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In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
Answer:
$2.72
Step-by-step explanation:
The increase from last week is the fraction ...
(new price)/(old price) -1 = (1.82/1.65) -1 = 17/165
so the amount of increase Sally will pay this week is ...
17/165×$26.40 = $2.72
_____
<em>Comment on the working</em>
We could work this several ways. Perhaps most straightforward would be to determine how many gallons Sally bought last week, and multiply that by the change in price. Or, the number of gallons could be multiplied by the new price per gallon and the difference from the old purchase amount found.
If you look at the numbers, you see that we have effectively done it the first way. The change in price is $0.17 per gallon, and the number of gallons Sally bought is $26.40/$1.65.
1 inch = 13.5 feet
5 inches = 5 * 13.5 = 67.5 feet
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