Pythagorean theorem
for a right triangle with legs legnth a and b and hytponuse c
a^2+b^2=c^2
the legnht of th eladder is the hypotnuse
the 3 feet is bottom leg
height is other leg
10=c
3=a
b=?
3^2+b^2=10^2
9+b^2=100
minus 9 both sides
b^2=91
sqrt both sides
b=√91
aprox
b=9.53939
answer is √91 feet or aprox 9.53939
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Answer:
x=12
Step-by-step explanation:
we know that
If the two chords are equidistant from the center of the circle, then the chords must be congruent.
so
JK=LM
substitute the given values

solve for x

well then, the volume of the nose cone will just be the sum of the volume of the cylinder below and the cone above.
since the diameter for both is 8, then their radius is half that, or 4.
![\bf \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\cfrac{\pi (4)^2(6)}{3}\implies V=32\pi \\\\\\ \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\pi (4)^2(6)\implies V=96\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the nose cone}}{32\pi +96\pi \implies 128\pi }\qquad \approx \qquad 402.12](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20a%20cone%7D%7D%7BV%3D%5Ccfrac%7B%5Cpi%20r%5E2%20h%7D%7B3%7D%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20r%3D4%5C%5C%20h%3D6%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B%5Cpi%20%284%29%5E2%286%29%7D%7B3%7D%5Cimplies%20V%3D32%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20a%20cylinder%7D%7D%7BV%3D%5Cpi%20r%5E2%20h%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20r%3D4%5C%5C%20h%3D6%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Cpi%20%284%29%5E2%286%29%5Cimplies%20V%3D96%5Cpi%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20the%20nose%20cone%7D%7D%7B32%5Cpi%20%2B96%5Cpi%20%5Cimplies%20128%5Cpi%20%7D%5Cqquad%20%5Capprox%20%5Cqquad%20402.12)