In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration. Pluto The perihelion of Pluto is 4551 million miles, and the distance from the center of its elliptical orbit to the Sun is 897.5 million miles. Find the aphelion of Pluto. What is the mean distance of Pluto from the Sun? Write an equation for the orbit of Pluto about the Sun.
In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration. Pluto The perihelion of Pluto is 4551 million miles, and the distance from the center of its elliptical orbit to the Sun is 897.5 million miles. Find the aphelion of Pluto. What is the mean distance of Pluto from the Sun? Write an equation for the orbit of Pluto about the Sun.
In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration.
Pluto The perihelion of Pluto is 4551 million miles, and the distance from the center of its elliptical orbit to the Sun is
million miles. Find the aphelion of Pluto. What is the mean distance of Pluto from the Sun? Write an equation for the orbit of Pluto about the Sun.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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