I'm guessing you are talking about the surface area of a cone?
<span>Also by length of the edge, do you mean slant height?
Here is the area formula for a cone:
Lateral Area = (<span>π<span> • r •<span> slant height)
Solving for "r" we get:
</span></span></span></span>
radius = Lateral Area / (<span>π<span> • </span></span><span><span>slant height)</span><span><span /></span></span>
When you calculate the radius, you can solve for the height by
height^2 = slant height^2 - radius^2
X, X+2, X+4 ARE THE 3 POSITIVE CONSECUTIVE INTEGERS.
X(X+2)=8+38(X+4)
X^2+2X=8+38X+152
X^2+2X-38X-8-152=0
X^2-36X-160=0
(X-40)(X+4)=0
X-40=0
X=40 ANSWER FOR THE FIRST INTEGER.
40+2=42 FOR THE SECOND INTEGER.
Answer:
# 4 (-5,2) should be placed one more place to the right
#5 (5,1) should be moved once up
Step-by-step explanation:
:)
Answer:
![x=-11](https://tex.z-dn.net/?f=x%3D-11)
Step-by-step explanation:
![6x-2=7x+9](https://tex.z-dn.net/?f=6x-2%3D7x%2B9)
Add 2 to both sides:
![6x-2+2=7x+9+2](https://tex.z-dn.net/?f=6x-2%2B2%3D7x%2B9%2B2)
![6x=7x+11](https://tex.z-dn.net/?f=6x%3D7x%2B11)
Subtract 7x from both sides:
![6x-7x=7x+11-7x](https://tex.z-dn.net/?f=6x-7x%3D7x%2B11-7x)
![-x=11](https://tex.z-dn.net/?f=-x%3D11)
Divide both sides by -1:
![\frac{-x}{-1}=\frac{11}{-1}](https://tex.z-dn.net/?f=%5Cfrac%7B-x%7D%7B-1%7D%3D%5Cfrac%7B11%7D%7B-1%7D)
![x=-11](https://tex.z-dn.net/?f=x%3D-11)
Answer:
![W=2452.5 J](https://tex.z-dn.net/?f=W%3D2452.5%20J)
Step-by-step explanation:
The work is define as the integral of the force times distance. So we have:
![W=\int^{a}_{b}Fxdx](https://tex.z-dn.net/?f=W%3D%5Cint%5E%7Ba%7D_%7Bb%7DFxdx)
Now, we can write the force in terms of density.
![F=m*g=\rho Vg](https://tex.z-dn.net/?f=F%3Dm%2Ag%3D%5Crho%20Vg%20)
V is the volume (V=2*1*1=2 m³)
So the work will be:
![W=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0}19620xdx=19620(\frac{x^{2}}{2})|^{0.5}_{0}](https://tex.z-dn.net/?f=W%3D%5Cint%5E%7B0.5%7D_%7B0%7D%202%2A1000%2A9.81%2Axdx%3D%5Cint%5E%7B0.5%7D_%7B0%7D%202%2A1000%2A9.81%2Axdx%3D%5Cint%5E%7B0.5%7D_%7B0%7D19620xdx%3D19620%28%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%29%7C%5E%7B0.5%7D_%7B0%7D)
The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.
![W=19620(\frac{x^{2}}{2})|^{0.5}_{0}=19620(\frac{0.5^{2}}{2})](https://tex.z-dn.net/?f=W%3D19620%28%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%29%7C%5E%7B0.5%7D_%7B0%7D%3D19620%28%5Cfrac%7B0.5%5E%7B2%7D%7D%7B2%7D%29)
![W=2452.5 J](https://tex.z-dn.net/?f=W%3D2452.5%20J)
I hope it helps you!