Determine the centroid of the first-quadrant region bounded by the parabola y = 4 – x²

Q: An object moves along a line, where its velocity function is as described by the graph below. What…

A: answer is in next step

Q: Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the…

A: Write an iterated triple integral in the order dz dy dx for the volume of the region in the first…

Q: Evaluate the integral. 4 (5 - t)Vt dt

A: The objective of the question is evaluate the definite integral.

Q: 22-1+9 22+5x2-3z

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Q: 4. Evaluate •5 (4 – 2.x) dx - 2,

A: topic - definite integral

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: We have to integrate the function to calculate volume

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = -x2 -…

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c - C 3 은(1-x) 2+C

A: We have to solve above question and find integral

Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

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Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

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Q: Adjust the domain of the rectangular equation, if necessary. y = x^2-7

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Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: x³dx is equivalent to Using trigonometric substitution, Vx² –4 A 6/ tan*0 seco do B) None © 8 sec0…

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Q: S- 3 dy 3y - sin n -1 4-9y2 3 A True B False

A: We have to find out

Q: Determine the vector field of F. F(x, y) yi-xj

A: see below the answer and explanation

Q: Find the general solution of y' =y sec x. A. y = C (secx+ tan x) B. y= C (sec x – tan x) C. y = C…

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Q: Describe the graph of the equation. r = 15 sin 18t i + 15 cos 18t j O It is an ellipse in the…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: (a) x = 0: dy/dt (b) x = 2: dy/dt (c) z = 3: dy/dt

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Q: Problem 3 Find a power series representation for the function and determine its radius of…

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Q: dx 2. x²/4-x² V4-x2

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Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

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Q: 1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the…

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Q: Verify the identity. csc 0- sin 0= cot 0 cos 0 To verify the identity, start with the more…

A: Solved below

Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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Q: A general solution of the differential equation - 3+4 = 0 is 1. A. y = c,e* +cze2x + c3xe²x B. y =…

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Q: Given the vector function ř(t) = (– 3t, 5t°, 2t° + 3) Find the velocity and acceleration vectors at…

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Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

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Q: Evaluate the line integral g. y² dx – x²dy, where Cis the positively oriented circle of radius 2…

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Q: Find V. (V × F) if F(x, y, z) = 7 sin xi + 2 cos(2x – 3y)j+ 6zk. V·(V × F)

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Q: [y sxy dy is equal to -y cony - J cony A (B у сoly - coty dy Scory dy C у coly + -y coty + J coty D…

A: Solution is given below..

Q: Describe the graph of the equation. r = 3 cos t i – 18 sin tj+ k O An ellipse in the plane z = 1,…

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Q: Find V. (V x F), if F(x, y, z) = 7e**i+ 8xej – 3elk.

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Q: To earn an A in a course, a boy must have a final average of at least 84%. On the first four…

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Q: y" + y = sec 0 tan 0

A: The given differential equation is  y''+y=sec(theta)tan(theta).

Q: L 32 da = 65 %3D Select one: O True O False A2Vadx = 104/3 Select one: O True O False S (+4)(a+3)da…

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Q: S(e3x-e 2x -e*)*dx

A: ∫e3x-e-2x-e-x4dx=∫…

Q: 3x. If sales are increasing ompany's revenue from selling a units of an item is given as R = he rate…

A: Given query is to find rate of change of revenue.

Q: 2e- 2 Consider the indefinite integral dz: (e- 27 + 3) This can be transformed into a basic integral…

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Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: 7. Sketch the region of integration, and evaluate the integral. 22л г JI * zdz d0 dr 0 л 0

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Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

A: The understanding of radioactive decay is required. The explanation part is given below.

Q: For the given cost function C(x) = 25600 + 500z + x², %3D First, find the average cost function. Use…

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Q: Find the magnitude of vector AB. 1. A = (4, -3) and B 2. A = (-2, 11) and B = (2, 8) = (-8, 2) %3D…

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Q: n2 1. Determine whether the series En=1 is convergent and explain why 2n++1 (In n)

A: We will use Ratio-Test to determine converge.

Q: ||r'(t) x r" (t)|| Use the formula k(t) to find k(t). r(t) = eti+e*j 42 est K(t) %3D (36 el2t +…

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Q: ..... .... .............. ............... The values y (in billions of dollars) of U.S. currency in…

A: topic- inequality

Q: d Calculate ri(t) · r2(t)] and d [ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Let f(x) = y = 4x² In(). Differentiate y = 4x2 In() with respect to x and simplify. + 4x2 )(()이) -A…

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