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irakobra [83]
3 years ago
5

Mr. Ramsey just finished bathing his kids, and now he is draining the tub. The tub contains 32 gallons of water and is draining

at a rate of 3 gallons per minute. After 7 minutes, how many gallons are left in the tub?
Mathematics
1 answer:
KIM [24]3 years ago
7 0
The answer would be 11 gallons.

The tub starts with 32 gallons. Every minute it loses 3 gallons.

So after 1 minute it has lost 3 gallons. For example:
32-3= 29 Meaning that after 1 minute the tub has 29 gallons left.

Now you have to remember that the tub is draining for 7 minutes. So it is losing 3 gallons 7 times, because it loses 3 gallons each minute and there are 7 minutes.

We can use multiplication to find how many gallons the tub loses after 7 minutes. This sign “X” basically means “groups of”. We have 7 groups of 3, or
7 X 3

This is the same as saying we have 3, 7 times. Written like this:

3+3 +3 +3 +3 +3 +3 = 21

So after 7 minutes the tub has lost 21 gallons.

Now we take the original number of gallons and take away what was lost:

32-21=11

So there are 11 gallons left after 7 minutes.

Please let me know if you need any further explanation. Hope this helped.

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a. sin (17pi / 4 )

We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to 2\pi:

17 \pi/4 - 2\pi = \frac{9\pi}{4} -2\pi = \pi/4

For this case we know that sin (\pi/4) = \frac{\sqrt{2}}{2}

So then sin(\frac{17 \pi}{4}) = \frac{\sqrt{2}}{2}

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We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to 2\pi:

19 \pi/6 - 2\pi = \frac{7\pi}{6}

For this case we know that cos (\pi/6) = \frac{\sqrt{3}}{2}

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c. tan(450pi)

For this case that any factor of \pi the sin function is equal to 0.

So from definition of tan we have this:

tan (450\pi) = \frac{sin(450 \pi)}{cos(450 \pi)}= \frac{0}{cos(450\pi)}= 0

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3 years ago
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