Use cylindrical coordinates. Evaluate 8x(x² + y²) dv, where E is the solid in the first octant that lies beneath the paraboloid z = 1 – x² - y².

Q: Use the following information on pH. Chemists define pH by the formula pH = -log10[H], where [H+] is…

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Q: $1850 is invested at 5.5% compounded continuously. How long will it take for the balance to reach…

A: P=$1850A=$3700r=5.5%=5.5100=0.055

Q: The total cost (in dollars) of producing x food processors is C(x) = 2200 + 70x-0 -0.2x². (A) Find…

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Q: Find the equation of the tangent plane to at the point (3, 0, 21), showing the work below. z = f(…

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Q: Evaluate the definite integral 2x c²+4 dr

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Q: Evaluate the following definite integral by using the method of integration by parts. So a x ln(x)…

A: Assume  1st function is ln(x) 2nd function is x  Then proceed using integration by parts  As I have…

Q: Which formula is not equivalent to the other two? (-1)k-3 k-3 6 (2) Σ k=4 Choose the correct answer…

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Q: open interval(s) B. The function f is increasing on the open interval(s) C. The function f is…

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Q: 3. The axes of two right circular cylinders of equal radius 36 cm intersect at right angles. Find…

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Q: What is the perimeter of the curve r = 4(1 4. sin q)?

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Q: Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. f(x)…

A: To find the degree, leading coefficients, and the maximum number of  real zeros of the following…

Q: A colony of bacteria grows at an exponential rate according to the function P(t) = 1350e0.06t,…

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Q: The reaction of the body to a dose of medicine can sometimes be represented by an equation of the…

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Q: Evaluate the indicated limit or explain why it does not exists:

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find the directional derivative of the function f(x, y) = x³-y³ at the point (4,3), in the direction…

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Q: For the following exercises, find f'(x) for each function. 107. f(x) = 5x³x+1 425 109. (x) = 8x4 +…

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Q: Determine all critical points for the function. f(x) = 45x³ – 3x5 A. x= -3 O B. x=0, x= -3, and x =…

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Q: A solid has an elliptical base with major axis 18 inches and a minor axis of 12 7. inches. Find the…

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Q: Solve the equation for 2: log30 + log30 (z - 1) = 1. If a solution doesnt work, enter DNE. Make sure…

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Q: Learning Target IAI: I can compute the area between two curves. 1. Set up the integral to find the…

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Q: Given f(x, y) = 3x²y + y3 - 3x² - 3y² + 12 (a) Determine the second-order partials: • fxx = • fyy =…

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Q: Find the vertical asymptotes of the function r(0) =tan(0-4) in the interval 0≤ 0 ≤ 2. Number of…

A: rθ=tanθ-4

Q: Suppose that the profit from the sale of Kisses and Kreams is given by P(x, y) = 10x + 7.4y0.001x² -…

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Q: Let r(t) Find =

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Q: 2=0. Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on…

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Q: Let r(t) = Find a parametric equation of the line tangent to r(t) at the point (- 46, 24, x(t) = 46…

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Q: 2. A street sign is being designed to meet local city requirements and specifications. The sign…

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Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: Consider the function f(x) = 10x + 6x + 7x + 20. For what value(s) of x a. Find the turning points…

A: f(x) = 10 x3 + 6 x2 + 7 x + 20

Q: Draw a picture of the following vectors, then calculate them algebraically. Make sure you label the…

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Q: Find derivartive of y = 1/x

A: Recall the formula: ddxxn=nxn-1

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Find the critical points and determine if the function is increasing or decreasing on the given…

A: For critical points then the first derivative is equal to zero

Q: Find all possible functions with the given derivative. y' = 2x² - 6x 2 O A. 3x³ + C 2 O B. 3x³-3x² +…

A: Given,             y' = 2x2 - 6x

Q: . The concentration C(t) of a salt solution is given by the formula to the right, where t is…

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Q: The Pear company sells pPhones. The cost to manufacture a pPhones is C(x) = -21x² +63000x +21714…

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Q: find derivative of y = √√x x¹/2 Onone of the above (1/2)x 1/2 O

A: The solution is shown in step-2

Q: 4. Describe the long run behavior of f(t) = -5t6-2t4+3t³+2 As t-∞, f(t)→? As too, f(t) → ? ✓

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Q: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where…

A: Spherical Coordinates

Q: For each of the following integrals find an appropriate trigonometric substitution of the form =…

A: For each of the following integrals to find an appropriate trigonometric substitution  of the form…

Q: Find the curvature of the curve r(t) = (2 cos(3t), 2 sin(3t), 4t) at the point t = 0 Give your…

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Q: Solve the initial value problem. 0- +y=7 sin 0,0>0, y dy ᏧᎾ 元 (7)=₁ 1 2

A: θdydθ+y=7sinθ

Q: Use the graph shown below to answer the questions. (a) Amplitude = (b) Period= y 10- 4 8 (c) Write…

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Q: 2. Use the method of Substitution to find the following indefinite integrals a) √3x√√x² +9 dx e) f…

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

Q: Evaluate the iterated integral. √64 - y² ST 0 10 (x + y) dx dy

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Q: Calculate M6 for f(x) = 7 · ln(x²) over [1,2]. M6 =

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Q: Find the absolute maximum and minimum values of f (x, y) = x + y − xy on the set D. D is the closed…

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Q: . Find the value of a so that the following function has a point of inflection at x=6 f(x) = ax³ -…

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Q: A particle is moving as given by the data below: s(t) = 0 v(t) = 5 sin(t) - 4 cos(t); s(0) = 0

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Q: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where…

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