2.625 gallons a day
14 oz x 24 hours = 336 oz per day
336 oz converted to gallons is 2.625 gallons
The answer would be 1,053
<span>since sin and cos = each other at pi/4; take your integrals from 0 to pi/4
</span><span>[S] cos(t) dt - [S] sin(t) dt ;[0,pi/4]
</span>
<span>to revolve it around the x axis;
we do a sum of areas
[S] 2pi [f(x)]^2 dx
</span>
<span>take the cos first and subtract out the sin next; like cutting a hole out of a donuts.
</span><span>pi [S] cos(x)^2 dx - [S] sin(x)^2 dx ; [0,pi/4]
</span>
<span>cos(2t) = 2cos^2 - 1
cos^2 = (1+cos(2t))/2
</span>
<span>1/sqrt(2) - (-1/sqrt(2) +1)
1/sqrt(2) + 1/sqrt(2) -1
(2sqrt(2) - sqrt(2))/sqrt(2) = sqrt(2)/sqrt(2) = 1</span>
Bring the 3 to the other side, which makes 11-3 = 8
divide the whole equation by 2, which makes it Root (3x/5) = 8/2
square the whole equation which gives
, 3x/5 = 16
Multiply the equation by 5 which makes it, 3x = 80
finally divide the equation to find x, x= 80/3
