A tunnel has vertical sides of 7 ft with a semielliptical top. The width of the tunnel is 10 ft, and the height at the top is 10 ft. a. Write an equation of the semiellipse. For convenience, place the coordinate system with 0 , 0 at the center of the ellipse. b. To construct the tunnel, an engineer needs to find the location of the foci. How far from the center are the foci?
A tunnel has vertical sides of 7 ft with a semielliptical top. The width of the tunnel is 10 ft, and the height at the top is 10 ft. a. Write an equation of the semiellipse. For convenience, place the coordinate system with 0 , 0 at the center of the ellipse. b. To construct the tunnel, an engineer needs to find the location of the foci. How far from the center are the foci?
Solution Summary: The author explains the standard equation of an ellipse, which is given by the formula x2a2,&b=1.
A tunnel has vertical sides of
7
ft with a semielliptical top. The width of the tunnel is
10
ft, and the height at the top is
10
ft.
a. Write an equation of the semiellipse. For convenience, place the coordinate system with
0
,
0
at the center of the ellipse.
b. To construct the tunnel, an engineer needs to find the location of the foci. How far from the center are the foci?
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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.
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