16x² Determine the intervals on which g is decreasing. g is…

A: In this question, we will find the interval of increasing and decreasing and local maximum and…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x²² In(x),…

A:

Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

A: