Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 6 cubic feet per minute. If the pool has radius 7 feet and height 7 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 3 feet? (Include help (units) with your answer.)

Q: A spherical snowball is melting. If its volume is decreasing by 450 cubic centimeters per hour when…

A:

Q: y₁ y=9x ∞013 8 y = X =3x y=52-x X

A: To find the area of the shaded region in the following figure.

Q: a. f(x) = x³ tan x + 9x-4 b. f(x) = cos x 5 18-secx iniog srt 16 S+x8-x=xvius srit of enil Inggrist…

A: (a)  f(x)=x3tanx+9x-4formula used (i) d dx(xn)=nxn-1(ii) d dx(tanx)=sec2x(iii)  d…

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A:

Q: 2 2 Find the volume V of the solid below the paraboloid z=4-x-y and above the following region. T…

A:

Q: Find the absolute maximum and minimum y-values of f(x) = 6x on the interval [-6, 3], as well as the…

A: Application of derivatives.

Q: QUESTION 6 Determine if the given function y = f(x) is a solution of the accompanying differential…

A:

Q: (a) Find the derivative, din (tan(t) - arctan(t)) de. In

A:

Q: 16. If f is even, then f' is even. 17. If f is periodic, then f' is periodic.

A: If f is even, then f' is even.

Q: √ √ √³x - Use the Midpoint Rule with m = n = 2 to estimate the value for R= [0,8] × [0, 2] 3x + 4ydA…

A: We have to use the mid point rule to find the value of integral.

Q: = 1. *Estimate* the area under the curve of f(x) = 3x + x² from z = 0 to z and left endpoints. 6…

A: We have to estimate the area of f(x) using left endpoints which is also called Left Reimann sum.

Q: Write an equation for the 4th degree polynomial graphed below. Use k if your leading coefficient is…

A:

Q: 5) Let the position vector of a moving particle be: r(t) = t'i-2tj+(2+2t)k, where t is in seconds.…

A:

Q: b.) lim z-3 r²-2r-3 2-3

A: K=limx→3(x2-2x-3x-3)(i)∂ ∂x(xn)=nxn-1(ii) ∂ ∂x(constnat)=0

Q: MV -1 -2 -3- (a) List all intervals where fis increasing and decreasing. (Enter your answers using…

A: Function is increasing in the interval where value of derivative graph positive and Function is…

Q: The area of an ellipse is given by A = πa-b. Suppose the lengths a and b are changing with time. (a)…

A:

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n) = k = 1…

A:

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Given that, the function is   g(x) = 8 sinx ,   [0, π] , 6 rectangles i.e.  n =6. △x = b-an = π-06 =…

Q: Suppose f is a differentiable function, where the values of f and f' are given in the table below to…

A:

Q: Find the x-intercept, y-intercept and z-intercept of the plane: [x, y, z]= [5, 4, 3] + s[1, 0, 1] +…

A:

Q: The curves sr₁(t) = (t, t², - t5) and 72(t) = (sin( - 2t), sin(-3t), t-T) intersect at the origin.

A: By the answering guidelines of Bartleby, We can answer only first question from multiple questions,…

Q: A small company produces two products, I and II, at three facilities, A, B, and C. It has orders for…

A: Orders of product I = 1800 Orders of Product II = 1400 Let the number of weeks taken by facility A =…

Q: Write the first expression in terms of the second if the terminal point determined by t is in the…

A: First function = sint second function = tant Formula used sin2t + cos2t = 1

Q: Suppose that f(x, y): = ♫ D and the region D is given by {(x, y) | 2 ≤ x ≤4,3≤ y ≤6}.

A: f( x , y ) = xy2 ≤ x  ≤ 43 ≤  y  ≤ 6

Q: the demand function q = D(p) = 424 -p, find the following. For a) The elasticity b) The elasticity…

A: demand function q=424-p, we need to find the elasticity.

Q: 64. x-2" In the following exercises, use the graph of the function y = g(x) shown here to find the…

A:

Q: Bank A is lending money at 5.5% interest compounded monthly. The rate at Bank B is 5.55% compounded…

A:

Q: Evaluate the following integral. 1/4 SS S 000 3 48p sin do de dp

A:

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

A:

Q: a. 2f(x), x=2 b. f(x) + g(x), x= 3 c. f(x) g(x), x=3 3 3

A:

Q: B. Let f(x) be an odd, differentiable function. This means that f(x)= -f(-x) We know that f'(x)= O…

A: Let f(x) be an odd, differentiable function this means that f(−x)=-f(x)

Q: In the following exercises, use the graph of the function y = f(x) shown here to find the values, if…

A: A graph of function y = f(x) is given  By which Find the limx-> 0- f(x)  and limx-> 2 f(x)

Q: Find the minimum distance from the point to the sun (-2,-2, 0) 2y. (Hint: to simply the…

A:

Q: 27, 28, 29, and 30 Compare the values of Ay and dy if a changes from 1 to 1.05. What if a changes…

A:

Q: (b) A 1 m length of wire is to be cut into two pieces. The first piece will be bent to form a…

A: Length of the wire = 1 m The wire cut into two pieces such that The first piece will be bent to form…

Q: In economics, the most economical quantity Q of goods (TVs, dresses, gallons of paint, etc.) for a…

A:

Q: Top, Bottom, Right, Intervals is incorrect

A: The region D is given as ,

Q: 27, 28, 29, and 30 Compare the values of Ay and dy if a changes from 1 to 1.05. What if a changes…

A:

Q: y = (2y^4 + 2x)y' How can I solve it?

A:

Q: Each of the graphs below is of a polynomial. The windows are large enough to show end behavior. (I)…

A: The minimum possible degree of the polynomialWhich polynomial has a positive leading coefficient?

Q: Find the area of the shaded region bounded by the x-axis and one arch of the cycloid given below. dx…

A:

Q: Let f(x) = x2 − 7x. Give the equation of the tangent line at x = 3.

A:

Q: Find the area of the region. x = 3 sin(0) y = 2 cos(0) -75057025 <

A: given  curve is :-x = 3sin(θ)and     y = 2 cos(θ)and   -π2≤θ≤π2then we have  to find area of the…

Q: π Find the average value of the function f(p, $, 0) = psin over the solid upper ball p≤2, 0≤ ≤ 2.…

A:

Q: Solve the following equations in the interval [0, 2*]. Note: Give the answer as a multiple of x. Do…

A:

Q: For the following demand function, find a. E, and b. the values of q (if any) at which total revenue…

A:

Q: Find the derivative of y with respect to x. dy dx y = 6 In 11 5 X

A:

Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: For a given function f( x )  First find critical points by f'( x ) = 0  for relative maxima → f''( x…

Q: Suppose the total income in dollars from a machine is given by the following. I = 10e0.5t, 0sts 6,…

A:

Q: Use the intermediate value theorem to show that f(x) = 2x7 +6x3+1 has a root in the interval [-1,1]

A: