Show the derivation of formula for the conversion from spherical coordinates to rectangular coordinates.

Q: How did it became -2pi/27 from the equation (-2pi/3+2pi(0))/9? Please explain.

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Q: Let T: P3 Pa be the linear transformation defined by T(at3 + bt2 + ct + d) = (a - b)t3+ (c- d)t. The...

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Q: Let y be a solution of the differential equation * + (1+ )y= =, where x > 0 such that y(1) =1+÷. If ...

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Q: kit emint the squar rool of Z= Z [ cos (E) i inn (4)7

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Q: Let y be a solution of the differential equation V = +3, where x > 0, y > 0 2ay such that y(2) = 6 ....

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Q: What s S Snteget gsenta that divides the no. s the Smalleset Positine than 1 2021 2021 (7) |

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Q: Let f and g be functions from the positive integers to the positive integers defined by the equation...

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Q: 3y"' + 2y" = 0. y(0)=-1,y'(0)=0,y"(0)=1 Solve this

A: First of all write the characteristic equation of given differential equation and solve it for root'...

Q: Consider the solid Q that is generated in the first octant by the surfaces S1: X + y = 4, S2: y +z =...

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Q: Solution by Gauss seidel method. 15x + 2y – z = -200 2x + 12y + z = -250 1x + 2y + 8z = 30

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Q: Use the Euclidean Algorithm and the solving for remainders method to find the f 32-mod2007= 32 (Your...

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Q: Find y as a function of x if x²y" – 3xy' + 4y = x", y(1) = 3, y'(1) = –5. y =

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Q: Consider the mapping diagram of the relation R below. 2. 3 a) State a counterexample from the diagra...

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Q: Part 2: Find each of the probabilities when a state is chosen at random: A. P(A or B) В. Р(А) С. Р(В...

A: Part 2. P(A) = Probability that the state name begins with A through M          = (11+15)/(11+15+13+...

Q: Q1 Assuming that the equations in Exercises 25-26 define y as a differen- tiable function of x, use ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Solve xy" + y = 0.

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Q: Write the negation of the following statement in words. Some odd numbers are divisible by 4.

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Q: The dissecting room of a certain coroner is kept at a constant temperature of 5° C. One day the coro...

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Q: Use mathematical induction I to prove that for all integers n2 3, 2·3 + 3 · 4 + ·· ·+ (n – 1) · n = ...

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Q: Is the thinking illustrated inductive or deductive

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Q: Maximize: P=12xj +10x2 subject to: 5x1 +3x2 <15 X1 +x2 54 x 2 0, x2 2 0

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Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for t...

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Q: Being fa function with continuous second derivatives, defined by: z = f (xy, a² + y*) If we take u =...

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Q: Suppose TE L(V) and By : v1, V2, ..., Vn is a basis for V such that for By 3 2 1] 0 1 0 0 0 2 M(T) (...

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Q: Use the method of undetermined coefficients to find the particular solution y, y" – 4y" + 4y' = 2x –...

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Q: Let a, b E N, with a > 0 and b > 0. (a) Let p, q, r, s be the unique integers such that a = qb +r, 0...

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Q: An organization sponsored a raffle where they were to sell all 500 tickets sequentially numbered fro...

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Q: 555 Y= x*+ Y = 4 2. Z²

A: Multiple variable calculus

Q: Official with all four sides equal. ng a

A: We have to show that angel x and angel y congruent. Step by step with properties of rhombus.

Q: Newton's Method will fail to approximate the solution to f(z) 0 with initial guess ro when: Oco is n...

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Q: Consider a closed storage tank S with walls given by the curved surfaces x = y', z > 0 and r = 2 – y...

A: 1st we will draw the diagram of tank and then find limit for all variable to use integration as surf...

Q: Let y be a solution of the differential equation cos y sin y de = ), where sin y > 0, for all y such...

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Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² | 3x + ...

A: We have to draw the solid Q in first octant and is generated by the surfaces  y- 1=( x- 2)2 3x+2z=11...

Q: Differentiate a circle from a parabola?

A: A circle is (geometry) a two-dimensional geometric figure, a line, consisting of the set of all thos...

Q: Factor 977101 by Pollard's p-methond; use the function f(x) =x+1 with seed xo = 2.

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Q: Find the determinant of the following: Kindly show the step-by-step solution. Thank you!

A: To find- Find the determinant of the following: 2 lnx01ex221ln2x-1

Q: For the PDE z-2+ = 1. (i) Is the PDE is quasilinear? Justify your answer. (ii) Find two independent ...

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Q: Determine the value of p (where |p| corresponds to the distance from the vertex to the focus) of the...

A: Given: Parabola whose vertex is 6, 7 and the x-intercepts are 3, 0 and 9, 0. To determine: Value of ...

Q: 3.) Let set S = {x, e*, sin x, cos x} be a solution to a 4th-order homogeneous differential equation...

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Q: Let n e Z. Prove that n² + 4 is divisible by 8 if and only if 3n + 6 is divisible by 12. (Hint: the ...

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Q: =a /2[1+3cose +3cos20 + cos*0 -1] cosed0.. %3D ... .... (32+15x) 24 %3D

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Q: Let y be a solution of the differential equation 2 T+y- I+y+I , where x + y +1>0 for all x, y such t...

A: We will solve the given differential equation using substitution and initial value .

Q: Question: Write a Python program to construct Newton's Divided difference interpolating polynomial t...

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Q: 1. Fill in the blanks Let y be a solution of the differential equation cos y sin y de = (1), where s...

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Q: If p(x) is the total value of production when there are x workers in a plant, then the average produ...

A: Given- If px is the total value of production when there are x workers in a plant, then the average ...

Q: Find the general solution of (y + 1)dx + (x – 1)dy = 0. O zy+x – y= C O ry – 2x – 2y = C xy + x + y ...

A: By Bartleby policy I have to solve only first one as these are all unrelated &amp; lengthy problems....

Q: Evaluate the integral sin^4 e de from 0 to Tt/2 * T/4 O 2r/3 O 31/16 О З1/5

A: We have to evaluate the integral ∫0π2sin4θdθ. Use the reduction integral formula, which is given bel...

Q: y= x²+Z %3D y = 4 %3D SSSX du +ye

A: Volume bounded by the curuves , conversion yo polar coordinates

Q: a Q#01:- Let W be the set of all vectors in R3 of the form where a and La + b! b are any real number...

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Q: (1) If A and B are positive semidefinite matrices, then the eigenvalues of A.B are all nonnegative. ...

A: Solution:-