Find the centroid of the region bounded by the graphs of the functions y = 5x², y = x² + 6 The centroid is at (x, y) where

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 768 on the interval [-20, -10]. Find the H plute extrema for the function on the given interval.…

A: * As per policy only first question is answered. Please refer to the image below

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Q: 1. A) Express 0 1 4 1+x dx as a power series.

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Q: Find the limit. lim (x,y) → (1,−4) 3x²y 2 1+xy²

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

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Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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Q: 8. Consider the differential equation e* (y - x) dx + (1 + e*) dy = 0. (a) Show that this is an…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

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Q: Let y = sin (5x). If Ax= Ay~ = error = Find the percentage error - Question Help: Video Submit…

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Q: Find a unit vector u in the direction opposite of v = (2,8,-3).

A: Solution ) v =  { 2 , 8 , -3 }   vector with same magnitude and opposite direction   = { -2 , -8 , 3…

Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

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Q: Given: f(t) = 8 t 2 Evaluate: F(2) Round-off answer to 2 decimal places.

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Q: -9-8-7-6-54-3-2-1 8 7 > Next Question 1 65 6 4 3 2 + -2 -3 -5- 5 7 -6 7 -8- 9 y be 1 2 3 4 5 6 7 8 9…

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Q: Use the graph to determine the intervals on r concave downward. 10 4 1.5 X 10 а.

A: Here we have concave upward and concave downward.

Q: If u = X + y+z a) 0 y 2+x ди + then the value of x x+y x b) 1 c) u d) None ax +y + ay +2 ди əz IS:

A: Question - 21 Given, u=xy+z+yz+x+zx+y To find, x∂u∂x+y∂u∂y+z∂u∂z Formulas used:…

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A: Here the age A (in years) is given by, A=-8267lnDD0 It is given that the amount D of carbon-14 that…

Q: II. Consider the function f(x, y) defined for all (x, y) by ƒ(x, y) = 232/32 + 2xy + 4x²y (a) Find…

A: Here we have to find the critical points.

Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: Given: F(s) = (5s+6)/(s²+9). Evaluate: f(1)

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Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: To use alternating series remainder theorem to determine the smallest number of terms required to…

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Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

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Q: -5-4-3 fa 7 The function graphed above is: Increasing on the interval(s) Decreasing on the…

A: Given data÷

Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 2, t> 0

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Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: Find the critical numbers of the function f(x) = -x55x¹ +5x³ answers to three decimal places. X = X…

A: Given,            fx=-x5-5x4+5x3-9To find : Find the critical numbers of the function

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Q: Find the area of the inner loop of the limacon given by r = 1+2sin 0.

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Q: Use the Fourier sine transform to solve the following BVP with 0 0 10₂4+02=0, მყ2 u(0, y) = 0, u(π,…

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Q: 4 ANSWERS Screenshot (1603) y + 4y = 1²-t +7. Screenshot (1597).png Determine the values of r for…

A: Need to find out the solution and also the values of r

Q: Answer true or false. The function f(t) = (et)10 is not of exponential order. True O False

A: Let's solve.

Q: Question Find the linear approximation L(x) of the function f(x) (Enter an exact answer.) Provide…

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Q: Find the minimum value of the function f(x) = 2x² +18.3x + 45 to the nearest hundredth. Answer:…

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Q: The eigenvalues of a square matrix A are the numbers À for which the matrix A-XI is regular.

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Q: 16.s) How long it will take for $39,440 to double if it is invested at 6.1% compound- quarterly?…

A: Topic = Algebra As per guidelines , At a  time only one question can be answered.

Q: Answer true or false. If £{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). True O…

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Q: Sketch a graph of the polar equation. 3 2+3 cos 0

A: The given polar curve r=32cosθ

Q: 1. Determine the value for the number "a" so that lim x-2 3x² + ax + a +3 x²+x-6 will exist. Also…

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Q: 3. Find the Taylor polynomial of degree 3 centered at x = 4 for the function defined by f(x)=√x.…

A: To find out the Taylor polynomial of degree 3 for the given function and also find out the value of…

Q: Find div F and curl F if F(x, y, z) = 9y¹zºi – 14x³z7j — 5xy³k. div F= curl F=

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. $…

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Q: 8 1 3√x 1² O 0.5 O 6.5 O 4.5 O 0.5 dx

A: Given a definite integral ∫181x3dx We have to choose one of the given option solving the given…