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Match the equation with its graph (labeled I-VIII). Give reasons for your choice.

$ 9x^2 + 4y^2 + z^2 = 1 $

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01:23

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Johns Hopkins University

Missouri State University

University of Nottingham

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Match the equation with it…

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So for problem 22. We want to match the equation with its respective figure. So in this case, what we're given is a nine X squared plus four y squared plus Z squared equals one. This is going to be an ellipse oId. So that's the first thing that's helpful. But what's going to differentiate it from the other lip sides? Well, what's gonna differentiate it is the A value the B value and the C value. Recall that this, um the Ellipse ovoid form is X squared over a squared. So in order to get a nine here, are is gonna be one third in order to get a four. Here are B is going to be one half in order to get a one here, R C is going to be one. Using this information. We see that the lips oId um is more elongated along the Z axis. Um, and the one which is the C value than the number under Z squared is greater than the one half and the one third. So because it's more elongated along the Z axis, we see that figure four is going to be our correct answer

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