1. Sand is pouring from a hole at the rate of 25 cu ft/s and is forming a conical pile on the ground. If the conical formation has an altitude always ¼ of the diameter of the base, how fast is the altitude increasing when the conical pile is 5 feet high.

Q: Evaluate the limit. Leave results in exact form. V9 + 7r2 lim 11 + 3x

A: This question is based on limits of inf/inf form.

Q: Evaluate the following limits. If needed, enter INF for o and MINF for -0. (a) It – 9 lim t²+5t +5…

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Q: Determine whether Rolle's theorem applies to the function shown below on the given interval. If so,…

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Q: Entertainment In a survey of 100 Enormous State University students, 22 enjoyed classical music, 20…

A: In a survey of 100 Enormous State University students, 22 enjoyed classical music, 20 enjoyed rock…

Q: Find the first partial derivatives of the function. f(x, y) = (e* + e)3 f, = fy =

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Q: Answer 1 only. Upvote if it is typewritten.

A: We have to find the integral

Q: Find the limit. 6x +2 lim 13x 9 > Next Question

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Q: Find the Solution (1+12) ds + 2t[st² – 3(1+12) 2]dt = 0; when t = 0, s = 2. %3D

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Q: Solve the Indefinite Integral. S sin Vædz

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Q: 2 1. Given: h (t) = : ; Find h'(t). On (t) = 8t° (1+t²) (1²+2)³ 8° (t² –1) (1²+2)° ON (t)* O (t)…

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Q: i an arithmetic series is 38. irst 40 terms of the series is 1250. the common difference of this…

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Q: (a) log2 r = 3 I+2 (b) 8. = 4* %3D (c) 5 = 7+1 %3D

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

Q: Sx² e**dx 1.

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Q: Consider the following curve. f(x) = Vx2 + 2x - x Determine the domain of the curve. (Enter your…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

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Q: PROBLEM SET NO. 3 Using the techniques of integration, evaluate the following integrals by applying…

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A: We need to find population model and solve.

Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: Suppose H (x) = V4x-8. Find two functions fand g such that (fog)(x) = H (x). Neither function can be…

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Q: 3.x1 + 2x2 6.x1 + 2x2

A: Solution: The equation can be written in matrix form

Q: Find the absolute maximum and minimum values of each function, if they exist, over the indicated…

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Q: Find the points on the ellipse x+3y =1 where f(x.y) = xy has its extreme values. The points are…

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Q: Follow the solution in the picture below and show checking.  348610  B2 B8 B16

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Q: dx 4. S x²+4x+13

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Q: Compute the following limit. If the limit goes to ∞ or -o enter INFINITY or -INFINITY, respectively.…

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Q: Find the arc length of the parametric curve. x = e', y = e, z = /2t; 0<t<7 L=

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Q: Which of the following surfaces cannot be described by setting a spherical variable equal to a…

A: Here, note that the cartesian to spherical coordinates conversion is given by: x=ρsin ϕcos θy=ρsin…

Q: 4x 20. Write log2 assthe sum and/or difference of ² - 3x - 18 logarithms. Express powers as factors.

A: The given logarthim expression,       log24x3x2-3x-18

Q: (1 point) Find a vector orthogonal to both (-5, –2, 0) and to (0, -2, 5) of the form (1,

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Q: Biologists stocked a lake with 240 fish and estimated the carrying capacity (the maximal population…

A: Given: Biologists stocked a lake with 240 fish. The carrying capacity (the maximal population for…

Q: 1.82 Let E CR be any unbounded set. Find an open cover of E that has no finite subcover. Prove that…

A: We will proceed as follows

Q: Calculate v X w: v = (0, 6, 6), = (8, 7, 3) W

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Q: Find PH)

A: inverse laplace transform of  1s2+s

Q: If your car gets 27 miles per gallon, how much does it cost to drive 440 miles when gasoline costs…

A: Total distance divided by distance per gallon gives the number of gallons required

Q: Apply the Direct Comparison Test to determine whether converg Vn3 + 1 n=2 erges.

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Q: Follow the format of solution of the picture below and show checking.  348610 B2 B8 B16

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Q: 3. S: (х2+2)2 dx

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Q: An open box is to be made from a square piece of cardboard measuring 15 inches on a side by cutting…

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Q: x =r' +1, y =r -t = t a) Find dy/dx

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Q: Evaluate the triple integral. y dv, where E = {(x, y, z) | 0 s x s 9,0 s ys x, x - y szsx + y}

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Q: Find a b if Ja = 8, |b| = 9, and the angle between and b is radians.

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Q: For a certain automobile, M(x) = - .015x + 1.49x - 7.9, 30 sx s 60, represents the miles per gallon…

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Q: A manufacturer of hospital supplies has a uniform annual demand for 500,000 boxes of bandages. It…

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Q: Find the first partial derivatives of the function. x9 - y5 f(x, y) = x + y fy =

A: The objective is to find the partial derivatives of the function.

Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

Q: The Pacific halibut fishery has been modeled by the differential equation dy dt where y(t) is the…

A: dydx =ky1-yM⇒y' =0.72y1-y9· 107⇒y=-90000000e0.72t+c11-e0.72t+c1