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:

Where r represents the radius.
From the figure, we have:

So, the equation becomes

Evaluate

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

Multiply both sides by r

Multiply by 2

This gives


The area of the semicircle is then calculated as:

This gives

Evaluate the square

Divide

Next, calculate the area of the chord using

Recall that:

Convert to radians

So, we have:

This gives

The area of the lune is then calculated as:

This gives

Expand

Evaluate the difference

Recall that the area of the isosceles triangle is

By comparison, we have:

This means that the areas of the lune and the isosceles triangle are equal
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Answer:
a. it is arithmentic - this is because for each term there is a constant increase of 4, and the change between each term <u>doesn't change</u>
b. you need to find the nth term, by using the equation difference x n + 0th term: the difference is (+)4 and the 0th term is -9 (-5 is the 1st term, so to go one back we subtract 4 - the inverse operation), so the nth term is 4n -9. Now we do the inverse operation on 119 to see if it's a term (it is a term if it's an integer. So, first we do 119 <u>plus</u> 9 (inverse of - 9) to get 128, then divide it by 4 rather than multiplying. This gives us 32, and that tells us that 119 is the 32nd term of the sequence.
Answer:
48
Step-by-step explanation:
6(miles per day) * 8(days) = 48
Factor the equation so...
(r^2-pr) and (p^2q-pqr)
Factor out (r^2-pr) = r(r-p)
Factor out (p^2q-pqr) = pq(p-r)
Add a negative to r(r-p) to make it -r(p-r)
(pq-r)(p-r) is the answer... I'm sorry I can't explain things well, but I tried.
Answer:
d
Step-by-step explanation:
there is only 4 of her ponies that are over 96 centimeters but it is not 40 percent but 27 percent because she has 14 ponies not 10 ponies