Integrate by change of variable, ∫∫R(x-7)/(2x-y)dA where R is the parallelogram enclosed by lines x  − 7y = 0. x − 7y = 9, 2x − y = 6 and 2x − y = 10.

Q: Q2 A rectangle is inscribed under the curve a² + 4y2 = 1 with its base on the x-axis, as shown in…

A: To find out the coordinates of (x,y) that will maximize the area of the rectangle.

Q: Use the binomial series to find f(10)(0) term for the f(x)= sqrt(1-x2)

A: f(x)=1-x2=(1-x2)12

Q: 42. f(x, y) if f(x, y) = x² +9y² – 4 2

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Q: nswer as a whole or exact number.) nt: m

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Q: 2. A toolbox is shaped like a rectangular prism with a square bottom.. Its top and front are…

A: Let the length=L Width=W Height =H The surface area of the four metal faces =  176 square inches

Q: 2. Find the function y(t) that solves the initial-value problem: (a)=1+2,t>0, y(1)=5 (b) = 26, 20,…

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Q: Calculate the consumer surplus and producer surplus for a market where D(q) = (q - 3)^2 and S(q) =…

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Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

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Q: 13. f(x, y)=x²-2y³ - 5x+6y-5

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Q: The velocity of a particle moving along the z-axis is given by f(t)= 18-6t cm/sec. Use the graph of…

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Q: Evaluate cos(2x) dx. Show how to do this by hand, and round the final answer to 3 decimal places.

A: ∫12cos2xdx

Q: (a) State the conditions that must be satisfied in order to apply the integral test to deter- ine…

A: a.

Q: Q3 Find constants a and b in the function q(z) = a(z³ bz) such that q(z) has a local minimum at z =…

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Q: If y' = and y (In 3) = 3, find y.

A: Here the differential equation is y'=exy2, with initial condition y(ln(3))=3.

Q: The price p (in dollars) and demand x for wireless headphones are related by x = 7,000 -0.1p². The…

A: Given: x = 7000 - 0.1 p2 The current price (p) is $110. And, the price is decreasing at a rate of $5…

Q: Find the indefinite integral for the function (2y — 9)-5 dy = - (2y - 9)-5dy AY

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Q: Question Given the integral expressions for F and G below, select all statements that are true. F =…

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Q: 14. Find the interval and radius of converence for 3x √n+1 n=0

A: The given series is:∑n=0∞ (-3)nxnn+1

Q: Use the binomial series to expand the function f(¹) = (1-4)1/4 as a power series M8 Cnzn 1-0

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Q: S 2x е e +3 ¡dx

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Q: C{(1 (A) (B) (C) (D) 3/12 - s² 1 t)(3 + 2 sin 5t)}= 3 10 s(s²+25) 1 + + + 10 s²+25 10 s²+25 + 20 s²…

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Q: The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial…

A:

Q: The velocity, in kilometres per hour, of a car as it begins to slow down is given by the equation…

A: v(t) = 90- 30In(3t+1)     a. as the driver begins to brake , t = 0 v(t)=90- 30In(3t+1)v(0)=90-…

Q: Which statement best describes creating a hyperbola? A. A place slices a double-napped cone…

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Q: Differen have the following function S. 0₂ y = (2x²-x+1) ² } €) y = (4x-2) ²³ 6 Y = √3x+5 (€) y =…

A: Since, you have posted multiple parts . As per guidelines, we are supposed to answer only first…

Q: David has available 520 yards of fencing and wishes to enclose a rectangular area. (a) Express the…

A: Length of fencing =520 yards

Q: Consider the following graph. 5-4-3 -2 f(x) = 5 4 3 2 1 -1-1 -2 -3 -4 5 to -7 8 -9 10 1 2 Identify…

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A: Area between the x axis and f( x ) is given by from a to b  A = ∫x = ax = bf( x )dx Given function…

Q: Simplify the trigonometric expression. 2 + cos(y) 1 + 2 sec(y)

A: To simplify the following trigonometric expression. 2+cosy1+2 secy

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = x³ - 6x² + 2 (a) Find the…

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Q: 2 d) ²₂t(t4 +3t)dt -2

A: We need to solve ∫-22t(t4+3t)dt

Q: What combination(s) of vertical, horizontal, and oblique asymptotes are possible for a rational…

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Q: In Problems 51-60, find the indicated function or value if C(x, y) = 3x² + 10xy − 8y² + 4x 15y 120.…

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Q: Find the curvature of the curve F(t) = (5 cos(t), 5 sin(t), 2t) at the point t = 0 Give your answer…

A: Vector r(t)=<5cos(t),5sin(t),2t>  We have to find curvature of curve r(t)

Q: Expected answer: 718 + 11991 718 + 1199i (iii) (-2-j)º x Input the anwer in a + bi form, with…

A: De Moivre's Theorem z = r( cosθ + isinθ )then zn = rn( cosnθ + isinnθ ) where r is the modulus θ is…

Q: Consider the following. f(x, y, z) = 3 z=4-x XX E ZA (a) Express the triple integral z=4+x SIS f(x,…

A: We need to evaluate integral.

Q: Determine the work done by the vector field F along the curve y. F(x, y, z) = (x sin(2y), 2e²²,…

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Q: 6) Evaluate using series, and simplify the series formula as much as possible: 1 fexz ¹ dx

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Q: g(x)=√1 + 2x

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. 4…

A: ∫abg( x )dx represents the area under the curve g( x ) with sign from a to b

Q: find coordinates on the point y = 3x^2+5x+1 that has a slope of -7

A: given  y=3x2+5x+1 given slope is -7

Q: Convert the point (x, y, z) = ( − 5, — 4, 1) to cylindrical coordinates. Give answers either…

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Q: Question Given du = ux² where u(3) = 1, solve for u. dx Provide your answer below: u=

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Q: State the domain for the function h(x) = -ex-1: O (-00,00) O (-∞0, 0) O (0,00) O (-00, -1)

A: given function is h(x)=-ex-1

Q: The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial…

A: We have to find the interval which doesn't satisfy the intermediate mean value theorem.

Q: Find the limit as x goes to 4 without using l'hopital's rule ((sqrt2x+1)-3)/(x^3-64)

A: To find the given limit

Q: Evaluate the indefinite integral. [5 sin³ 5 sin3 x cos xd + C

A: An integral,

Q: For the following polynomial function f(x) = -x - 4x + 3, find the upper bound within which all of…

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Q: A homeowner wants to build a fence to enclose a 320 square yard rectangular area in his backyard.…

A: x=length of the rectangle y=width of the rectangle

Q: We are given the following power series and must determine the radius of convergence, R.

A: