Answer:
37.699 cubic inches of water
Step-by-step explanation:
Volume of a cone is V= 1/3 pi r^2 h
We are given that the height is 5 in and the radius is 2 in.
Plug that into the formula: V= 1/3 pi 2^2 9
1/3 x 4 x 9 = 12
Now we are left with 12 pi.
Use a calculator and multiply 12 by pi to get:
37.699
Answer:
The correct equation is "y=30x+6147". A further explanation is given below.
Step-by-step explanation:
The given values are:
(x1, y1) = (50, 7647)
(x2, y2) = (100, 9147)
As we know,
The slope is,
⇒ ![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
On substituting the given values, we get
⇒ ![=\frac{9147-7642}{100-50}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B9147-7642%7D%7B100-50%7D)
⇒ ![=\frac{1500}{50}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1500%7D%7B50%7D)
⇒ ![=30](https://tex.z-dn.net/?f=%3D30)
Now,
⇒ ![(y-y1)=m(x-x1)](https://tex.z-dn.net/?f=%28y-y1%29%3Dm%28x-x1%29)
On substituting the given values in the above equation, we get
⇒ ![y-7647=30(x-50)](https://tex.z-dn.net/?f=y-7647%3D30%28x-50%29)
⇒ ![y-7647=30x-1500](https://tex.z-dn.net/?f=y-7647%3D30x-1500)
On adding "7647" both sides, we get
⇒ ![y-7647+7647=30x-1500+7647](https://tex.z-dn.net/?f=y-7647%2B7647%3D30x-1500%2B7647)
⇒ ![y=30x+6147](https://tex.z-dn.net/?f=y%3D30x%2B6147)
Answer:
x = -0.17 and x = -5.83
Step-by-step explanation:
We are asked to solve the quadratic equation
![x^2+6\,x+1=0](https://tex.z-dn.net/?f=x%5E2%2B6%5C%2Cx%2B1%3D0)
We use the quadratic formula using a = 1, b = 6 and c = 1
for a general quadratic equation of the form: ![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Then, the solutions are given by;
![x=\frac{-6+/-\sqrt{36-4\,(1)\,(1)} }{2} =\frac{-6+/-\sqrt{32} }{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%2B%2F-%5Csqrt%7B36-4%5C%2C%281%29%5C%2C%281%29%7D%20%7D%7B2%7D%20%3D%5Cfrac%7B-6%2B%2F-%5Csqrt%7B32%7D%20%7D%7B2%7D)
which produces the two following answers (rounded to two decimals):
x = -0.17 and x = -5.83