What is the y=x^2 - 4 and O 1/4 O 1/2 01 03/2 Ο ΝΑ x-coordinate of the centroid of the plane region bounded by y = 2x - x^2 ? 12

Q: If tant=−3/4 and π/2 <t< π, find sin, cost, sect, csct, cott.   Enter the exact answers.   sint=…

A: We have to find value

Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: Find the directional derivative of the function f(x, y) = √√√x + 2y at the point (2, 1) in the…

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Q: (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a…

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Q: Evaluate fx² cosh x dx

A: To evaluate the integral.

Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

Q: Test for convergence / divergence. Find the limit if result is convergence.

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines

Q: 1. Use Comparison Test to determine the converges or diverges of the series Σ: 8 n=1 (n+1)√n

A: By using Comparison Test to determine the convergence or divergence of the series ∑n=1∞ 1n+1n.

Q: 3. You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

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Q: 5. Evaluate lim x→2 x² - 16 X x-2

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Q: Find T,N and k for the curve:

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Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Let x and y be the dimensions of the rectangular field. According to given , Area(A)= xy= 4000…

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: Q2: find the Laplace of the following functions: a- f(x) = (cosw, for 0<t< (o for,=<t<² 0

A: If ft is a periodic function with period T, then        Lft=11-e-sT∫0Tft e-sT dt So,…

Q: . A family wants to build a fence in their backyard for their dogs, but the cost for the previous…

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Q: Compute the effective rate of interest corresponding to a nominal rate of 4.8% compounded…

A: We need to use effective interest formula.

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

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Q: Evaluate the following integrals. Show the solution. 1. fcsc² (7x + 5) dx 2. x² sec (4x³ +9) dx dx…

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Q: of convergence of too0 n 3"x" na n Find the interval the power series

A: Given problem:-

Q: Solve the following matrix equation for a, b, c, and d. a-b b + c |-|8 8 3 88 3d+c 2a - 4d a = b =…

A: We will find the value of a ,b ,c ,d by solving the given matrix equation in the following step.

Q: ƒ sin (3x³) dx

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Q: Determine the x - y coordinates of the points where the parametric equation x = 5 sin²t y = 2 cost 0…

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Q: Your farm encompasses 900 acres, and you are planning to grow soybeans, corn, and wheat in the…

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Q: Find the line integral of F= 2√zi-4xj + 3√√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: For the function f(x,y) = √y² + 5x², find f(2, - 5), f(− 1,2), f( – 3, – 5), and f(0,9). f(2,-5)=…

A: Given query is to find the value of the function at indicated points

Q: 1-) x ² ( xdx tydy) = (x² + y²) dx ; x =1 when y=2

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Q: solve by the method of undetermined coefficients. b.) y''+4y=5sin(4x)

A: We need to find D.E.

Q: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

Q: (b) lim *+1 √√2x+6-2 x²-1

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Q: y''-5y=sinx

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Q: 3. Find f'(a) if f(x)= e7x 2x + sin³ x

A: In this question, we want to differentiate the given function f(x) with respect to x.

Q: Partial Sums An arithmetic sequence has a first term of -1 and a common difference of -17. If S₁,…

A: We have to find the sum

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Using derivative

Q: Using the Law of Sines to find a triangle with one obtuse angle if ZA = 50°, a= 23, b = 25. If no…

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Q: You deposit $2000 in an account with 3% annual compound interest. Complete the following, assuming…

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Q: Life expectancy in the United States has been rising since the nineteenth century. The table shows…

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Q: Question 138 of 190 FINAL-Mathematics Temperatures in degrees Celsius (C) may be changed to degrees…

A: A detailed solution is given below.

Q: Find the present value of a continuous stream of income over 4 years when the rate of income is…

A: I have appended the formula used in the solution part of the question.

Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

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Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

Q: Given Cost and Price (demand) functions C(q) = 120q+40000 and p(q) = -2.2q +800, what is the…

A: Given functions cost c(q)=120q+40000                             price p(q)=-2.2q+800…

Q: (a) Find the dimensions of a box with a square base with volume 125 and the minimal surface area.…

A: According to our guidelines, In case of multiple questions, we are supposed to answer the first…

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

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Q: A bacteria culture initially contains 1000 bacteria and is growing at the rate of N' (t) = 2tt-2/3…

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Q: - 6 = ₁6 -X

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Q: Evaluate 2y"+3y'-2y-te-2t ,y(0)=0, y'(0)=-2

A: answer is in next step. please give a like !!

Q: The height of the ball when its velocity is 0 ft/sec. is feet.

A: First, we will find the velocity of the ball at t second. Then we will find the value of t for which…

Q: Given v (2, -9) and w = (7,-8), what is 2w - vv

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