Given v=4i+j and w=i+4j (a) find the dot product v. w; (b) find the angle between v and w. (a) v.w= (Simplify your answer.)

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A: As per our company guidelines we are advised to solve only the first three sub parts. Kindly repost…

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A: To solve the differential equation: such that with initial conditions:

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A: As per guidelines, only the first question is solved. Please repost the other questions…

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A: We have The radius    r=4cm and angle    θ=45 degree

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Q: (1). The following series does it converge? (a). Enzo(5)". n=0

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Q: 5. For the following statement disprove using a counter example. r→q q^p S-P rvs ..

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Q: (a). 2t²u" + 3tu'- u = 0,t> 0

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Q: SSS (V.F) dr over the region x² + y² + 2² ≤ 25, where F = (x² + y² +2²) (xi+yj + zk).

A: Region:

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Q: S where t is the time in seconds. Approximate the average velocity of the object over each time…

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Q: (a) Consider the following function and its periodic extension: f(x) = sin z], where and F(x) =…

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Q: Problem 5: Given the triangle, express 4 in terms of a, b, and B. a. A=√B²+C²-2AB cos(a) b. A=√…

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Q: Exercise 1.4.26 The steady state temperature, u, of a plate solves Laplace's equation, Au= 0. One…

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Q: Consider the line L₁ described by r₁ (t) = (-t, 5+ 2t, 7 - 3t) and L₂ described by r₂(t) = (2+t,…

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Q: Consider the following implication, where n stands for an unknown integer. “If n is divisible by 10,…

A: Consider the following implication, where n stands for an unknown integer.“If n is divisible by 10,…

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Q: Consider the initial value problem y' + y = 9+2 cos 2t, y(0) = 0. 2 a) Find the solution of this…

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Q: We want to solve the following system using the Gauss-Jordan (i.e., Elementary Row Operations)…

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Q: Exercise 6: Let S be a monempty subset of R that is bounded below. Prove that inf S= - sup { -…

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Q: How many injective functions are there from {1, 2} to {a, b, c, d}?

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Q: 2] (A) Evaluate the integral , Ixyz] dV where V is the solid + ≤1

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Q: Two objects E and F are traveling by the following parametrically defined functions x = 2t - 4…

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Q: Winter temperatures tend to be cold in the city of Johnstown. The table of values represents the…

A: We can solve one part of above question.For remaining subparts you can repost the question again.

Q: Given real numbers a and b, establish the following formulas max{a,b} = (a + b + |a-b|) min{a,b} =…

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Q: 8. Prove that n!+1 and (n+1)!+1 are integer n. relatively prime for every positive

A: Given, and are two numbers and to prove that they are relatively prime.