1. Given the graphs below: -14 The blue graph is r = √√3 sin and the red graph is r = cos 0. Use a double integral (or two double integrals) in polar coordinates to find the exact value of the area between both graphs.

Q: A cable hangs between two poles that are 70-ft apart. The two poles are both 40 foot high. Sag is…

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Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j +…

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Q: Find the average cost function if cost and revenue are given by C(x) = 164 +8.9x and R(x) = 3x…

A: Given;  C(x)=164+8.9x R(x)=3x-0.07x2.

Q: Identify the increasing and decreasing intervals for f(x) = x + 5 X-4'

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Q: Lateral surface area = Sc C: x² + y² = 64 from (8, 0) to (0,8) f(x, y) = x + y p f(x, y) ds (X, Y)…

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Q: Express e in the form a + ib. (Simplify your answer completely.) z = −7+3″ i 447

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Q: III) Let f, g, and h be the functions defined below: f(x) = 5* To (²²4) 1) Find h¹(r) and obtain the…

A: Given the function, hx=6-x2x-5 we have to find the inverse function of h and range of h

Q: Identify the vertical and horizontal asymptotes of f(x) = 2x+1 X-4 vertical: x = horizontal: y…

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Q: Use Lagrange Multipliers to find the maximum and minimum values of the function f(x,y)=x^2+y^2…

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Q: The graph of y = f(x) is shown below (dashed curve). Manipulate the green draggable points to obtain…

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Q: Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are…

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Q: Find the graph of the polynomial function f(x) = -x3.

A: we write a table for x=-3 to x=3 and calculate the values of f(x) for all these values and plot the…

Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: When demonstrating that lim suffices? 1 x-1 4x + 4 08= 0.0000025062656641604 OS=0.0000025 08=…

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Q: 4. Compute the total volume of the shaded area of the figure below where the cross-sections are…

A: We need to find volume.

Q: Compute the general term an of the series with the partial sum Sn = √n, n > =

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Q: Find the divergence and curl of the vector field F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz) at…

A: Here we have to find the divergence and curl of given vector field.

Q: If the revenue function for a particular commodity is R(p) = q(p) = Give a reason for your answer. R…

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Q: Select all invertible transformations from the list below: Shearing Translation Scaling Projection…

A: Projections are not invertible transformation except we projects onto an entire space.

Q: Use the Product Rule or Quotient Rule to find the derivative. f(z) = (3x-²+5) (-4x−³+4). ○ f'(z) =…

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Q: Which of the following functions is symmetric about the y-axis? A.f(x) = x4 - 4 B.f(x) = x5 - 4

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Q: L4Q15. In a display, there are 50 toys in the first row, 45 toys in the second row, and so on in an…

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Q: x³ + 8x² Consider the function f(x) = may be helpful to factor by grouping. 81x648 x + 8 O Answer…

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Q: V. Consider the power series +∞0 n=1 (x + 1)" +1 1. Determine whether the resulting series when x =…

A: We need to find convergence and radius of convergence.

Q: Consider the basis S = {V₁, V₂] for R2, where v₁ = (1, 1) and v₂ = (1, 0), and let T:R2 R2 be the…

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Q: An employee has two options for positions in a large corporation. One position pays $14.25 per hour…

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Q: Use the indicated change of variables to evaluate the double integral. JS4 4(x² + y²) da X = = 1/2…

A: Let's solve given double integration by changing variables.

Q: Recently, a certain bank offered a 10-year CD that earns 2.16% compounded continuously. Use the…

A: We have to find gross amount

Q: 2. Given a tetrahedron with vertices (0,0,0), (3, 0, 0), (0,6 0), and (0, 0, 4). Express the volume…

A: Given:- A tetrahedron with vertices (0,0,0), (3, 0, 0), (0,6 0), and (0, 0, 4).

Q: f(x) = 5* g(x) = log5 (²²= 4) Find (fog)(x) and obtain its domain. h(x): - 6 <- x 2x-5

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Q: Suppose f (x, y) = 25 −4x2−3y2. Calculate both fx(1, −1) and fy(1, −1). Sketch (by hand, or, better,…

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Q: Q3. Change the order of integration and evaluate * * dy dx.

A: To evaluate ∫04∫0xdy dx using the change of the order integration. From the limit of integration the…

Q: L4Q12. Write an explicit formula for the sequence: - 2, 2, 6, 10, ... A.an = - 2 + 4n B.an = - 6 +…

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Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

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Q: L1Q16.Which of the following could be the end behavior of f(x) = -x6 + 3x4 + 8x3 – 4x2 – 6?   f(x) →…

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Q: State the range of f(x): {y € Ry> 4 -3} {ye Ry - 4 3 {y € Ry#0} {y € Ry>0} } = 1 3x +4'

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Q: Determine L-1 (-1(1+81) S³ 1 (a) =—=t+2₁² (b)t+4t² (c) t+8t² 1 (c) t+8t²

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Q: Chelsea received a loan of $1,300 at 5.75% compounded quarterly. She had to make payments at the end…

A: We need to find payments.

Q: 8-x-1² if x 2 Calculate the following limits. Enter "DNE" if the limit does not exis f(x) Let f(x)…

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Q: 6. Revenue: Pacific Sunwear The annual revenue of Pacific Sunwear of California over the period…

A: Concept: Here the annual revenue is given by the expression p(t)=-0.075t+0.975+0.75 Where t is the…

Q: A crate is supported by two ropes. One rope makes an angle of 25° 30' with the horizontal and has a…

A: We will find the required.

Q: 10+200

A: Using sum rule

Q: Find the derivative of the function f(z) = √2 O None of these. 37 Of(z) = √2z f(2)=

A: We will find the derivative.

Q: Find f'(x) and find the value(s) of x where f'(x) = 0. f(x) = f'(x) = X x² +49

A: We need to find x values where f'(x)=0

Q: Suppose that f(x) is a continuous function on the interval [-1, 3] with f( − 1) = − 3 and f(3) = 3.…

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Q: y = 9x6 - 81x4 (Use symbolic notation and fractions where needed. Give your answers in the form of…

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Q: an = (1 + ² (1 + 2.6) "

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Q: The diameter of the base of a circular cylinder is 8 fteet and the elements are inclined to the base…

A: We have to find the volume of the cylinder.

Q: Case problem: a) A Cement company hires you to provide financial information to their Finance…

A: NOTE: Refresh your page if you can't see any equations. . the marginal cost function is  and the…