Radius r = 3inches
Arc A = 8 inches
We need formula that connects lenght of arc with central angle. That one is fallowing one:
A = 2*r*pi*α/360 where α is central angle. we can see that if α=360, A = 2*r*pi which is exactly the formula for parimeter of circle.
Further more we can express 360 in radians which is 2* pi and get
A = r*α as simpler formula
α = A/r = 8/3 = 2.66666667 ≈ 2.7
Answer:
£70.40
Step-by-step explanation:
352 / 5 = £70.40
so he earns £70.40 per day
B
2+-2=0
0 is greater than -8
SOLUTION:
Let's establish the formula for a cylinder as displayed below:
Let volume of cylinder = V
V = ( Pi )r^2h
Now let's substitute the values from the problem into the formula to find the volume.
V = ?
r = 8
h = 4
V = ( Pi )( 8 )^2( 4 )
V = ( Pi )( 64 )( 4 )
V = ( Pi )( 256 )
V = 256( Pi )
FINAL ANSWER:
Therefore, the answer is:
C. 256( Pi ) units^3
Hope this helps! :)
Have a lovely day! <3
Answer:
![2\sqrt {2}](https://tex.z-dn.net/?f=2%5Csqrt%20%7B2%7D)
Step-by-step explanation:
<u>Distance From a Point to a Line</u>
Given a line with an equation
:
ax + by + c = 0
And the point ![(x_0,y_0)](https://tex.z-dn.net/?f=%28x_0%2Cy_0%29)
The distance from the line to the point is given by
![\displaystyle d=\frac {|ax_{0}+by_{0}+c|}{\sqrt {a^{2}+b^{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B%7Cax_%7B0%7D%2Bby_%7B0%7D%2Bc%7C%7D%7B%5Csqrt%20%7Ba%5E%7B2%7D%2Bb%5E%7B2%7D%7D%7D)
The triangle has a vertex at (1,-2) and the base lies on the equation
x + y = 3
Rearranging:
x + y - 3 = 0
The altitude of the triangle is the distance from the point to the line.
The values to use in the formula of the distance are: a=1, b=1, c=-3, xo=1, yo=-2:
![\displaystyle d=\frac {|1*1+1*(-2)-3|}{\sqrt {1^{2}+1^{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B%7C1%2A1%2B1%2A%28-2%29-3%7C%7D%7B%5Csqrt%20%7B1%5E%7B2%7D%2B1%5E%7B2%7D%7D%7D)
![\displaystyle d=\frac {|1-2-3|}{\sqrt {2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B%7C1-2-3%7C%7D%7B%5Csqrt%20%7B2%7D%7D)
![\displaystyle d=\frac {4}{\sqrt {2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B4%7D%7B%5Csqrt%20%7B2%7D%7D)
Rationalizing:
![\displaystyle d=\frac {4}{\sqrt {2}}\cdot\frac{\sqrt {2}}{\sqrt {2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B4%7D%7B%5Csqrt%20%7B2%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%20%7B2%7D%7D%7B%5Csqrt%20%7B2%7D%7D)
![\displaystyle d=2\sqrt {2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D2%5Csqrt%20%7B2%7D)
The altitude of the triangle is ![\mathbf{4\sqrt {2}}](https://tex.z-dn.net/?f=%5Cmathbf%7B4%5Csqrt%20%7B2%7D%7D)