Answer:
- length 100 ft
- height 30 ft
Step-by-step explanation:
The center is 40 ft from the focus, so the wall is 40+10 = 50 ft from the center. From wall to wall must be 2×50 ft = 100 ft.
The length is 100 ft.
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Assuming the gallery has an elliptical vertical cross section, the distance from the focus to the center ceiling is the same as half the length of the gallery, so we can use the Pythagorean theorem to find the height:
50² = 40² + h²
h = √(2500 -1600) = √900 = 30
The height of the ceiling at the center is 30 feet.
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<em>Comment on the geometry</em>
We expect the gallery to have an elliptical floor plan, rather than an elliptical vertical cross section. In the latter case, the focus would have to be above the floor for it to work, so the ceiling at center would have to be higher than 30 ft. by the distance that the focus is above the floor.
Yes
Y varies directly with x, it is a direct relationship between the two.
Answer:
C = 5.
Step-by-step explanation:
First, you need to remember that:
For the function:
h(x) = Sinh(k*x)
We have:
h'(x) = k*Cosh(k*x)
and for the Cosh function:
g(x) = Cosh(k*x)
g'(x) = k*Cosh(k*x).
Now let's go to our problem:
We have f(x) = A*cosh(C*x) + B*Sinh(C*x)
We want to find the value of C such that:
f''(x) = 25*f(x)
So let's derive f(x):
f'(x) = A*C*Sinh(C*x) + B*C*Cosh(C*x)
and again:
f''(x) = A*C*C*Cosh(C*x) + B*C*C*Sinh(C*x)
f''(x) = C^2*(A*cosh(C*x) + B*Sinh(C*x)) = C^2*f(x)
And we wanted to get:
f''(x) = 25*f(x) = C^2*f(x)
then:
25 = C^2
√25 = C
And because we know that C > 0, we take the positive solution of the square root, then:
C = 5
Answer:
round cake - 82.42 in^2
rectangular cake - 114 in^2
Round cake:
d = 7 in
r= d/2 = 7 in /2 = 3.5 in
h = 2
The surface area of a cylinder is: A = 2pie r^2 + 2pie rh The surface are of the round cake (cylindrical cake) excluding the bottom is
Area = 2pie r^2 + 2pie rh - pie r^2
Area = pie r^2 + 2pie rh
Area = 3.14 * 3.5² + 2 * 3.14 * 3.5 * 2
= 38.46 + 43.96
= 82.42 in^2
Rectangular cake:
w = 6 in |= 9 in h = 2 in
The surface area of a rectangle
A = 2wl + 2wh + 2lh
The surface are of the rectangular cake excluding the bottom is
A = 2wl + 2wh + 2lh - wl
A = wl + 2wh + 2lh
A = 6 * 9 + 2* 6 * 2 +2 *9 * 2
= 54 + 24 +36
= 114 in^2