A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b. Explain how you know that this plane passes through the origin. c. Write the coordinates of three points on this plane.

Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

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A: A manufacturer of tin boxes wishes to make open boxes from pieces of tin withdimensions 8 in. by 15…

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A: Bn

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A: Topic = Vector

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Q: Q3/ solve the differential equation below: 1. 2-3x+2y=0 (Complementary Function) k

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A: linearization

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A: We have to set up the integral that will give the volume.

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A: Solution: ∫7cos 6xdx Apply integration by parts

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A: Given:  r(t)=<5cot(t), 3 sin(t), 4 sin(t)>To find:  Arc length form t=0 to t=2π

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A: Use algebraic concept

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Q: 1. 2y"" Hardcore 0 7y"+12y + 8y

A: To solve the given differential equation.2y'''-7y''+12y'+8y=0

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Q: By the definition of derivative prove that f(x) = = √x² + 5 is differen- 4. tiable at x=2.

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A: As per bartleby guidelines we only give first question answers.