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2 months ago

A merry-go-round has a radius of 18 feet. If a passenger gets on a

Mathematics

1 answer:

Zina [12.3K]2 months ago

6 0

Answer:

The rotation angle measures 2.11 °

Step-by-step explanation:

Stated as follows:

The radius of the circular path = r = 18 feet

The distance rolled by the wheel = l = 38 feet

Let us denote the angle of rotation as Ф

Now, according to the problem:

∵ the length of an arc at the center corresponds to an angle Ф

Thus,

distance rolled by the wheel = π × radius × $\frac{\Theta }{180^{\circ}}$

As 180° represents π radians

And π approximates to 3.14

Thus, distance rolled by the wheel = 180 °× radius × $\frac{\Theta }{180^{\circ}}$

That is l = r × Ф

So, Ф = $\frac{l}{r}$

Consequently, Ф = $\frac{38 feet}{18 feet}$

Therefore, Ф = 2.11 °

Thus, the rotation angle is Ф = 2.11 °

Hence, the rotation angle is 2.11 ° Answer

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13 days ago

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Answer:

2.1%

Step-by-step explanation:

The compound interest formula can be expressed as:

$A=P(1+I)^n\\\\P-Principal \\A-amount\\i-compound \ interest \ rate$

Starting with a Principal amount of $6000 and applying an interest rate of 1.5% for the first two years:

$A=P(1+i)^n\\\\A_2=6000(1+0.015)^2\\\\A_2=6181.35$

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1 month ago

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Find x if a =13 and C = 47 need help

Inessa [12570]

You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)

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2 months ago

Imagine that after washing 5 distinct pairs of socks, you discover that two socks are missing! of course, you would like to have

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Part A:

Considering the best possible outcome

The ideal case occurs if the two missing socks are from the same pair.
Consequently, there are 4 complete pairs remaining.

To choose 2 from the total of 10 socks (5 pairs), the number of combinations is given by 10C2 = 45.

Choosing 2 that are from the same pair means selecting one from 5 pairs, so the count is 5C1 = 5.

Thus, the probability for this best case is 5 / 45 = 1 / 9.

Part B:

Considering the worst-case outcome

This scenario occurs when the two missing socks are from different pairs.
As a result, we have 3 complete pairs left.

The total ways to select 2 socks from 10, again, is 10C2 = 45.

To select 2 that do not belong to the same pair, we calculate as follows: 10C2 - 5C1 = 45 - 5 = 40.

Therefore, the probability for the worst-case scenario is 40 / 45 = 8 / 9.

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1 month ago

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