In this project, you play the role of a consultant to a bedding manufacturer. The manufacturer is interested in constructing a sleeping pod. In particular, you will use a number of tools from Calculus III (including optimization and parameterization) to advise the client on the construction of such a pod. The pod is to be in the shape of the ellipsoid + y² +2²=1. 1. Use a graphing utility to graph the ellipsoid in 3-space. 2. Derive a parameterization of the ellipsoid in terms of p and 8 (as in spherical coordinates). Find the volume of the ellipsoid. 3

Q: how do i graph the parabola y=3x2-1

A: NOTE: Refresh your page if you can't see any equations. . to graph the function we need a few…

Q: −8(y−3)=(x+2)^2

A:

Q: find the coordinates of the vertex and the focus for the parabola given by x2+6x+24y-111=0

A: SOLUTION-

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A: The graph of the function y=x2 is given.  The general form of a quadratic is y=ax2+bx+c. In the…

Q: Please solve part d) for attached question. Thanks

A: Step 1: Step 2: Step 3:Step 4:

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Q: 3x2 − 6x − 4y + 8 = 0 identify the standard form, vertex, focus, ends of latus rectum, directrix;

A: the solution is following.

Q: Which equation would shift the parabola down 3 units? A y=z² B y=z² +3 C_y=(z-3)² Dy=(z+3)²³ E =…

A: which equation would shift the parabola down to 3 units.

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Q: Define the term parabola?

A: Given: The term parabola.

Q: If the vertex of the parabola f (x)= x² +bx+c is at (7, -4), find b and c. (Note: a = 1).

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Q: 1) f(x)=x²-8x + 17

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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