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3 years ago

After completing 60 laps in a race, the runner has completed 24% of the race. How many laps does the race have?

Mathematics

1 answer:

steposvetlana [31]3 years ago

3 0

250 laps total. I used cross multiplication to solve it

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Find the length of the arc and express your answer as a fraction times pie

Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

4 0

1 year ago

Try It for Example 3: Is 3.14144144414444... a rational number? Explain your reasoning. *

chubhunter [2.5K]

it's irrational

A rational number can be put over a fraction, while this number continues forever

5 0

3 years ago

Read 2 more answers

A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels,

VLD [36.1K]

He would use 9 bills, and 5 coins. (fours $10, one $5, four $1. three quarters, one dime, and one penny). I calculated it all to make sure the total came out as 49.86

8 0

3 years ago

Read 2 more answers

What is the value of RT or x

Anna007 [38]

Write and solve an equation of ratios:

x 9

---- = ----

16 x

Cross mult., we get x^2 = (16)(9)

Taking the sqrt of both sides, we get x = plus or minus (4)(3), or

x= plus or minus 12

Since x is measure of distance here, omit the -12 result. x = +12 units

7 0

3 years ago

Which problem can be represented by the equation 100x+50=710?

andrew-mc [135]

Answer: The first answer

A coin bank can hold 710 coins. There are 50 coins in the bank. A student puts in 100 coins per week. How many weeks until the bank is full?

Step-by-step explanation:

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3 years ago