In one of the warehouses of a construction firm, cement is being released from an elevated storage bin at a rate of 29 ft/min. A wide and flat metallic sheet below the bin catches the cement which forms a conical pile. The base diameter and the height of the pile is maintained at a 1:1 ratio. Find the rate at which the area of the base of the cone is increasing when the diameter is 14 feet. Provide both the working equation and the differentiated equation of this problem; include this in the summary of answers.

Q: Find the sum of the convergent series. n = 0

A:

Q: For the following functions, find: 1. the critical values of the first derivative 2. the intervals w...

A: Given information:- g(x) =x2+3x+8  To find:- 1. the critical values of the first derivative 2. the i...

Q: x+6 7)

A: Given problem:- (x+6)/(x-1) >0 Solve the given inequality

Q: For each differential equation in Problems 1–21, find the general solution by finding the homogeneou...

A:

Q: b b-a b-a Use the equation f(x)dx= lim 2 fa+k- to evaluate the following definite integral. n→0 k = ...

A: Given query is to find value of the integral.

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx - (...

Q: Use the Divergence Theorem to evaluate the following integral and find the outward flux of F through...

A:

Q: (3) Find a degree-4 polynomial that has integer coefficients and zeros v3 and 2i (A) P(x) = (x² – 3)...

A: We are asked to find the polynomial

Q: r.(t) = (0.5, 14.5, 0.5) + t (1,3, 3) r_(t) = (-6, 11, –1) +t (-2, 2,3) %3D Find the point of inters...

A: Given problem:-

Q: Let the function f be defined by tan(x) - 1 f(x) = sec(x) (a) Use the Quotient Rule to differentiate...

A:

Q: 1. lim In (x –9) 2. lim log, (8x-x*) x3* x-2" 3. lim In (cos x) 4. lim In (sin x)

A:

Q: 9) In a local art museum, a moving spotlight projects geometric figures on the wall in front of it. ...

A:

Q: 6. DETAILS BERRAPCALC7 3.6.025. 0/2 Submissions Used For the equation, find dy/dx evaluated at the g...

A: We will find the implicit differentiation at a point. 

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given point...

A:

Q: Area of Surface of Revolution Find the area of the surface of revolution generated when the given c...

A: Surface of revolution

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis. (R...

A:

Q: Determine the vertical asymptote(s) of the graph of the function. x+9 4) f(x) = 7x + 9x - 10

A: We have to find out vertical asymptote

Q: Calculate the directional derivative of g(x, y, z) = z² – xy + 3y in the direction v = (1,–4,5) at t...

A:

Q: x" +x +1 = 0 Homogeneous O Not homogeneous

A:

Q: Determine the particular solution. 4y" – 2y' – 2y = 0; v(0) = 2, v'(0) = 1 Oy- 2ew2 3 Oy- dew2) Oy- ...

A:

Q: 3x=3y in polar form

A:

Q: Approximate cos(91∘) by using a linear approximation of f(x)=cos(x) at x=π2. Give your answer round...

A:

Q: Evaluate the following integral using partial fractions: 2x2 +1 dx J(x – 1)(x – 2)(x – 3) -

A: Given: I=∫2x2+1x-1x-2x-3dx   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx ; where a is cons...

Q: If y? In(x) = 5, find dy/dx. dy dx

A: This question is based on differentiation with respect to x.

Q: Evaluate the following integral where S is the closed surface bounded by the graphs of x = 2, z = 9 ...

A:

Q: If xy² – y3 = 5, find y'. y' =

A:

Q: A population grows according to an exponential growth model. The initial population is P0=4P0=4, and...

A:

Q: n one of the warehouses of a construction firm, cement is being released from an elevated storage bi...

A: Volume of cone=13πr2hRatio of diameter and height is 1:1Dh=11h=DVolume of cone=13πD22DV=112πD3 ...(1...

Q: OA rectangular field is enclosed by on Four sides by a fence. Fencing costs foot för two opposite si...

A:

Q: Let h(x, y) = , x = 41|12, y = 517t2. Use the Chain Rule to calculate the partial derivative. (Use s...

A:

Q: P = xi + yj +zk Q = x²i -z²k R = xy²j – yzk PROVE THAT (QX R) *(dot) P = R *(dot) (P X Q)

A:

Q: Evaluate the following integral using partial fractions: x - 1 dx x3 + 2x2 – x- 2

A:

Q: 1 -dx 2 xV 64 + 9x°

A:

Q: For each of the following functions, find the indicated derivative using the definition. f(x) : 1+ s...

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

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. ye2xdx = (4 + e2x)dy

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

A: To find out the parametric equation and symmetric equation of the line. 

Q: The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is 25 yd long b...

A: It is given that,   1 yard = 3 feet Length = 25 yd = 75 ft Width = 14 yd =42 ft Depth = 5 yd = 15 ft...

Q: Please illustrate the difference between a function being continuous and differentiable by presentin...

A: We have to  illustrate the difference between a function being continuous and differentiable functio...

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.  (1−x)y′= ?2

A: (1 - x)y' = 2 y' = 2/(1 - x) dy/dx = [2/(1 - x)] dy = [2/(1 - x)] dx Integrating : y = 2 ln(1 - x) +...

Q: х4—х2+1 - [3] S [3] s e*ve*-1dx еx+3

A:

Q: Find the equation of the circle, in general form, that is tangent to the line X=−6 andX=10, and pas...

A:

Q: In a circle, a central angle of 2.5 radians intercepts an arc of 15 inches. Find the number of inche...

A: Given:   Angle ( θ ) = 2.5 radians     Arc length (S) = 15 inches  

Q: If. the.work.required to stretch a spring 3 ft beyond its natural length is 9 ft-lb, how much work i...

A: We have the relation,   Work = ∫abfdx Where f is the force and dx is the distance. According to Hook...

Q: You are given the parametric equations a = 10 – t2, y = t – 12t. (a) List all of the points (x, y) w...

A:

Q: Evaluate the integral using the following values. 4 4 4 | x³ dx = 60, х dx 3D 6, dx = 2 2

A: As per bartleby guidelines we can do first 3 subparts

Q: Gravel is being dumped from a conveyor belt at a rate of 40 ft/min, and its coarseness is such that ...

A:

Q: 4ln? (x) dx

A: I have stated the used formulas in the solution

Q: This question has two parts. You may open the second part after you submit correct answers to the fi...

A: Given query is to apply ratio test.  

Q: Use linear approximation to estimate the following quantity. Choose a value of a to produce a small ...

A:

Q: Two variable quantities A and B are found to be related by the equation given below. What is the rat...

A: