Find the angle between the vectors. u=3i-j, v = -2i+5j+2k The angle between the vectors is 0 (Round to the nearest hundredth as needed.) radian(s).

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A: sinh⁡(x)=34sinh⁡x=12(ex−e−x)

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A: The given integral is .The aim is to find the value of the integral.Formula used:

Q: Find the average value of the function f(x)=√ x over the interval [0, 4]

A: f(x)=x over the interval [0,4]Average value of the function f(x) on [a,b] is given asfave…

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Q: Use the Comparison Test to determine the convergence of the following series. n=1 n sin² n n³ + 1

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Q: Solve the rational inequality x²-9 x² - 49 -≤0.

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Q: Find the area under the given curve over the indicated interval. y = 4x; x =1 to x = 3

A: y=4x, x=1 to x=3

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Q: Find the area between the graph of f(t) = -2t for 0 ≤ t ≤ 4 and the t-axis using areas of triangles.…

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Q: Find the area under the given curve. y = √√x +6; from x=0 to x = 16

A: Consider the curve

Q: Find the domain of the function. f(x) = -5x + 3

A: f(x)=-5x+3

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: The objective of this question is to find the relative extrema of the function f(x) = sqrt(25 - x^2)…

Q: Sketch the slope field and sketch two solutions for the differential equation. (a)

A: Since you have posted multiple questions in a single request, we will solve first question for you.…

Q: A cup of coffee has cooled from 98°C to 50°C after 10 minutes in a room at 25°C. How long will it…

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Q: Suppose f(x) = 3x -2. Find f (x+²) 3 (x+2) 3 (Simplify your answer.)

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Q: ηλη Σ (2η)! n=1

A: The given series .The aim is to determine whether the given series is converges or diverges.Ratio…

Q: Evaluate the limit, use L'Hospital's Rule when possible. limx→0 5x In(x+2) O-5 01/2 0 5 Not Possible

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Q: 31. 3 1-25x2 dx

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: d) Write an expression that represents the approximate value of g(x) for a generic value x in the…

A: The graph of the function g'(x) is shown as,

Q: Find the linearization L(x) of f(x) at x = a. f(x)=x+, a= 2 3 O A. L(x)=x+1 3 2 23 OB. L(x)= x+3 5…

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Q: The graph of f(x) is given below. Select each true statement about the continuity of f (x) at x = 3.…

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Q: Given f'(x) = 6x + 5, compute f(4) – f(1). -

A: Explaination of the answer is as follows

Q: Find the area A of the region that is bounded between the curve f(x) and the curve g(x) sin (x) over…

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Q: 17. The amount, A, of 108 grams of a certain radioactive material remaining after years can be found…

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Q: Solve the initial value problem below using the method of Laplace transforms. ty'' - ty' + y = 5,…

A: The initial value problem is given as,solve the problem.

Q: Find the sum of the series: n=3 3n+2 57-3

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Q: The population of the world in 1987 was 5 billion and the continuous growth rate was estimated at…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

A: To simplify the following expression.

Q: S 3 6x²4x³ dx 24

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Q: Evaluate I = (sin x + 2y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. y C B A=…

A: Here  we have to find the integral along closed path.

Q: For f(x) = (a) fog 7 x-3 2 =, find the following composite functions and state the domain of each. X…

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Q: 1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke…

A: Here given a different sentences.The objective is to check that the given sentences are valid,…

Q: Graph the following function. Then use geometry (not Riemann sums) to find the area and the net area…

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Q: Determine the area of the given region under the curve. 1 y X

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Q: Find f such that f'(x) = 9 √x f(9) = 59.

A: f′(x)=9x,f(9)=59

Q: Find all solutions of the equation in the interval [0,2+). 2 sin 20-3 sin 0+1=0

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Q: 2) Find the derivative of the function f(x)= x arctan(2x) ——In(1+4x²).

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Q: Given the three functions below, which expression equals (zo go t) (x)? g(x) = |3x| Answer 6 ○ |3 (8…

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Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: Find the center, foci, and vertices of the ellipse. Graph the equation. 4(x+4)² +8(y - 3)² = 32 Find…

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Q: 37. se sec² (10x + 7) dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: (c) (d) (e) creasing? Does g(x) have any critical points? If any, identify all critical points. On…

A: Given: To Find: (c) To find the critical points if any of g(x).(d) To find the interval(s) on which…