The radius of a right circular cone is increasing at the rate of 6cm/sec while  its altitude is decreasing at 3cm/sec. Find the rate of change of its volume  when its radius is 8cm and its altitude is 20cm.  Show detailed solution. (Draw the illustration of the given problem)

Q: Q2: Solve the following int (1) dx 1 (x+3)(x+7)

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

Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: Write the polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial…

A:

Q: 3. Find the Laplace transformation of the function: f(t) = cos (2wt) cos (3wt). Hint: write cos(20t)…

A:

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: Given that 2 ≤ f(x) ≤ 4 for 4 ≤ x ≤ 5, estimate the value of 5 0³/ [ f(x)dx 5 [²₁ <5 f(x)dx

A: Given 2≤f(x)≤44≤x≤5To find range of∫45f(x)dx

Q: There were approximately 2.69 million deaths in the United States in 2015 express this quantity in…

A: It is given that, in 2015, there were approximately 2.69 million deaths in the United States.

Q: 38.Calculate the surface area of the surface obtained by revolving the curve y = √9-x² around the…

A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

Q: STJ (x (x + sin x) dx Jo

A:

Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

A:

Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

A:

Q: (B): Find the tangent equation to the curve y = sin²x at point x =

A:

Q: 12. x² sin(x + y) = 1, -

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

A:

Q: (a) Find S 1+ (x + 2)² dx and 1+ (x + 2)² dx.

A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

Q: Find the length of the following three-dimensional curv r(t) = (9+5t,3-2t,-1+2t), for 1sts6

A: To find the length of the given three dimensional curve.

Q: A circular swimming pool has a diameter of 16 ft, the sides are 6 ft high, and the depth of the…

A:

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞((√x^2+2x) −x) You…

A: Given :limx→∞x2+2x-x

Q: Exercise (b) the centroid of the region bounded by the graphs of the equations Step 1 The region is…

A: Please see the answer below.

Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

A:

Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

A:

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A:

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: 28. For each of the following equations, find the most general function N(x, y) so that the equation…

A:

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

A:

Q: ddw? dt (C): If w = tan x and x = 4t³ + t ; Find

A:

Q: The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = π. dA = ( A =…

A: Here is your solution

Q: The volume of the solid obtained by rotating the region enclosed by y = 1/x³, y = 0, x = 3, x = 4…

A:

Q: Q5: Find dx for the following functions: (1) xcinh 2x coch 2x (3) y = e* sin² x In√x

A:

Q: Let f(x) = 6x√√x + f'(x) = -∞0 8

A:

Q: 15,0-20³²4 2. 3. चं 5. T cos 2x dx sin(³) cos²( :-) / dx 2x - 1 4x dx dx 6. 7. [² (x² + 0²³) dx (x -…

A:

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: -9 (x-1) 8. √x dx

A:

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A:

Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

A:

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

A:

Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

A:

Q: 4. C(x-xxx

A: 4. ∫-342x5-3x4+4x3dx Note:    Multiple questions are given, we are answer only one question. If you…

Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 4xy +…

A:

Q: 11. According to the College Board, the average in-state tuition and fees for public 4-year colleges…

A:

Q: The following function is positive and negative on the given interval. f(x) = 8 - 2x²; [0,4] a.…

A:

Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ce as…

A:

Q: 1. (1) E (14) (1) Choose the correct option (Multiple Choice Questions): Which of the following is a…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: (B): Find the tangent equation to the curve y = sin² x at point x = T-3 π .

A:

Q: sin 8 cose √cos²0-9 c. f S do

A: Since, we have been asked to solve Part-C in which we have to evaluate the integral given…

Q: Consider the position function below. r(t) = (1-1²,3-5t4) for t≥ 0 a. Find the velocity and the…

A: Given;  r(t)=&lt;1-t2,3-5t4).

Q: k [[ x=0&y=0 x cos(xy) dydx =

A:

Q: dw (C): If w = tan x and x = 4t³ + t ; Find dt

A:

Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative