What fraction OF the float were form either a dance group or a radio station? Written in simplest form

Please look at the picture, I need help ASAP.

forsale [732]

See below for the proof that the areas of the lune and the isosceles triangle are equal

<h3>How to prove the areas?</h3>

The area of the isosceles triangle is:

$A_1 = \frac 12r^2\sin(\theta)$

Where r represents the radius.

From the figure, we have:

$\theta = 90$

So, the equation becomes

$A_1 = \frac 12r^2\sin(90)$

Evaluate

$A_1 = \frac 12r^2$

Next, we calculate the length (L) of the chord as follows:

$\sin(45) = \frac{\frac 12L}{r}$

Multiply both sides by r

$r\sin(45) = \frac 12L$

Multiply by 2

$L = 2r\sin(45)$

This gives

$L = 2r\times \frac{\sqrt 2}{2}$

$L = r\sqrt 2$

The area of the semicircle is then calculated as:

$A_2 = \frac 12 \pi (\frac{L}{2})^2$

This gives

$A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2$

Evaluate the square

$A_2 = \frac 12 \pi (\frac{2r^2}{4})$

Divide

$A_2 = \frac{\pi r^2}{4}$

Next, calculate the area of the chord using

$A_3 = \frac 12r^2(\theta - \sin(\theta))$

Recall that:

$\theta = 90$

Convert to radians

$\theta = \frac{\pi}{2}$

So, we have:

$A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))$

This gives

$A_3 = \frac 12r^2(\frac{\pi}{2} - 1)$

The area of the lune is then calculated as:

$A = A_2 - A_3$

This gives

$A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)$

Expand

$A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2$

Evaluate the difference

$A = \frac 12r^2$

Recall that the area of the isosceles triangle is

$A_1 = \frac 12r^2$

By comparison, we have:

$A = A_1 = \frac 12r^2$

This means that the areas of the lune and the isosceles triangle are equal

Read more about areas at:

brainly.com/question/27683633

#SPJ1

5 0

1 year ago

Reggie will finance a car with a sticker price of $9,250. he pays $1,500 down payment he finances the car and makes 48 monthly p

Minchanka [31]

Answer: Reggie will end up paying $9900 for the car.

Step-by-step explanation:

Down-payment = $1500

48 monthly payments x $175/month = $8400

Total cost = $1500 + $8400 = $9900

5 0

3 years ago

What is angle 2? I don’t know this please help me

cricket20 [7]

Answer:

Acute angle

Step-by-step explanation:

Since it's measure is less than 90 degrees

6 0

3 years ago

A tire shop starts off with the same number of tires every month. In January,

7nadin3 [17]

Answer:

the answer is B

Step-by-step explanation:

4 0

3 years ago

The aorta is the largest artery in the human body. In the average adult, the aorta attains a maximum diameter of about 1.18 inch

Sholpan [36]

Well we know that 1 inch is 2.54 cm. But how wide is .18? Lets do .18 x 2.54 to get 0.4572. Now lets add 2.54 + 0.4572 to get 2.9972. This means that the maximum width of the aorta is 2.9972 cm. Hope this helped :)

3 0

3 years ago