A box is partially filled with liquid. The length of the box is 18 inches. The width of the box is 12 inches. If the volume of the liquid is increasing at a rate of 569 cubic inches per second, what is the rate, in inches per second, at which the height of the liquid is changing when the height of the liquid is 4 inches? Submit an exact answer. Do not forget to include a negative sign if the height is decreasing.

Q: Obtain a family of solutions for the following First-Order Differential Equations. 2(2x2 + 2y2 )dx –...

A:

Q: Find the curvature of the curve at the given position. r(1) = (r, t², 31), at t=1

A:

Q: For the demand function q =D(x) = 100 find the following a) The elasticity b) The elasticity at x 7,...

A: Given

Q: 2 sinx V1-2cosx 3

A: ∫π3π2sinx1-2cosxdx=12∫π3π22sinx1-2cosxdx=12∫π3π21-2cosx-122sinx dxSince ∫f(x)nf'(x)dx=f(x)n+1n+1+C=1...

Q: A. Generate the first 50 Fibonacci numbers. Get the ratio (higher value divided by the lower value) ...

A: Definition of Fibonacci numbers:  Fibonacci numbers are from Fibonacci sequence. In this sequence ea...

Q: Determine whether the Series is convergent diveryent.Write or the exact test that you Use. 1t2

A: ∑n=1∞(-1)n1+2nn

Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at'x = =. (Enter an exac...

A:

Q: A potato is launched vertically upward with an initial velocity of 147 ft/s from a potato gun at the...

A:

Q: 7t + 4 lim t→-∞ t2 + 1 – 7t

A:

Q: 2 5. f(x) = x3

A: We will use the definition of a derivative to solve this question.

Q: Find the vector component of v = (4, – 1, 7) along b = (2, 3, –6) and the vector component of v orth...

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions specify...

Q: 2х + 6, х 6 From the following results, determine whether the function f(x) = is continuous at x = ...

A:

Q: Graph f (x) = (1/2)* and g (x) =(1/2) ~*+3. Plot three points and also the asymptote.

A: The answer is in step 2.

Q: dy = 3y + 2t dt %3D Given the above differential equation with the initial condition y(t=D0) = 5.0 a...

A: Solution is written in below steps.

Q: consider the following  5^3x+1 = 3^x-5 a) find the exact solution of the exponential equation in t...

A:

Q: 1. In Figure 3, RK is the angle bisector of 2ORC. a. Name the postulate/theorem that justifies the c...

A: Find your answer below 

Q: Set up the double integral that finds the volume of the solid under the surface z = 8x² + 3y over th...

A:

Q: 2x +6, r 6 is continuous at I = 6. Justify the conclusion. (i) f(6)=| (ii) lim f(x)= (iii) lim f(x)=...

A:

Q: Suppose " f(x)dx = 8, f(x)dx = 10, S, g(x)dx = 4 , S g(x)dx = 5 Find : f(x)dx =? f(x)dx =? | [3f(x) ...

A:

Q: Use the quotient rule to find the derivative, h' (x), of the following function. 3x h(x) = 8 - 5x

A:

Q: Evaluate the following integral (b) / cosh" x sinh x dx (4 + sinh? x)²

A:

Q: 1a)Find the length of the curve: x=t^3,y=3t^2/2; 0 ≤ t ≤ 224 b) Find the length of the curve: x=t^3...

A: Given,  a) x=t3,y=3t2/2 b)x=t3,y=3t2/2.

Q: Evaluate p dA, where Dis the shaded part inside the semicircle of radius 2 in the figure. y = 4- (Us...

A:

Q: Find all solutions to the equation on the interval (0, 27) : cos (a - %3D 5m T 47 3' 3 47 57 3 3 * 2...

A: Topic:- trigonometry ratios

Q: how do we identify the minimum and maximum value of the graph of a function at a given intetval?

A:

Q: Find the radius of convergence for 2" -(4x–8)" n n=1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: 1. lim(2x + 4) x-3 2. lim f(x) if f(x) = {- ifx 1 %3! x² - 4x + 3 X-1

A: Here we will solve the given limits,

Q: z is jointly proportional to the square of x and the square of y. If z=364 when x=6 and y=5, find z ...

A:

Q: (플, ) (-1) Which point is the inflection point of the function f(x)? A)(-n,0) B) (0,0) C) (T, 0) DI-...

A:

Q: e table gives the required standard weight, w, in kilograms, of American soldiers, age timeters.1 da...

A: Formula From the table  Because w increased by 2.7 kg as h increased by 4 cm  

Q: The demand function for a good isp = 42 – 0.01q. Round your numeric answers to one decimal place. a)...

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of int...

A: Given problem:- Evaluate the integral using the indicated trigonometric substitution. (Use C for the...

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

Q: Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations.) 0...

A: To find out the asymptotes.

Q: The curve -4x – 3y³ – 7x + 5y = 2 is shown in the graph below in blue. Use the graph below to draw l...

A:

Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

A:

Q: prove tañcy) dy

A:

Q: Find the length of the curve x = from y = 1 to y = 3. The length of the curve is (Type an integer or...

A:

Q: Solve the initial value problem y" + y – 12y = 0, y(0) = a, y'(0) = -28. Find a so that the solution...

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: Distance from the point P to line AB is AP→sinθ, here θ is the angle between AP →and BA→

Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x - In 7x, ...

A:

Q: Evaluate the integral. [HINT: Use a shortcut.] | 12(2x + 1)5 dx

A:

Q: Let f be a function defined by z = f(x, y) = 3xy? – 4y. Find the actual change in z when x changes f...

A:

Q: Expand completely, write all exponents as factors In (x+1) 3 Recall Vx : X = (x – 1) 5

A: Given query is to expand logarithmic expression.

Q: 1.a)Find the area of the surface generated by revolving the curve y=√(121-x^2), −1 ≤ x ≤ 1 about the...

A:

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an...

A: The x-intercept is where a graph crosses the x-axis and the y-intercept is where a graph crosses the...

Q: State the trigonometric substitution you would use to find the indefinite integral. Do not integrate...

A: We have to find substitution of x

Q: Find the derivative of y = cos³*+8 (x). Provide your answer below: y =

A: Given query is to find the series of the expression.

Q: e2x dx 10. V1+e2x

A:

Q: (a). Write the distance from point P(, y) on the line y = 2x to the point (3, 3) as a function of c....

A: