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Q: Find the centroid of the given region.

A: We have to find the centroid of the given region.

Q: 1. Consider the curve C with parametric equations Sæ(t) = t³ – 3t +1 lu(t) = t(t + 1) defined for t…

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Q: Find the volume of the solid that results when the region enclosed by y = e", y = 0, x = 0, r = In…

A: Curve y=ex,y=0,x=0   and x=ln5 intersection point of the curvx:0→ln5                            a=0…

Q: The evaluation of SiS 3y e*ydxdy is

A: The solution is given as

Q: I. Given the matrices below, compute for the matrix operations asked from No. 1 to 5. A = 20 B =| 4…

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Q: c) Given the recurrence relation as an=5n+an-1 where the initial value aj=4. i. Find the solution…

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Q: 2. A parabolic antenna has a width across the top of 36 inches and the depth at the center is 6…

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Q: Consider the Cobb-Douglas function n f (X1,x2,..,Xn) = x"x. i=1 where x; > 0, and a¡ > 0 for all i=…

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Q: Suppone that fand q ane diffentiable fonctious on IR veh that, Cx+1)f')+ 3x$cx) xe+7x on IR. If f is…

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Q: true or false  1.) If a │b then a │b^n for n ϵ N 2.) n^4 + 4 is composite for all n > 1 3.)If p is…

A: Due to our terms and condition I have solve just first three questions in your question. Please…

Q: 8. Let S be the surface {(x, y, 2) | a = y? + 22 + 1}. Find every point (ro, yo, zo) on S so that…

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Q: 1. Calculate the following Legendre symbols (i) using Euler's criterion, Jacobi symbols: 3 (a) 17 15…

A: To find the Legendre symbol for  (a)    317 Using the Euler's criterion We know by the definition of…

Q: Example 2: A food product is made from soybean meal (50% protein, 10% moisture) and corn flour (10%…

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Q: Show tht if x is an integer, then gcd(x+1, x2-x+1) divides 3.

A: Sol

Q: A quadrivector AH has components (1, 1, 1, 0, 1)' in the system S. Calculate the T components of AH…

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Q: y"' + 3y" - 3y' - 2y = e'

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Q: nd ,I:J ar

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Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

Q: -3 8. Let v = 2 and ts be given vectors in R. Which of the following vectors is a linear combination…

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Q: er the ideals I = (x, y²) and J = (x- 2y) in Qlr, y)- %3D %3D

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Q: The rate of increase of the temperature of water being heated in a kettle at any time t is mod the…

A: We will solve the differential equation by using variable separable method and then use initial…

Q: Determine the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for f (x, y) = x e-a-y"…

A: Consider the given function fx,y=e−x2−y2cosxy. We have to determine the first and second degree…

Q: b) (1eoy2+64tse*) do + (Gx?y+2x)dy=o c) 24 dx + (6x³ - xy+x) dy=0

A: We can solve this using substitution and exact equation

Q: A. ((x+1)? -y? ) dy dx

A: Sol

Q: tan(r) = sin(-4cjs32°) solve for x %3D a. 1.5241cjs9.0104 b. 1.5053+0.2387j c. 1.5241e0.01573j d.…

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Q: se Indirect Proof to prove that if a and b are both positive, and a2 < bi

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Q: Let C be the parametric curve defined by x(t) = t² – 2, y(t) = t³ – 3t + 1. Determine if C is…

A: Given that,A parametric curve C is defined byx(t)=t2-2y(t)=t3-3t+1The concavity of the parametric…

Q: 4. (a) Prove that H, { f(x) [Hn-1{f(x)} + Hn+1{f(x)}] and hence find T. 2n S (x – a) Hn ,a > 0, k >…

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: 16) Rewrite the integral 10 3(1 – z/10) 7(1- y/3 – z/10) dx dy dz in the order dz dy dx.

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Q: Let (sn) be an increasing sequence of positive numbers and define on = ÷(s1 + 82 ++ Sn). Prove (on)…

A: This is a problem of sequence.

Q: View S' as the boundary of the 2-disk D² = {(x, y) E R² | x² + y? < 1}. Fix To E S', and let X = (S'…

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Q: Let R be the region bounded by the functions f(x) =-3x²+3 and g(x) = 3x2 - 3 as shown in the diagram…

A: Given: f(x)=-3x2+3g(x)=3x2-3 Concept: Here the area shall be given by: A=∫abgx-fxdx

Q: The magnitude of the cross (vector) product between unit vector theta and unit vector rho (unit…

A: Sol

Q: in fuzzy graph theory what is the threshold graph? And give examples

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Q: Which of the following pieces of graph are concave up? i. i. iii. iv. A i. only B ii. and iv. C i.…

A: As we know that, A curve is said to be concave up if it is open in upward direction. From the given…

Q: Q2/ Solve the following differential equation: e2y dx + 2(xe2y – y)dy = 0

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Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

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Q: (i) ( Let y: [a, b) → C be a curve. Explain what it means for y to be: (a) piecewise smooth; (b)…

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Q: Solve the problem P.D.E. u, = u,xx 0<x<1 0<t< 00 fu(0, t) = 0 lu(1,t) = cost u(x,0) = x B.C.s 0<t<00…

A: Sol

Q: у- 4y/ + 4y — е?" (12л? — 6х); у(0) — 1, у/ (0) — 0 %3D

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Q: (a)((x+1)² – y²)ª– (2(x+1)y – 10(x+1)²) = 0 dx

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Q: С. Show that f (x) = x³ + 4x2 - 10 = 0 has a root in [1, 2] and use the Bisection method to…

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Q: cosh In(-3+ 2j)]

A: The expression of coshx is coshx=ex+e-x2. Break the given hyperbolic function into exponential form.…

Q: Let S be the upper half of the unit sphere x +y +=1 and take n as the upper unit normal. Use Stokes'…

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Q: Let C be the parametric curve defined by                         x(t) = t2 - 2;…

A: The given curve C is xt=t2-2yt=t3-3t+1. We need to find that the C is concave up or concave down at…

Q: 2.52 Prove that Ca, b] is a vector space.

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Q: 2.54 For each n e N, let X„ be the set of polynomials of degree equal to n, and let Pn = U-o Xk.…

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Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: (x, y) - arty! - b where x is the amount of money expended on labor, y is the amount expended on…

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