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ra1l [238]
3 years ago
10

A water wheel has a radius measuring between 13 feet and 24 feet. The wheel is able to turn 7π9 radians from its starting positi

on before getting stuck. Which distances could the wheel spin before it would no longer be able move?
Mathematics
1 answer:
madam [21]3 years ago
4 0

Answer:

31.76 ft and 58.64 ft

Step-by-step explanation:

The radius measures between 13 feet and 24 feet.

The wheel is able to turn 7π/9 radians before getting stuck.

We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.

Length of an arc is given as:

L = \frac{\theta}{2\pi} * 2\pi r

where θ = central angle = 7π/9 radians

r = radius of the circle

Therefore, for 13 feet:

L = \frac{7\pi}{18 \pi} * 2 * \pi * 13\\\\L = 31.76 ft

For 24 feet:

L = \frac{7\pi}{18 \pi} * 2 * \pi * 24\\\\L = 58.64 ft

The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.

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Isolate the t, divide 48.3 from both sides

(545.79)/48.3 = 48.3t/48.3

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1. Write the following in exponential form and as a multiplication sentence using only 10 as a factor
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1. a. 1,000 = 10³ = 10 × 10 × 10

b. 100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

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Step-by-step explanation:

3. a. 1,000

There are 3 zeros in 1000. This is equivalent to 10 raised to the power of 3. Writing this in multiplication sentence using 19 as the only factor, we would have:

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800 ÷ 1,000 = 0.8

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754.2 ÷ 100 = 7.542

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