To solve this, we are going to use the formula for the area of the sector of a circle:
where
is the area of the circular sector.
is the radius of the circle.
is the central angle in radians.
We know form our problem that that the measure of the central angle is 1 radian, so
. We can also infer from the picture that the radius of the circle is 3in, so
. Lets replace those values in our formula to find
:
We can conclude that the area of the circular sector in the picture is
4.5 square inches.
To prove that the arc length is indeed 3 inches, we are going to use the formula:
where
is the arc length.
us the radius of the circle.
is the central angle.
We know from our problem that
, and
, so lets replace those values in our formula:
We can conclude that the length of the arc is indeed
3 inches.
We have two formulas:
Adult tickets plus Student tickets = 550 tickets or A + S = 550
and
Adult tickets times $20 plus Student ticket times $10 = $7500 or
(A * 20) + (S * 10) = 7500
First let's get rid of one of the variables by re-balancing the simplest formula
A+S = 550
A+S-A = 550-A
S = 550-A
Now we can restate the second formula replacing "S" with it's equivalent "550-A"
(A * 20) + (S * 10) = 7500
(A * 20) + ((550-A) *10) = 7500
Then do the multiplication
20A + 5500 - 10A = 7500
and simplifiy
20A + 5500 - 5500 - 10A = 7500 - 5500
20A - 10A = 2000
10A = 2000
A = 200
S = 550 - 200 = 350
Now we should test the answers to be sure our work
is correct:
200 Adult tickets times $20 = $4000
350 Student tickets times $10 = $3500
$4000 + $3500 = 7500
7p <span>≥ 40
p </span><span>≥ 5 2/7
There is no such thing as 5 and 2/7 of a friend, so he can buy lunch for 5 people.</span>
To find the rate of commission, divide the amount of commission by his total sales:
2704.94 / 38642.00 = 0.07 = 7%
The answer is D. 7%
Step-by-step explanation:
hmph................