If 3cm is the radius and 14cm is the height, the volume would be 131.95cm^3. In terms of pi it would be 9pi(14/3).
Step-by-step explanation:
We have got the lines :
![y=ax+b\\y=cx+d](https://tex.z-dn.net/?f=y%3Dax%2Bb%5C%5Cy%3Dcx%2Bd)
Both lines intercept the x-axis in the point :
![I = (i_{1} ,i_{2})](https://tex.z-dn.net/?f=I%20%3D%20%28i_%7B1%7D%20%2Ci_%7B2%7D%29)
In all point from x-axis the y-component is equal to 0.
![I=(i_{1},o)](https://tex.z-dn.net/?f=I%3D%28i_%7B1%7D%2Co%29)
We replace the I point in the lines equations:
![0=a(i_{1})+b \\0=c(i_{1})+d](https://tex.z-dn.net/?f=0%3Da%28i_%7B1%7D%29%2Bb%20%5C%5C0%3Dc%28i_%7B1%7D%29%2Bd)
From the first equation :
![0=a(i_{1})+b \\-b=a(i_{1})\\i_{1}=\frac{-b}{a}](https://tex.z-dn.net/?f=0%3Da%28i_%7B1%7D%29%2Bb%20%5C%5C-b%3Da%28i_%7B1%7D%29%5C%5Ci_%7B1%7D%3D%5Cfrac%7B-b%7D%7Ba%7D)
From the second equation :
![0=c(i_{1})+d\\ -d=c(i_{1})\\i_{1}=\frac{-d}{c}](https://tex.z-dn.net/?f=0%3Dc%28i_%7B1%7D%29%2Bd%5C%5C%20-d%3Dc%28i_%7B1%7D%29%5C%5Ci_%7B1%7D%3D%5Cfrac%7B-d%7D%7Bc%7D)
Then ![i_{1}=i_{1}](https://tex.z-dn.net/?f=i_%7B1%7D%3Di_%7B1%7D)
Finally :
![\frac{-b}{a}=\frac{-d}{c} \\\frac{b}{a}=\frac{d}{c} \\ad=bc](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7Ba%7D%3D%5Cfrac%7B-d%7D%7Bc%7D%20%5C%5C%5Cfrac%7Bb%7D%7Ba%7D%3D%5Cfrac%7Bd%7D%7Bc%7D%20%5C%5Cad%3Dbc)
y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc
Answer:
129
Step-by-step explanation:
Divide 1290 by 10 and you get 129
I would compute sqrt(1 + 160pi^2) first to get approximately 39.75093337
Add this to 1 and we have 40.75093337
Then divide over 2pi to get a final approximate result of 6.48571248
So x = 6.48571248 is one approximate solution
In short, I computed
only focusing on the plus for now.
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If you were to compute
you should get roughly -6.167402596 as your other solution. Each solution can then be plugged into the original equation to check if you get 0 or not. You likely won't land exactly on 0 but you'll get close enough.
He has to drive around the track about 1.5 times.
We first find the circumference:
C = 2πr = 2(3.14)(1.6) = 10.048
We now divide 15 by this:
15/10.048 ≈ 1.5