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.
Evaluate the following integrals as they are written
Calculus lll
May I please have the blank lines completed, and final statement defined as a result?
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3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i,
and i.
(a) Verify the relations between this roots and the coefficients of the polynomial.
(b) Find the annulus region in which the roots lie.
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