Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w is u· (v × w)| to determine the volume of the tetrahedron with vertices P(-3,2,0), Q(2, 1, –3), R(1,0, 1) and S(3, –2, 3). NotE: Enter the exact answer. V =

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Q: 10. Maximize f(x, y) = 25 – ² - y² subject to 2x + y = 10

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A: A detailed solution is given below.

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A: Let's find.

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A: Given query is to find intererval where function is decreasing and local minimum location.

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Q: 3X 812x

A: To solve the following problem

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Q: Test the series below for convergence using the Ratio Test. n+5 52n +4 The limit of the ratio test…

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A: First we integrate r"(t) twice and then imposing given initial conditions we get our required…

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Q: For numbers 4-10, answer the following questions for the piecewise defined function f(t). t2 t+6 for…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: This is a problem related to vector calculation. Based on the general formula we will find the…

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A: a)β=10ln(10)lnI10-16β=10ln(10)lnI10-16β=10ln(10)ln(I)-ln(10)-16β=10ln(I)ln(10)+16ln(10)ln(10)β=10log…

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Q: The solution is y = (Type an expression.)

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Q: Find the particular solution determined by the initial condition. ds 16t2 + 5t – 5; s(0) = 100 dt

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Q: 4. Let f(x) be a function that satisfies f(3x) dx = 1 and 3f(x) dx = 15. Calculate f(x) dx. Show all…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the ezact answers in terms of i.j…

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Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: (3y²+ 2x³)dy + 2xydx=0

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution…

Q: log, r – log, (x + 10) = log, k. %3D 1 Find x if k 8

A: Log

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Q: Area inside the circle r = 3 cos 0 and outside the cardiod r = 1+ cos 0

A: The region which is inside the circle r=3 cos θ and outside the cardioid r=1+cos θ is:

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A: The given function,  f(x)=1x,if x≤1x2-1,if x>1

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Q: Find the vector component of v = (4, – 1,7) along b = (2, 6, –9) and the vector component of v…

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Q: 2. Determine the critical points, the maxima and minima, and the inflection points of the function y…

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Q: Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: Let the three positive integrar are x, y and z

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Q: Find the vector component of v = (4, -1,7) along b = (2, 3, –6) and the vector component of v…

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Q: th (a) Write a nonrecursive formula for the n term of the arithmetic sequence a based on the given…

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Q: sinh x 1+ cosh x

A: sinh x1+cosh x

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Q: If Arctan gx 3. dx =b Arctan* 3x +C, what is b?

A: Solving the given integral by substitution.

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Q: 3. Prove the following using the epsilon-delta definition of a lir a. lim (2x – 1) = 3 x→2

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Q: A Use the method of Lagrange multipliers in Problems 7-10. I SL.

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Q: Find a formula for f'(x) and determine the slopef'(-5) for the following function. 6e f(x) - Te* + 6…

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Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: Arctan°9x dx =b Arctan 3x+C, i+9x2 what is b?

A: Solving the given integral by substitution.