Evaluate the definite integral. NOTE: Enter the exact answer. ti + t²j 0.

Q: Use the Babylonian's formula to calculate the area of a circle with diameter of 12 units. 1.1…

A: Babylonian's gives the Area of circle = 3r^2 where r is radius of circle.

Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5,x=4 , and…

A: volume of the solid of revolution about x axis of a curve y=fx, from x = a to x = b is given by…

Q: 1. Determine whether the series 2 is convergent or divergent. If it's n=1 e"+1 convergent, find its…

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Q: Describe the graph of the equation. r = 8sin 14ti – 8cos 14tj O It is a parabola in the xy-plane,…

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Q: Use Power Series to Solve the following Differential Equations y' - x² y = 0

A: To find the solution of the differential equation by power series method, we first consider the…

Q: V4-y² c8-x²-y² z?dzdxdy. Use cylindrical or spherical coordinates to evaluate the integral. J.J. A…

A: In cylindrical coordinates  x=r cosθy=r sin θz=zalsox2+y2=r2dzdxdy=r dzdrdθ

Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: Evaluate the triple integral. /I | ry sin(yz) dV, where G is the rectangular box defined by the…

A: We need to evaluate ∫∫∫Gxy sinyz dV 0≤x≤π  , 0≤y≤9,  0≤z≤π54 So, we need to find ∫09∫0π54∫0πxy sinyz…

Q: Find the inverse transform of the given functions: 35+5s+5 1. F(s) = (s3+852+195+12)(s³)

A: Factor the denominator of 3s2+5s+5(s3+8s2+19s+12)s3. 3s2+5s+5(s3+8s2+19s+12)s3=3s2+5s+5s+1s+3s+4s3…

Q: Ifan is an even number, show that a2 = 0 (mod 4), and if an is an odd number, show that a2 = 1 (mod…

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Q: 2х 64X 3 8+ 9+ 3+ 1

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Q: To improve her handwriting, Hope practices writing the numbers from 1 to 200. How many times will…

A: Polya's Technique has 4 steps:- 1. understanding the problem 2. Devise a plan 3. Carry out the plan…

Q: r(t) = 4 cos(t)i + 5 sin(t)j + 6tk; t= 2

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Q: (4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

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Q: aw the graph a

A: Given, the curve                  r=63-2cosθ

Q: Solve the Dirichlet problem 22 + y? < 1 a2 + y? = 1 Au(x, y) = 0 u(z, y) = y?

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Q: Find the inverse transform of the given functions: 4s2-4s+1 1. F(s) = (s3–4s2+s+6)(s²+5) 3s-6 5s 3.…

A: Inverse Laplace transferom of the function

Q: Which line passing through G is parallel to line IEC? 34 H CGJ BGH AIG O EFG

A: To find the line passing through G is parallel to line IEC .

Q: 2. Is the graph below a tree? Why or why not?

A: To identify given graph is tree or not

Q: 5: F(s) = (+2s+1) +7

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Q: f(t) = v1+ sin t + (6t)13 + t² sin 4t

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Q: Use the mixed congruential method to generate a sequence of 32 random numbers with Xo=8, a=9, c=13,…

A: By mixed congruential  (µ) method Xn+1 = (aXn +  c) mod (m) Rn = Xn /32

Q: Solve a following ordinary differential equation y'' + 2y  = sec(x)   PLEASE!!!

A: Given differential equation is y''+2y=secx. We have to solve the given differential equation. Write…

Q: 3. Let f : (R\{0},-) (R\{0}, -) be group homomorphism defined by f(a) = |a|. Then ker(f) %3D =...

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Q: Evaluate using Laplace Transform: tcos 3t dt e-4t f(t) =

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Q: Evaluate cot (0.64i) Select the correct response: O 0.565 O -1.77 O 0.565i O -1.77i

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Q: 8. Interval -c<x< c; function, f(x) = ex

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Q: Find the first four nonzero terms in a power series expansion of the solution to the given initial…

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Q: Choose two figures which are topologically equivalent to each other

A: In a topological space two figure are topologically equivalent if one can be form from other by…

Q: Use the graph of g(xgiven in the figure below and the fact that g(0) = to select the correct graph…

A: Here we have to use relation between f(x) , f'(x) and f "(x) to find graph of f'(x) from graph of…

Q: For each of the following series determine if the series converges or diverges. 00 In(n) n n=2 n3…

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Q: Perform the indicated operation and express in lowest terms. Зр - 3 5p? 9p - 9

A: All we have to do is take out the common factors. The detailed solution typeset in LaTeX is…

Q: 1. Find the (a) true error and (b) relative error of the following: 1. The derivative of /(x) = x +…

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Q: During a sneeze, the radius of windpipe decreases. Suppose that the normal radius of the windpipe is…

A: Here we need to find maximum value of V(r) For absolute maximum or minimum  i) verify that the…

Q: 2 6.xy + 2z how that G(r, y, 2) = (3y? + ( 3y2 + 2x , x, y, z > 0 is conservative %3D 22 a) without…

A: Scalar potential function

Q: x + y ) The function f(x, y) = (x, y) + (0,0), is x - y 0 (a, y) = (0,0) (a) continuous at (0,0) but…

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Q: y - 3y + 2y = 3e* + 2e2*

A: Given differential equation is y''−3y'+2y=3ex+2e2x......1. We have to find the general solution of…

Q: Find the inverse transform of the given functions: 4s2 -4s+1 1. F(s) = (s3-4s2 +s+6)(s²+5) 3s-6 5s…

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Q: Evaluate using Laplace Transform: tsin3 3t dt e-3t 00 f(t) ||

A: We have to apply the Laplace transform method.

Q: 3. Find a Maclaurin series expansion for f(x) = cosh x 4. Find a Taylor series expansion around x =…

A: Macluarin series expansion of the function

Q: The complex number z is defined by z= 3-z+4.j where z is real. a) Find, in terms of z, the real and…

A: We have to find the values of real and imaginary parts in terms of x.

Q: 7) Finol the arymptotes to the cunne n chich are parallel. dothe axis)

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Q: Find the inverse transform of the given functions: 3s2+5s+5 1. F(s) = (s3+8s2+19s+12)(s³)

A: According to guidelines I can do 1 question at a time.

Q: Give atleast two examples of each iterative method.

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: Which of the following statements is/are a restatement of Euclid's Fifth Postulate? 1. Through a…

A: Given information is I.  Through a point P not on a line l, there exists exactly one line parallel…

Q: 9. Interval 0 < x< T; function, f(x) = cos x COS X

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Q: 4. 2y"+xy'-4y = 0

A: Power series solution of the differential equation

Q: Use the Egyptian's formula to calculate the area of a circle with diameter of 8 units. (roundoff…

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Q: An open tank has the shape of a right circular cone (see figure). The tank is 8 meters across the…

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Q: 1. Given the sum and difference between two vectors A + B = -3ax + 5ay – 4az А - В %3D ба, — 2а,…

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