Write a mathematical model for each of the following statements. Use k as the constant of variation. a varies jointly as d and inversely as g. ▶ gd kd O a= ka kg Oa=kgd

Q: A ball of radius 10 has a round hole of radius 7 drilled through its center. Find the volume of the…

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Q: Draw the spin field F = - 3y √x² + y² -i+ 3x j along with its horizontal and vertical components at…

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Q: Show that the particular solution of dy x=y; y(2)=4 is y = 2x. 1 Add File

A: I am attaching an image so that you understand each and every step.

Q: For quality control purposes, a local toy company inspects two yo-yo’s out of every shipment…

A: For quality control purposes, a local toy company inspects two yo-yo’s out of everyshipment…

Q: Find f(g(x)) and g(f(x)). f(x) = x-3 and g(x) = 4x - 12 f(g(x)) = [?]x+ [] g(f(x)) = x+[] Enter

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: For the function g whose graph is given, state the following. 0 2 AM

A: from the graph we need to find the limits

Q: Suppose that f(x, y) = ²/3 on the domain D = {(z,y) |0 ≤ y ≤ 1,0 ≤ z ≤y³}. D Then the double…

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Q: Find a linear approximation of the function f(x) = 1 x at a = 0.

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Q: Approximate the area under the graph of F(x)=0.5x³ +5x²-0.5x -5 over the interval [-7, -2] using 5…

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Q: 17 /58° X 30 Q (Round the answer to the nearest hundredth.) The length of side is

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Q: The proportion of students in a psychology experiment who could remember an eight-digit number…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: Equation of parabola  y = 7 - x2  Find the dimension of the rectangle of largest area that has its…

Q: find the domain of the function -identify any symmetries - find the first and second -identify any…

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Q: A box with a square base and open top is to have a volume of 147000 cubic inches. The material for…

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Q: Use f(x) = 4x¹/2 to evaluate the following definite integrals. [^ F(X) f(x) dx = [ (a) 4 (b) fa (f…

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Q: f f(x) = ex − 1, 0 ≤ x ≤ 2, find the Riemann sum with n = 4 correct to six decimal places,…

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Q: If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air…

A: We have given function of speed and we have to find the limit.

Q: Rolle's Theorem on the

A: Given that fx=cos2x   The three conditions for Rolle's Theorem to hold on the interval a,b are: 1.…

Q: a) Find the equation of the tangent plane to z = f (x, y) = 3x² + 2y² +5 at the point (1,1,10). b)…

A: Here we will define equation and using formula

Q: Find the second and the third components of a vector n normal to the plane with the equation 6x + 6y…

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Q: Find all angles ? between 0° and 180° satisfying the given equation. Round your answer to one…

A: sin(Θ)=19 Find the angle Θ between 0∘ and 180∘ satisfying the given equation.

Q: e. (use the Limit Comparison test): ∞ 1 लोग n1/2 n=2 - 1

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Q: For the function f whose graph is given, state the following -1 x

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Q: 2. the line x = 3. Non-Calculator: Let R be the region in the first quadrant bounded by the graph of…

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Q: Convert the point (x, y, z) = ( − 3, 4, 3) to cylindrical coordinates. Give answers as positive…

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Q: Let ƒ(x) = = 1 (x³ - 2x+6)³ 5 Find f'(x).

A: Let fx=1x5-2x+65, then to find f'x.

Q: Find an equation in spherical coordinates for the rectangular equation ² + y² + 2² − 4z = 0 Do not…

A: Given equation in rectangular coordinates x2 + y2 + z2 - 4z = 0

Q: Total expenditures in a country (in billions of dollars) are increasing at a rate of f(x) = 9.28x +…

A: Tootal expenditures in a country (in billions of dollars) are increasing at a rate of f(x) = 9.28x +…

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint .05 cm thick to a…

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Q: Suppose f(x, y) = xy-ax-by. (A) How many local minimum points does f have in R²? (The answer is an…

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Q: S dx= In |5x + 8 + C, x# 5 5x+8 -85 The definition of an antiderivative can be used to verify the…

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Q: Consider z² + xyz + y² = x² + 6z + 24, where = f(x,y). a) Using the Implicit Function Theorem (not…

A: Using partial differentiation

Q: (a) Find a function f that has y = 4 - 3x as a tangent line and whose derivative is equal to · ƒ'(x)…

A: Function f has tangent line equation is y=4-3x and its derivative f'x=x2+4x+1 Note:- As per the…

Q: III. Find the values of the constants a and b that make the function f continuous on (-∞, +∞ ). [3x…

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Q: Find the linearization L(x) of y = (81 + 4x²)-¹/² at a = 0. L(x) =

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Q: x² Graph the function y = by identifying the domain and any symmetries, finding the derivatives y'…

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Q: 1 Use the transformation u = 3x + y, v = x + 3y to evaluate the given integral for the region R…

A: Here  u = 3x+y ; v= x+3y and lines are  y= -3x+1 ; y= -3x+2 ; y= -(1/3)x ; y = -(1/3)x +3.

Q: The velocity of an object (in km per minute) t minutes after it begins moving along the positive…

A: We need to solve integral problem and interpret it.

Q: The equation for the standard normal (bell) curve is f a. Find the 3rd derivative. b. Use the 3rd…

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Q: Consider the polar curve r = 20 + cos(0) for 0≤ 0≤ 2л. (a) Find the area in the second quadrant…

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Q: Use f(t) = (t =7) to answer the questions below. t (a) In order to find the general antiderivative…

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Q: Find the indefinite integral [7x (3-x¯6) dx. 7x x (3-x¯6) dx =

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Q: (c) In terms of m and n (with 1 ≤ m <n), find a formula for: Σi². i=m

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Q: Evaluate the integral. 1 3л 3л SS S y cos zdx dy dz 000

A: Integration

Q: Find the limit. lim √√b(b-7) b→-∞

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Q: Let G be a function whose derivative is shown below. Assume the domains of G and G'are 0 ≤ x ≤ 12. 8…

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Q: Suppose you are given the derivative of some function p(t) as p '(t) = t.cos(10t) (a) Find the exact…

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Q: Approximate the area under the graph of f(x)=0.04x4 -2.89x² +94 over the interval [5,9] by dividing…

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Q: Graph the function y=x² - 6x² = x²(x²-6) by identifying the domain and any symmetries, finding the…

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Q: Use the function g(x) = k² - x² to answer the questions below. Remember to give exact answers. (a)…

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