Find the center of mass of a thin plate of constant density 6 covering the given region. The region bounded by the parabola y = 3x - 2x² and the line y= - 3x The center of mass isO (Type an ordered pair.)

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A: We will use the cylindrical coordinates to find the required volume.

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A: There are total of 24 students. let the number of female students = x therefore number of male stude...

Q: ollowing integral by using Trigonometric substitutions Method: dx y = V4 + 25x2 ーマ

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Q: Convert 1100101, to decimal notation.

A: Given binary number 11001012 we have to convert into decimal notation (base 10)

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Q: (a) Find parametric equations for the line through (S, 5, 6) that is perpendicular to the plane x-y+...

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Q: [(5230°)(1+)][/cos(5 + j3)] log(2-) (1 - 12) Z =

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Q: subject direction : mathem atics in the modern world Determine The Truth OF each pre position T iF i...

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Q: Approximate the sum of the series correct to within 0.00001. Σ (-1)" (3n)! n = 1 8.

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Q: 3. Use De Moivre's Theorem to find the identity of the following: a. cos 80 b. sin 90 c. cos 100

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Q: G0o Suppose the random variable has the cdf 0, x < -3 F(z) = 12-3 <I<: -3<I<

A: Introduction: A random variable has two types of the distribution functions. These are the probabili...

Q: (4) Decide if the following statements are true or false. If true, explain why. If false, give a cou...

A: (A) FALSE Consider the following series, ∑n=0∞anx-πn   such that  an = 1·3·5 . . . (2n-1)2·5·8 . . ....

Q: Question 3 Captain Picard and the rest of the crew of the Rocinante are defending their position on ...

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Q: Question 1. Let G is a finite group and ø : G → G' be a surjective homomorphism (that is, ø is a hom...

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Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere ...

A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper hemisp...

Q: Part A Which number in the equation indicates the growth rate? O 300 e O 0.75 O time Part B Calculat...

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Q: By applying Rolle's theorem, check whether it is possible that the function roots. Answer: ?

A: The given equation is f(x)=x9+x-6 f'(x)=09x8+1=09x8=-1 If f(x) has two real roots then By Rolle's th...

Q: use method of frobenius to obtain series solution of the equation; xy''+(4-x)y'+y=0

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Q: Question 2. Let G be a finite group, H 3 G, N 4G, and gcd(|H|, |G/N|) = 1. Prove that H 3N.

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Q: 1. y,=e"; y;=e*; L.I. 2. y, =xe"; y:=e"; L.I. 3. y, =senx + cos 2x; y;=3; L.D. 4. y, =x; y, =e; y,=x...

A: We have to check whether the given expression is linearly independent or not.

Q: Find F(s) for f(t) = sin? 4t

A: Solution

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Q: Consider the function f : [–1,2] → R defined by f(æ) = x² – 1. On the interval [-1,0] the maximum va...

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0. Answer:

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Q: Let H= Span(u, U2,u3 and K= Span{v,,v2,V3}, where each vector is defined below. Find bases for H, K,...

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Q: 4- solve the following differential equations (a) x +3x +2x = g(t) = {0 (10st<10 0 t2 10 ,x(0) = 0,x...

A: Applications of Laplace transferom, solve the differential equation by using Laplace transferom

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Q: z2+ 25 (b) lim Z 5i z-5i

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Q: You have two windows: a rectangular window y inches by z inches and a square window measuring x inch...

A: We will use Lagrange Multiplier method to  maximize / minimize a function f(x,,y,z) subject to g(x,y...

Q: Use the e – 8 defintion of a limit to show that lim (6z – 4) = 2+ 6i z→1+i

A: The given problem is to show and evaluate the given complex limit by using the epsilon-delta definit...

Q: y In 2 y = In(x + 1) x -In 2 x = -1 In the diagram the region bounded by the curve y = In(x+1) and t...

A: Solution is below.

Q: Find the volume of the solid enclosed by the paraboloids z = 1 (x2 + y²) and z 32 – 1 (x2 + y²).

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Q: Example 12 6-13 Simplify 4+17 Solution

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Q: Let be the vector space of polynomials of degree less than or equal to one with real coefficients an...

A: The given vector space is the set of all polynomials of degree less than or equal to one with real c...

Q: Letv = x2sin(v) + vexy, where X = s + 2t and y = st-

A: Solution is below.

Q: Compute the flux of F(r, y, z) = [1,–2, z] through the surface S, which is part of the graph z = f(r...

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Q: Assume A, B, and C are sets. Prove the following deductions are valid. a.  A ⊂ (B ∪ C), ∴ (A \ C) ⊂ ...

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Q: Find the location and type of all critical points by first converting the ODE to a system and then l...

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Q: roblem 7. Let G be an Abelian group. The torsion subgroup T of G is the set T = {g €G: ord(g) is fin...

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Q: х+ 2у + 3z %3D4 Зх + 6у + 92 %3D5 4х — 2у + 7z 3 1

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Q: 1 3 -1 5 9. Let A = -1 0 -2 -2 1 1 1 3 (a) Find a basis for the row space of A. (b) Find a basis for...

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Q: z- 7x+ y = 2 , 2y + x-z 6 , 3z = 0 use the inverse method to find x,y,z 6)

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Q: (Review) Determine whether the series (-1)"+1s converges absolutely, converges conditionally, or div...

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Q: How many nonzero terms of the Maclaurin series for ln(1 + x) do you need to use to estimate ln(1.2) ...

A: The expansion for ln1+x can be written as follows:

Q: Given (5,1,2) Qnd Find the projection Vo of V to U V= (4,-3.1) is ON -bas in RB Determine the angle ...

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Q: [2 + i 0 2i Lo 3il b. Value of y 北- 1 2i 6. a. Value of x C. Value of z

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Q: 18. There is a set X for which Ne X and NsX.

A: As N is set of natural numbers , so  for N to be subset of X and N belongs to X , we can consider X ...

Q: Is there a sequence of continuous functions: fn : [0,1]-->R that is pointwise convergent but the lim...

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Q: y = e-3* is a solution of the differential equation - - 6y = 0 dz2

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