A 120 -ft flight control tower in the shape of a hyperboloid has hyperbolic cross sections perpendicular to the ground. Placing the origin at the bottom and center of the tower, the center of a hyperbolic cross section is 0 , 30 with one focus at 15 10 , 30 and one vertex at 15 , 30 . All units are in feet. a. Write an equation of a hyperbolic cross section through the origin. Assume that there are no restrictions on x or y . b. Determine the diameter of the tower at the base. Round to the nearest foot. c. Determine the diameter of the tower at the top. Round to the nearest foot.
A 120 -ft flight control tower in the shape of a hyperboloid has hyperbolic cross sections perpendicular to the ground. Placing the origin at the bottom and center of the tower, the center of a hyperbolic cross section is 0 , 30 with one focus at 15 10 , 30 and one vertex at 15 , 30 . All units are in feet. a. Write an equation of a hyperbolic cross section through the origin. Assume that there are no restrictions on x or y . b. Determine the diameter of the tower at the base. Round to the nearest foot. c. Determine the diameter of the tower at the top. Round to the nearest foot.
Solution Summary: The author calculates the equation of a hyperbolic cross section through the origin.
A
120
-ft
flight control tower in the shape of a hyperboloid has hyperbolic cross sections perpendicular to the ground. Placing the origin at the bottom and center of the tower, the center of a hyperbolic cross section is
0
,
30
with one focus at
15
10
,
30
and one vertex at
15
,
30
.
All units are in feet.
a. Write an equation of a hyperbolic cross section through the origin. Assume that there are no restrictions on
x
or
y
.
b. Determine the diameter of the tower at the base. Round to the nearest foot.
c. Determine the diameter of the tower at the top. Round to the nearest foot.
The correct answer is Ccould you show me how to do it by finding a0 and and akas well as setting up the piecewise function and integrating
T
1
7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
≤
and the curve y
y =
about the line
x =
=플
2
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY