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.
Write the given third order linear equation as an equivalent system of first order equations with initial values.
Use
Y1 = Y, Y2 = y', and y3 = y".
-
-
√ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t²
\y(3) = 1, y′(3) = −2, y″(3) = −3
(8) - (888) -
with initial values
Y
=
If you don't get this in 3 tries, you can get a hint.
Question 2
1 pts
Let A be the value of the triple integral
SSS.
(x³ y² z) dV where D is the region
D
bounded by the planes 3z + 5y = 15, 4z — 5y = 20, x = 0, x = 1, and z = 0.
Then the value of sin(3A) is
-0.003
0.496
-0.408
-0.420
0.384
-0.162
0.367
0.364
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