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olchik [2.2K]
3 years ago
15

The sum of twelve and four times a number is 36. What is the number?

Mathematics
1 answer:
Greeley [361]3 years ago
3 0

Answer:

8

Step-by-step explanation:

12 +4x = 36

Then solve the linear eqn

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A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one comp
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y = 11 - 10cos(0.1\pi t)

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Suppose at t = 0 the person is 1m above the ground and going up

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2π / 20 = 0.1π rad/s

The height above ground would be the sum of the vertical distance from the ground to the bottom of the wheel and the vertical distance from the bottom of the wheel to the person, which is the wheel radius subtracted by the vertical distance of the person to the center of the wheel.

y = h_g + d_b = h_g + R - d_c (1)

where h_g = 1 is vertical distance from the ground to the bottom of the wheel, d_b is the vertical distance from the bottom of the wheel to the person, R = 10 is the wheel radius, d_c is the vertical distance of the person to the center of the wheel.

So solve for d_c in term of t, we just need to find the cosine of angle θ it has swept after time t and multiply it with R

d_c = Rcos(\theta(t)) = Rcos(\omega t) = 10cos(0.1\pi t)

Note that d_c is negative when angle θ gets between π/2 (90 degrees) and 3π/2 (270 degrees) but that is expected since it would mean adding the vertical distance to the wheel radius.

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