b) Find the value(s) of z such that the angle between the vectors U₁ = <3, 5, 0> and U₂ = <27, 45, z> is equal to 30°.

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A: The objective of the question is evaluate the indefinite integral.

Q: The alternating series En-1 (-1)" is diverge. n³ 2n³+3 True O False

A:

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A:

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A:

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A:

Q: Which of the following is a point on the sphere with radius r = 3 centered at the point (-1,0, -1)?…

A: We have given a center and radius of sphare

Q: Show that the following equations have at least one solution in the given intervals, rcos t 2x² +…

A:

Q: find the divergence of F. I Y F(x, y) = -√2²17³1 + √z²+z³³ +y O div F = 2(x+y+z) O div F= 1 1²+y²

A:

Q: The integrating factor for the differential equation (xy³)dx + (x²y² + 1)dy = 0 is

A:

Q: Let a = ( − 4, 4, − 3) and b = (0, 2, 1). Find the angle between the vector (in radians)

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Q: We want to use the Alternating Series Test to determine if the series: cos² (**)_~_~(*))) k 3k k=1…

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Q: 5. Obtain a polynomial P(x) such that f(x) = P₁(x) given the table -1 -3 x₁ f(x₂) -2 -13 1 -1 2 -9 3…

A:

Q: A lighthouse, L, is on an island 8 mi away from the closest point, P, on the beach. If the…

A:

Q: x fare cos = dx 2

A: Indefinite Integration

Q: S: x²(In x) dx

A: We can find the integration as below.

Q: 1. If y = sin x² x =²), ex find dy dx

A: Given y=sinx2-xex To find dydx

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A: We can solve the question as below.

Q: If f(x, y) = cos(2x) - x² e5y + 3y², then fxy = -10x e5y True False O

A:

Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then f xy = -10x e5y True O False O

A: I have stated the used formulas in the solution.

Q: (9) The differential equation M(x, y)dx + (2ye* + y²e³x) dy = = is exact if (a) M(x, y) = e2x y² +…

A:

Q: f(x) = 2 cos x - cos 2x.

A: Given function f(x) =2 cos x - cos 2 x    ; [0, 2π]

Q: Determine the Cartesian equation of the line passing through A(4, -2), which has 7=(5, 3) as its…

A:

Q: Question 12 a) 3] Find the value(s) of y such that the vectors U₁ = and U₂ = are parallel. b) Find…

A:

Q: If a xi = 0 and a x j = 0, then Select one: O a is equal to i + j a cannot be determined O a is…

A: Find out the correct option.

Q: 32. a) Determine the vector equation of the line of intersection of these 2 planes: x + 2y + 2z = -3…

A: According to Bartleby guidelines I can only answer the first question of the given two problems.

Q: Let D be the portion of z = 2x + 5y inside x² + y² = 1, oriented up, and let F = (3, 2, -2). Compute…

A:

Q: Use the Midpoint Rule with = 4 to approximate 0 tan x dx.

A:

Q: If # f(x) > 48 for x [2,10], then b [ f(a) da ≥ 384, where a =2 and b = 10. a Select one: O True O…

A: First I have written a property of integral and easily find the True is correct option.

Q: If the volume of the parallelepiped determined by the vectors A = i + ak, B = 8i - 5j + ak and C =…

A:

Q: What two positive real numbers whose product is 19have the smallest possible​ sum?

A: We want to find the two positive real numbers whose product is 19 and the smallest possible sum.

Q: (d) dx Oseparable exact linear in x linear in y homogeneous 0 Bernoulli in x Bernoulli in y Onone of…

A: Explanation of the answer is as follows

Q: Differentiate ex with respect to x, assuming that y is implicitly a function of x.

A: Here we have to use the concept of implicit derivative

Q: Q31 Find the Laplace Transform to the following function L sin2t cos3t

A:

Q: Find the point P on the line y=2xthat is closest to the point (25,0). What is the least distance…

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Q: 14. Find the volume of the tank shown below. 1.10 m | 1.48 m 4.25 m

A: Concept: Area of the segment: A Sector is made up of an Arc and Two Circle Radii. Together, these…

Q: dy (8) The solution of differential equation: + y = xy³ is dx (a) = x + ²+ce²ª, y (b) = x² + + ce²x,…

A: Using differential equations

Q: The radius of a circle is increased from 2cm to 2.03cm find approximately increase in area

A: Solving using differentiation

Q: (x²+1)³ .dx

A:

Q: Which of the following is the area of the region bounded by the function y = x ^ 2 the vertical…

A: To find area of the bounded by the function.

Q: SC₁+ Fuj³d₂ dn

A:

Q: b) Determine, showing steps, whether the line [x, y, z] = []+¹] intersects the plane: 3 x + 7y + 8z…

A: We have to find the intersection of plane and line.

Q: 2л 1. The region R is bounded by the x-axis, x = 0, x=- 3 A. Find the area of R. 3sin(). 2 and…

A: Given:

Q: Find the area of the region bounded by y² = 8x and y = 2x. A. 1.22 sq. units B. 1.33 sq. units C.…

A: We have given two curve in above problem. We have to find area between them

Q: <2, U = < 4, 5, x

A:

Q: 1.5(8x³ - 6x² + 12x − 9)dx - 2.S √x(x² − 3x + 2)dx • (x-1)² dx √x 3.f

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: a $0.9062 cos (1-√3x) dx = = : -0-1 a=0.5968

A: We have given a definite integral problem

Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A:

Q: 1.5(8x³ − 6x² + 12x - - 9)dx

A: Using the formula of integration x^n