Findd total collected
add everybody
fri+sat+sun+mon=
21+5 and 5/6+2.75+4 and 5/8
add what you can
21+5+2.75+4+5/6+5/8=
28.75+5/6+5/8
add the fractions by making denom same
5/6+5/8=20/24+15/24=35/24=1 and 9/24=1 and 3/8
28.75+1 and 3/8=29.75+3/8
that is how many barels total
times 205 since that is how many litesr in each bottle
205 times (29.75+3/8)=
205*29.75+205*(3/8)=
6098.75+76.875=
6175.625

29/30 is lost

1//30 remains
9175.625 times 1/30 (aka divided by 30)=205.854166666666666 litesr
205 bottles (and 0.85 partially full bottle)

3 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Only 1 try

vagabundo [1.1K]

Using the shell method, the volume is

$\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx$

Each cylindrical shell has radius $2-x$ (the horizontal distance from the axis of revolution to the curve $y=8x^3$ ); has height $8x^3$ (the vertical distance between a point on the $x$ -axis in $0\le x\le1$ and the curve $y=8x^3$ ).

Compute the integral.

$\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}$

6 0

1 year ago