The volume of a cube is decreasing at a constant rate of 2371 cubic centimeters per minute. At the instant when the volume of the cube is 914 cubic centimeters, what is the rate of change of the surface area of the cube? Round your answer to three decimal places (if necessary).

Q: Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) =…

A:

Q: 14. If a function f has an inverse and f(- 9) = 2, then what is f¹ (2)? f¹ (2)= [

A:

Q: Solve the given differential equation. All solutions should be found. =e¹x + 7y dy dx NOTE: Use c…

A: To solve the following differential equation.

Q: Let f(x) = g(x) h(x) and consider the following table of values: The value of f' (-9) is Number…

A:

Q: Calculate r' (t) and T(t), where 1668 T(t) = r(t)= (4t-4, 1- 4t, 6t – 1).

A:

Q: Given that y = (2³ – 3) (z + 7). Find the derivative using the product rule and simplify your…

A: If we have a function , where u and v are the functions of x  . Then, by the use of the product…

Q: two sides of a triangle have lengths 10 and 13. the angle between them is increasing at a rate of…

A: We have that the two sides of a triangle have lengths 10 and 13.Let x be the required third side of…

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 3. y' = x - 2y Ans.…

A:

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 1. (x5 + 3y) dx - x…

A: Comparing this with general differential equation We get, , Integrating Factor is given as IF IF =…

Q: The general term for the sequence 2, -6, 18, ... is

A: Given sequence is as follows From the sequence we can interpret as follows Given sequence is a…

Q: Find the area under the curve y = 2x -3 from x = 8 to x = t and evaluate it for t = 10, t = 100.…

A: ;

Q: dx Assume that x= x(t) and y = y(t). Let y = x² + 3 and dt Find dy dt || dy dt when x = 3. (Simplify…

A: Given.

Q: Suppose that the matrix A has the following eigenvalues and eigenvectors: [] A Write the solution to…

A: The given eigenvalues and eigenvectors are:

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

A:

Q: For the function f graphed below, find the following limits: 1. lim f(x) = ∞o help (limits) H--3- 2.…

A:

Q: 17. Evaluate these limits of h. a. b. Evaluate the limit, if it exists. (If an answer does not…

A: To evaluate the following limits.

Q: 6- x - x² if x ≤ 4 if x > 4 2x - 3 Calculate the following limits. Enter "DNE" if the limit does not…

A: we are given the piecewise function and we need to find out the limits given.

Q: A particle moves according to a law of motion s = f(t), t ≥ 0,  where t is measured in seconds and s…

A:

Q: Given the function f(x) = sqrt(3x), determine the slope of the tangent line of f at x=6 using the…

A:

Q: Solve the separable equation dy/dx + 4x2y4 = 0, with initial value y(0) = 1.

A: Take integration on both sides.

Q: Use the chain rule to find the derivative of f(x)=5(-527-82³) ¹4 Leave your answer in factored form.…

A: Consider the function

Q: Consider the function f(x) = 2³. Which of the following functions are equal to f(x)? Select all that…

A: We have given,   f(x) = 23x

Q: The function y(t) = 4e³t - 2e5t is a solution (but not the general solution) to y" + py' + qy = 0.…

A:

Q: let y = 2sqrt(x) a. find the differential dy = _____dx b. find the change in y / delta y when x = 3…

A:

Q: y=6x+9/x^3 find dy/dx at x=1

A:

Q: Əw ər Find when r = 5 and s= -5 if w= (x+y+z)²₁ x=r-s, y = cos (r+s), z = sin (r + s). Əw ər = |r =…

A:

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the integral X y…

A:

Q: Determine the derivative of the function k(x) = x6ï with respect to X. Ay

A:

Q: The bit strings of length 9 having exactly four 1s

A: Number of ways to select r objects out  of n objects  is given by

Q: Use the shell method to set up an integral that computes the volume of the solid generated by…

A:

Q: The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and…

A: This is question of calculusHere rate of change is given We have to find displacement.Further…

Q: Let the demand function for a product be given by the function D(q) == 1.6q+ 220, where q the…

A: Given demand function, D(q)=-1.6 q+ 220.Given fixed cost of production for the item is $3000 and…

Q: The total cost (in dollars) to produce q units of a good is given by the function: C(q) = 4.9q +…

A: Given, C(q)=4.9q+41000

Q: Find the directions in which the function increases and decreases most rapidly at P0. Then, find the…

A:

Q: Evaluate each limit analytically. - (a) lim sin(x + h) – sin(x) h→0 h (b) lim h→0 (c) (d) lim h→0…

A:

Q: Find the general solution of the given differential equation. dy X - y = x² sin(x) dx y(x) = Give…

A:

Q: -X x³ + 1 for the interval [-1,1]. Let f (x) = for x < 0 for x ≥ 0 Determine whether or not the IVT…

A:

Q: Find the solution to the initial value problem, y" - y' - 2y = 4cos(2x); y(0) = −1, y'(0) = −3/5.

A:

Q: 3. We study the function f defined below: { f(x) = (1) (2) if x is rational if x is irrational Prove…

A:

Q: 23 f(t) = (t, t Between = 0 and = 1, the point traverses certain path. The length of that path is

A:

Q: For the following trajectory, find the speed associated with the trajectory and then find the length…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Letc be a non-zera constant, & kad be any c sketch the curve of y=F(x), label asymptotes and…

A: Note: As per our guidelines, we can solve the first question. Please repost the remaining question.

Q: Define each integral Stan² tan²0 de S₁4,da (24/3 +524+n)dz

A:

Q: Consider the function f(z)=z²-4z +3 on the interval [0, 4]. Verify that this function satisfies the…

A:

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 6. u dx + (1 - 3u)x…

A: To find: The general solution of the above differential equation.

Q: Find F as a function of x and evaluate it at x = 4, X = 6, and x = 8. "X F(x) - [* - 2²/0 = dt Step…

A:

Q: Find the solution of the given initial value problem. ty' + 2y = sint, y() = 9, t> 0 y =

A:

Q: 0 2 V(t) An object moves with velocity function v (t) = sin(t) during the time interval [0; π]. The…

A:

Q: Apply Newton's Method using the given initial guess. y = x³ - 2x - 2, X₁ = 0 X₁ = 0 x₂ = x3 = X4 =…

A:

Q: USE INTEGRATING FACTORS 1. Find the General Solution: Answer is already given. 4. (y + 1) dx +…

A: