A rectangle is constructed with its base on the diameter of a semicircle with radius 27 and with its two other vertices on the semicircle. What are the The rectangle with maximum area has base and height. (Type exact answers, using radicals as needed.)

Q: Problem 2. Do both parts. 8 Part (a) Find the sum: 12 4 + +· 3 9 27 81 Part (b) Solve the equation…

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A: All the answers are given below

Q: 2. Let f(x)=x-3x² a. Determine all x-values where f(x)=0 b. Fill in the table below with the…

A: This question can be solved using the concept of points of inflection.

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Q: 4. A|-2,5 А = 2, B = 3 and the angle formed by A and B is 120°. Determine the unit vector in the…

A: Solving

Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: Dividing the polynomial P(x) by x-1 yields a quotient Q(x) and a remainder of 4.  If Q(-1)=3, Find…

A: P(x) =Q(x) (x-c) + R(x)when the factor is (x-1)R(x)=4P(x)=Q(x) (x-1)+4P(1) =0 +4P(1) =4

Q: 5. y = 2 sin x y

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Q: Current Attempt in Progress Evaluate the definite integral. e i + e='j+t k )dt

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A: The given equation is xln(y)=ztan-13zy ........................................ (1)  Here z =…

Q: Use Chain Rule to find ds given w = Vr² – 2y + z² and r = cos (st), y = -2s Int and z = s –

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Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: Solve the given initial-value problem. y'' + 4y' + 5y = 35e−4x,  y(0) = −2,  y'(0) = 1 y(x)=

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Q: Find the relative maximum and minimum values. f(x,y)=x² + y² + 12x - 2y Select the correct choice…

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Q: y= v-2² +2²-2x+ 8 (a) Find y'= f'(x). f'(x)=x²+x-2 (b) Find the critical values. (Enter your answers…

A: Solve it

Q: Let F = Vf and f = 2zy + 8xy + 6xz. Calculate F. dr for the path r₁ = (t,t,t), 0 ≤ t ≤ 1. (Give your…

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Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

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Q: (4n². En=1 2 - 2n + 6, - limit comparison test -1 (8,² + n – 8) 7

A: The given series,      ∑n=1∞4n2-2n+68n7+n-8

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Q: Solve the system using Cramer's Rule. - 6x + 6y3z = 15 x - 2y + z = 7 4x5y4z = - 28 Find the…

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Q: QUESTION 1 Find ay/dx?- X = t + sint, y = t- cost

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Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

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A: This is a problem related to mensuration. Based on the formula for volume of cone and derivative…

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Q: n E (4 + 2k)? = k=1 Hint: Start by multiplying out (4+ 2k)².

A: I am attaching image so that you understand each and every step.

Q: 1. JC y = f(x) is transformed to g(x) = 3 f (2x – 6) + 9. The domain and the range of each function…

A: Solving

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Q: + + Find the area of the portion of Sphere x² + y² + 2 = 9 betw= the planes Z=1 and 2 = 0. Draw

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Q: Evaluate the following integrals by substitution. Show your complete solution. Express your answer…

A: We have to find integral solution

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A: Here, the feasible region by the curves x+y≤1034x+y≤160y≥23x,y≥0 is:

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Q: Question Suppose that you are estimating sin (0.3) using the third Maclaurin polynomial for sin (x).…

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A: The below image has all the steps

Q: The eigenvalues of the matrix 139 - 84 240 145 (a) Find an eigenvector corresponding to X₁ = 1 X1 =…

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Q: 8. If the graph of h(x) goes thro following statements are true fc

A: 8) y=h(x)g =h(x)This transformation only affects y-value.A(-16, 4)y(x=-16)=4, g(x=-16)=4 =2A' (-16,…

Q: Select the representations that do not change the location of the point a. [-2.-357) D. (-2,-²5) b.…

A: -2, 7π5=-2cos7π5, -2sin7π5π+2π5=7π5=2 cos2π5, 2cos2π5  [FIRST Quadrant]A)-2 cos3π5,…

Q: 42. If g(0) = 0 sin 0, find g"(π/6).

A: Solve the given

Q: Let C be the parametric curve defined by x(t) = t² – t – 2, %3D |y(t) = t3 . 1 t² +t. 2 - (-2) 3…

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Q: X-Z The iterated integral J = g(x, y, z) dy dx dz is equivalent SS 0z0 to which of the following…

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Q: f(#n) for For the function f(x) 3x +1, write Newton's formula as , 1 - F(En) f'(an). solving f(x) 0.…

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Q: St-1.0t vemos anoitasu) InemzeozeA B C E M N K JH G Identify each of the following in the figure…

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Q: Figure (a) shows a vacant lot with an 80 ft frontage in a development. To estimate its area, we…

A: It is midpoint Riemann sum      here length of interval  △x=20

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