Step-by-step explanation:
7.3 when rounded to the nearest tenth
Answer:

Step-by-step explanation:
From similar triangles, see diagram in attachment

We solve for
to obtain,

The formula for calculating the volume of a cone is

We substitute the value of
to obtain,

This implies that,

We now differentiate both sides with respect to
to get,

We were given that water is drained out of the tank at a rate of 
This implies that
.
Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means
.
We substitute this values to obtain,




now, let's take a peek at the denominators, we have 3 and 8 and 12, we can get an LCD of 24 from that.
Let's multiply both sides by the LCD of 24, to do away with the denominators.
so, let's recall that a whole is "1", namely 500/500 = 1 = whole, or 5/5 = 1 = whole or 24/24 = 1 = whole. So the whole class will yield a fraction of 1/1 or just 1.
![\bf ~\hspace{7em}\stackrel{\textit{basketball}}{\cfrac{1}{3}}+\stackrel{\textit{soccer}}{\cfrac{1}{8}}+\stackrel{\textit{football}}{\cfrac{5}{12}}+\stackrel{\textit{baseball}}{x}~=~\stackrel{\textit{whole}}{1} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{24}}{24\left(\cfrac{1}{3}+\cfrac{1}{8}+\cfrac{5}{12}+x \right)=24(1)}\implies (8)1+(3)1+(2)5+(24)x=24 \\\\\\ 8+3+10+24x=24\implies 21+24x=24\implies 24x=3 \\\\\\ x=\cfrac{3}{24}\implies x=\cfrac{1}{8}](https://tex.z-dn.net/?f=%5Cbf%20~%5Chspace%7B7em%7D%5Cstackrel%7B%5Ctextit%7Bbasketball%7D%7D%7B%5Ccfrac%7B1%7D%7B3%7D%7D%2B%5Cstackrel%7B%5Ctextit%7Bsoccer%7D%7D%7B%5Ccfrac%7B1%7D%7B8%7D%7D%2B%5Cstackrel%7B%5Ctextit%7Bfootball%7D%7D%7B%5Ccfrac%7B5%7D%7B12%7D%7D%2B%5Cstackrel%7B%5Ctextit%7Bbaseball%7D%7D%7Bx%7D~%3D~%5Cstackrel%7B%5Ctextit%7Bwhole%7D%7D%7B1%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B24%7D%7D%7B24%5Cleft%28%5Ccfrac%7B1%7D%7B3%7D%2B%5Ccfrac%7B1%7D%7B8%7D%2B%5Ccfrac%7B5%7D%7B12%7D%2Bx%20%5Cright%29%3D24%281%29%7D%5Cimplies%20%288%291%2B%283%291%2B%282%295%2B%2824%29x%3D24%20%5C%5C%5C%5C%5C%5C%208%2B3%2B10%2B24x%3D24%5Cimplies%2021%2B24x%3D24%5Cimplies%2024x%3D3%20%5C%5C%5C%5C%5C%5C%20x%3D%5Ccfrac%7B3%7D%7B24%7D%5Cimplies%20x%3D%5Ccfrac%7B1%7D%7B8%7D)