Use polar coordinates to evaluate sin (a² + y²)³ dA, R

Q: Find the numbers A such that z = Ae¯* is a solution of y" – 6y + 8y = -2e¯* There are no values of A…

A: y"-6y'+8y=-2e-x                              (1) Given : z=Ae-x is a solution of (1)  So, z'=-Ae-x,…

Q: Convert to numbers 1. 3.937 x 105 = 2. 4.466 x 10 2 3. 1.2493 x 103 4. 7.295 x 10"

A: We have to convert into the given numbers

Q: Find the real numbers r such that x' is a solution of x²y' +3xy – 15y = 0. %3D a) Or = -3 andr = 5…

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Q: R. 5. From the figure above, if FA = (3x-3), IR = (2x + 6) what is the value of x ? a. 2 c. 5 d. 9…

A: FA=3x-3  &  IR=2x+6 5. Since the opposite sides of a parallelogram are equal, therefore…

Q: x² – xy² – x Evaluate lim (x,y) (1,0) Vx – 1+ y

A: We have to evaluate  lim(x, y)→(1, 0)x2-xy2-xx-1+y.

Q: (a) Assuming this to be the case, if a sample of 81 modified bars resulted in a sample average yield…

A: Let  be the population mean yield point of the modified bar.Given that,Population standard deviation…

Q: Determine the Laplace transforms of 3, 0 12

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Q: Utilize langrange multipliers to figure out the extreme values of f(x, y) =xy + 2 subject to the…

A: We have to find the extreme values of the function subject to the given constraints.

Q: Problem II: Find the shortest distance between the two skew lines x=1+2t,y=2– 3t,z=5t and…

A: The equations of two skew lines are, x=1+2t,y=2-3t,z=5tand x=2+s, y=3+2s ,z=1-s

Q: 2. A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x? – y² + 6y if they open…

A: Given: A cafe estimates a monthly profit, P(x, y)=27-x2-y2+6y and the region D=x, y∈ℝ2 : x2≤y≤4. To…

Q: The set of solutions of y = -2e-* – 12 cos(4x) + 2 is given by: a) O 2e-* + 3 sin(4x) + 2x + C b) O…

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Q: b. Here is a two-way table of the data. Regular Occasional No Total What proportion of males…

A: We are asked to look at parts d) and i) only here.

Q: c) Let f(x.y)= e. Find the directional derivative of f(xy) at the point (-3, 0) in the direction of…

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Q: Let t, be a specific value of t. Use the table of critical values t below to find tn-values such…

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Q: Question.4 (a) Use a graphing utility to estimate the absolute maximum and minimum values off, if…

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Q: differential equation y = C, sin(5x + C2) as its general solution. a) Oy" – 25y = 0 b) Oy" + 25y = 0…

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Q: Evaluate the following sum of iterated double integrals: -2у 2 •4–2y dr dy + | dx dy 0.

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Q: 1. 2 Question # 1: Consider the function f(x)= x e. In the following, the interpolating polynomial,…

A: We use the Taylor expansion of exponential function.

Q: Find the differential equation that has y = C1 + C2x as its general solution. a) Oxy" – 3y = 0 b) O…

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Q: Consider the transformation T: R³ R³ defined as (ED) - E T 3x-2y y+z-x 2 + 2y (a) Show that T is a…

A: Given :T xyz =3x-2yy+z-xz+2y To find : a T is a linear transformation                b  standard…

Q: Find the partial derivative indicated. Assume the variables are restricted to a domain on which the…

A: Given : ∂∂M4πr52GM

Q: Determine if y = Cx-+ C2x³ is the general solution of x²y" – xy – 3y = 0. If it is, find a solution…

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Q: Problem III: x'y + yz + xz' =9; P=(1, 4, 1) Find the following partial derivatives at the point P:…

A: given   x2y+yz++xz3=9     ...(1) ; P=(1,4,1)

Q: x' + xy? x' +x a) lim (x.y)-(0,0) x' - y b) lim (x,9)¬(0,0) X* + y* x* – 2x²y+ 4y² x* + 4y c) lim…

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Q: Find the real numbers r such that y = e"* is a solution of У + 5y + бу %3 0. a) Or = 3 andr = 2 b)…

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Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: Evaluate the given function ſ cos²xsin³dx cos$x а. cos³x + C 5 cos³x cos"x cos3 + C 3 b.- cosx с.…

A: Solution

Q: Suppose that one person in 1,000 people has a rare genetic disease. There is an excellent test for…

A: given data event A : have diseaseevent B : tests positiveP(A)  = 11000 = 0.001P(A') = 1 -0.001 =…

Q: 2x+5 (d)Using the method of Partial fractions find f- dx x2-8x+7

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Q: 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is…

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Q: Prove the following inequalities: Σ(1/ (1/1) ≤ logen, for all integer n ≥ 2. 1=2

A: