Answer:
h=31.4 cm
Step-by-step explanation:
A=lateral surface area
c=circumference
h=height
A= c*h
solving for h we get:
h=A/c=120pi/12=10pi
Answer:
1/4
Step-by-step explanation:
A P E X
Let
be the line that passes through both points.
We know that
and
. So:
![\begin{cases}5a+b = 1 \\ 8a+b = -2\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D5a%2Bb%20%3D%201%20%5C%5C%208a%2Bb%20%3D%20-2%5Cend%7Bcases%7D)
Solving the system, we get that a= -1 and b = 6.
So the line is equal to
.
Answer:
B. y= 1/2 x - 3
Step-by-step explanation:
base equation: y= mx+ b
slope(m) equation:
y2= -1 y1= -3
x2= 4 x1= 0
![\frac{-1 - (-3)}{4-0} =\frac{2}{4} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%20-%20%28-3%29%7D%7B4-0%7D%20%3D%5Cfrac%7B2%7D%7B4%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
y- intercept: -3
found by taking the y from (0,-3)
M is a midpoint of BC so:
![M=\left(\dfrac{\boxed{2}\boxed{a}+a}{\boxed{2}},\dfrac{\boxed{0}+b}{2}\right)=\left(\dfrac{\boxed{3}\boxed{a}}{\boxed{2}},\dfrac{\boxed{b}}{\boxed{2}}\right)](https://tex.z-dn.net/?f=M%3D%5Cleft%28%5Cdfrac%7B%5Cboxed%7B2%7D%5Cboxed%7Ba%7D%2Ba%7D%7B%5Cboxed%7B2%7D%7D%2C%5Cdfrac%7B%5Cboxed%7B0%7D%2Bb%7D%7B2%7D%5Cright%29%3D%5Cleft%28%5Cdfrac%7B%5Cboxed%7B3%7D%5Cboxed%7Ba%7D%7D%7B%5Cboxed%7B2%7D%7D%2C%5Cdfrac%7B%5Cboxed%7Bb%7D%7D%7B%5Cboxed%7B2%7D%7D%5Cright%29)
Length of MA:
![MA=\sqrt{\left(\dfrac{\boxed{3}a}{2}\boxed{-}\boxed{0}\right)^2+\left(\dfrac{\boxed{b}}{2}\boxed{-}\boxed{0}\right)^2}=\\\\\\= \sqrt{\left(\dfrac{\boxed{3}a}{\boxed{2}}\right)^2+\left(\dfrac{b}{2}\right)^2}=\sqrt{\dfrac{\boxed{9}a^2}{\boxed{4}}+\dfrac{\boxed{b}^2}{\boxed{4}}}](https://tex.z-dn.net/?f=MA%3D%5Csqrt%7B%5Cleft%28%5Cdfrac%7B%5Cboxed%7B3%7Da%7D%7B2%7D%5Cboxed%7B-%7D%5Cboxed%7B0%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Cboxed%7Bb%7D%7D%7B2%7D%5Cboxed%7B-%7D%5Cboxed%7B0%7D%5Cright%29%5E2%7D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csqrt%7B%5Cleft%28%5Cdfrac%7B%5Cboxed%7B3%7Da%7D%7B%5Cboxed%7B2%7D%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7Bb%7D%7B2%7D%5Cright%29%5E2%7D%3D%5Csqrt%7B%5Cdfrac%7B%5Cboxed%7B9%7Da%5E2%7D%7B%5Cboxed%7B4%7D%7D%2B%5Cdfrac%7B%5Cboxed%7Bb%7D%5E2%7D%7B%5Cboxed%7B4%7D%7D%7D)
Length of NB: