We can prove that if D is a region bounded by a simple closed path C in the xy-plane, then the coordinates of the centroid (x,y) of D are: 1 1 x² dy x = y == y² dx 2A Jc 2A C where A is the area of D. Use this to find the centroid of a quarter-circular region of radius a. -

Q: a =(−1)²¹ (n − 10)₂ - What is the 9th term of the sequence n

A:

Q: Do as indicated. 2. Use the Squeeze Theorem lim sin (sinh x)csch x. x-18 to evaluate

A: Given problem:-

Q: Solve the D.E ý - 25 +2y = 2X+3

A:

Q: D4 − 1)y = 0 -

A: Topic:- solution of differential equations

Q: Express the function as the sum of a power series by first using partial fractions. f(x) =  x + 4…

A: Solution: f(x)=x+42x2-5x-3

Q: Find a power series representation for the function. (Give your power series representation centered…

A: We have to find the Power series representation.

Q: Find the point on the curve y=x³ at which the tangent is parallel to the tangent at the point on the…

A:

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

A:

Q: [₁ [6x² arcsin(x)]dx

A:

Q: Evaluate the following. √(x²-2) e¹-6x dx

A: Use substitution method to solve the integral.

Q: 2. lim lim (x-i) tan (x 3 x) x>1 (x+1) sind (2x-2)

A: We have to find the limit of the given function without using l' hopital's rule.

Q: Find dy/dx by implicit differentiation. x²y³ -yax dy/dx =

A:

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² = 100 Or-10 sin 0 Or- 10…

A:

Q: Let an integer be chosen at random from the integers 1 to 30 inclusive. Find the probability that…

A: We have to find the probability.

Q: Radius of Convergence of a Power Series. (n!)x" Determine the radius of convergence for the series…

A:

Q: 8. The position function of an object is defined as: s(t)= t³-t²- 8t Find the minimum velocity of…

A: As per our guidelines we are supposed to answer only one. Kindly repost others question as a…

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

A:

Q: Find the volume of the th

A:

Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

A:

Q: Which of the following is the derivative of (x³ + 1)(x² + 2x)? 3x²(x² + 2x) + (x³ + 1)(2x + 2) 3x²…

A: This question is based on product rule of differentiation.

Q: [2,

A:

Q: P(x, y, z)= V = ( ])

A:

Q: Revers the order and Evaluate= s dx dy y

A:

Q: Suppose you deposit $1000 at 7% interest compounded continuously. Find the average value of your…

A: To find out the average value of account during first 4 years.

Q: Find the volume of the solid generated when the region enclosed by the given curves is revolved…

A: This question is based on application of integration.

Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

A:

Q: (D³ + D)²y = 0

A:

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i 137 u = 8i + 7j + k v = i + j…

A: Directly use the formula for the volume of parallelepiped.

Q: Question 2. Determine the equilibrium price(in hundered rand) and quanity (in thousand units) of a…

A: Find your answer below

Q: Problem 4 For x,y,z E R 5x +y Given: 2x - 2y 3x +3y and xyz = -48. Find: S = x+y+z +z = 0 +2z = 0…

A:

Q: d an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (4,…

A: Given; Points- (0,0,0),(4,0,6),(-4,-1,8)

Q: COS X d) f(x)=3sin √√x³ -3x+2___ _e) ƒ(x)=! f) h(w) = 3 cos(tan w)

A:

Q: For the graph below, the concavity switches at x = +1.7 and 0 and there are critical points at x =…

A:

Q: Use the figure to find the exact values of sin(2u), cos(2u), and tan(2u). X sin(2u) = cos(2u) =…

A:

Q: = fºx R/2 Given that evaluate - b² = g², use this result and the fact that 2 (6 cos(x) - 6x) dx. x…

A:

Q: 4. Find the Taylor series for f(x) centered at the given value of a. [Assume that has a power series…

A: First we will find expansion using general formula and then put the value .

Q: What are the first 5 terms of the sequence a₁ = 5₂ a = 2n-a n-1, where

A: We have to apply simple mathematics logic to solve the problem

Q: Find dy/dx by implicit differentiation. (sin mx + cos my)4 = 74 dy/dx=

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A:

Q: Find two positive integers such that the sum of the first number and four times the second number is…

A:

Q: Find the derivative of the function. f(t) = (9t+ 9)2/3 f"(t): =

A:

Q: Find the x-values (if any) at which fis not continuous. Which of the discontinuities are removable?…

A: Using property of rational function,

Q: Find T(t) and N(t) at the given point. (7) = N() = = T r(t) = 11 cos(t)i + 11 sin(t)j + tk; t = K|2

A: Given,…

Q: Determine the minimum cost of a retailer of motorized bicycles whose cost function is C(q) = 4860/q+…

A: Here the given cost function is: C(q)=4860q+15q+750000

Q: Homework 11 Parametric: Problem 3 Suppose a curve is traced by the parametric equations as t runs…

A:

Q: area enclosed by enclosed by the Curve Find the X = 2y² and x = 8

A: This question is based on application of integration.

Q: A B D Find the area, A, of the region enclosed by the cardioid r = 8 + 8 cos 0. 96 л 52 t 48 100 π

A: First I have written the area formula for polar curve , then draw the graph of given curve and then…

Q: 5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

A:

Q: 31. (a) 32. (a) 33. (a) 34. (a) ₁12x-11dx • S²₁₂ √2+ |x|dx 2+ |x| L₁ let |e* - 1|dx *) ₁²³-1-15|dx +…

A:

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A: