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Q: Using polar coordinates, evaluate the volume of the solid in the first octant bounded by the…

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Q: Suppose f: X→ Y, and A, B CY. Prove that (a) f¹(AUB) = f¹(A) U f¹(B).

A: Union of two sets A and B is denoted as A∪B  It contains all the elements that are either in A or in…

Q: The meaning of the decimal representation of a number 0.d₁d₂d3... (where the digit d, is one of the…

A: The decimal representation of a number 0.d1d2d3.... is as follows,…

Q: Write down the interpolation error term for the above polynomial, and identify the polynomial. 2.…

A: We are given the following polynomial and function.…

Q: Consider a retirement savings account where the monthly contribution is $110 for the first 25…

A: P1=PMT1+rnnt-1rn Where  PMT=$110,  t =  25 years,…

Q: Let p be an odd prime and a, b are integers with pła, płb. Show that ab ()-(()) = Р

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Q: 7. The height in meters of a projectile shot vertically upward from a point 2 m above the ground…

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Q: 2x²y" + xey'- (sin x)y = 0 about x = 0. It is sufficient to obtain the first three nonzero terms of…

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Q: Evaluate the following limit by expressing it as the limit of the right endpoint approximation of an…

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Q: (a) Find y' by implicit differentiation.(b) Solve the equation explicitly for and differentiate to…

A: Given: 9x2-y2=1 To Find : (a) y'             : (b) y' in terms of x. To check : (c) both the…

Q: Solve the equation for y in terms of x. Enter the exact answer. 2x = 3 - 3y Enclose numerators and…

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Q: 8. Give two examples of Fatou's Lemma, where one is an inequality. equality and the other a strict

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Q: . The bridge shown has dimensions as given where the arch measures 18 feet at its highest point. The…

A: Given CD= 18 feet and r is the radius that is OA=0B=r Therefore OD=OC-DC=r-18 Since AB= 60 feet…

Q: 11. Let f be integrable over E where E = AUB is a disjoint union of measurable sets. Prove that…

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Q: Use the graph of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

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Q: Assume that the demand of chocolate of a local producer is given by q = 9-√p in hundreds of…

A: Revenue = price x quantity  Marginal revenue is equal to rate of change in revenue i.e. R'.  We also…

Q: A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular…

A: 1st we will find point of intersection of given lines to find vertex of region R and then use…

Q: 7. fn(z)= 1-x" 1+x , 0≤x≤1. Evaluate lim 1 n++∞ fn. What limit result is/are applicable?

A: The given function is  fnx = 1 - xn1 + x We have to find limn→+∞ ∫0,1fn Here, we will use Lebesgue…

Q: Suppose that F is a field of characteristic 0 and E is the splittingfield for some polynomial over…

A: It is given that, F be a field of characteristic 0 and E be the splitting field for some polynomial…

Q: 1. Bayes' Nets Consider three random variables: (C)ovid, (N)ose running, (F)ever. Draw the structure…

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Q: Ana's Catering Service rendered a Service cost P 250 per head for 20 or less person, P 230 per head…

A: Let the number of person is represented by x. Since, it is given that a service cost $250 per head…

Q: Find the image of the set under the given transformation. a) S = {(u, v) |0 ≤u≤ 3, 0≤0 ≤ 2} x = 2u…

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Q: Consider the function f(x) = A+5 cos(6x) Bx + C 0 < x < 픔 1 < x < 1 12 on the interval (0, 2). Find…

A: A theorem for differentiability of a function's Fourier series states that: If f is a piecewise…

Q: 5. (i) Determine the sequence gnerated by the following generating functions: (ii) e(1+x) t (1-1)³

A: (5) (i)          Given generating function is t1-t3= t 1-t-3…

Q: At age 23​, someone sets up an IRA​ (individual retirement​ account) with an APR of 7​%. At the end…

A: Given that At age 23​, someone sets up an IRA​ (individual retirement​ account) with an APR of…

Q: Consider a pizzeria that sell pizzas for a revenue of R(x) = ax and total cost of C'(x) = b + cx +…

A: Given R(x)=ax ,C(x)=b+c x+d x2 a. profit P(x)=R(x)-C(x)                   =ax-b-cx-dx2 b. P'(x)=…

Q: c) Consider the vector X₁. -3 = [³3] i. Express x₁ as a linear combination of the standard basis…

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Q: Consider the recursively defined sequence (Hn)n>1 where 1. H₁ = 1 2. Hn+1 = Hn+n1 for n ≥ 1 >…

A: Table of H_{2^{n+1}} and H_{2^n}+1/2 for small values of n has been attached. This is just given an…

Q: Use the Laplace transform to solve x₁ = 2x1 + 3x₂ + 12e¹ x2 = x1 +4x2 with initial data x₁ (0) = -8…

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Q: 7. Suppose that A is an n x n matrix. a. For each eigenvalue λ of A, prove that λ² is an eigenvalue…

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Q: Let A = {1, 2, 3, 4, 5}, B = {3, 5, 6, 7}. Then An B = { B-A = { }.

A: Given A = {1, 2, 3, 4, 5} B = {3, 5, 6, 7}

Q: Determine whether the following statements are TRUE, FALSE, OR INDETERMINATE (could be either true…

A: Since  you have posted a multi subparts question according to guildlines I will solve first  three…

Q: Prove that every nonzero coefficient of the Taylor series of (1-x+x²) ex about x = 0 is a rational…

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Q: 1. Find solutions for the divergence and curl of the vector field v at (1, 0, -1). v (x, y, z) =…

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Q: 1. Let f be integrable over E where E = AUB is a disjoint union of measurable sets. Prove that [-]+]…

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Q: Ana's Catering Service rendered a Service cost Php250 per head for 20 or less person, Php 230 per…

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Q: Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A coin is flipped…

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Q: A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red…

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Q: Input-output pairs of four exponential functions are listed in the table. Complete the table. X 0 1…

A: Please find attachment

Q: 4. Find the median of the given quiz scores. 3 2- 1 0 Ind 3 4 1 2 5

A: median we know that the median is the middle number in a sorted data like ascending or descending…

Q: pi/8 is wrong. it should be 0

A: Here M=∫01xsin-1x dx-∫01πx2dx Use by parts in part 1. M=sin-1x∫xdx-∫ddxsin-1x∫xdxdx01-πx2401…

Q: QUESTION 1 ind the approximate (0.2) 2+3. (0.2) +1 √4.2 value of the expression using the…

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Q: xy + Let f: R2 → R where f(x, y) = 0 if (x, y) = (0,0) and f(x, y) = 72²² if (x, y) = (0,0). (a)…

A: Given: Let f:ℝ2→ℝ where                               fx,y=0                   if…

Q: Bounded by the planes z = x y = x x + y = 2 and z=0

A: Volume bound by the Planes

Q: Find the solution of the initial value problem. T8 3 -1 0 2 0 0 2-2 3 - 1 + t t² " x(0) = 1 0 2

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Q: . In answering the questions below, you will prove the statement Statement. For all positive…

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Q: Problem 4 Suppose we have a 3x9 grid of 27 squares, where each square is either orange or black.…

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Q: Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A coin is flipped…

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Q: Test the series below for convergence using the Ratio Test. n=1 n³ 0.5" The limit of the ratio test…

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Q: what is independent sets ? what is maximal independent set ? what is the independence number? what…

A: Independent set: An independent set is a set of vertices in which no two vertices are adjacent. That…