Answer:
see below
Step-by-step explanation:
72pi cubic inches
1/3 pi r ^2 * h = 72 pi
1/3 r^2 h = 72
You can theoretically find infinite answers to this and get enough points for the semester where you don't have to do work anymore. I will list a couple more possible answers below
r = radius, h = height
r = 2, h = 54
r = 3, h = 24
r = 4, h = 27/2
r = √(1/pi), h = 72pi
3+x=7Becayse you get the three and add it to a variable equals 7
The product is ![104 x^{4}+16 \sqrt{30} x^{4}](https://tex.z-dn.net/?f=104%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D)
Explanation:
The given expression is ![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D)
We need to determine the product of the given expression.
First, we shall simplify the given expression.
Thus, we have,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x \sqrt{5} x+2 x^{2} \sqrt{6}\right)^2](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%20%5Csqrt%7B5%7D%20x%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E2)
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)^2](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E2)
Expanding the expression, we have,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29)
Now, we shall apply FOIL, we get,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}\right)^{2}+2 ( 2 x^{2} \sqrt{6})(4 x^{2} \sqrt{5})+\left(2 x^{2} \sqrt{6}\right)^{2}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D%5Cleft%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%5Cright%29%5E%7B2%7D%2B2%20%28%202%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%29%284%20x%5E%7B2%7D%20%5Csqrt%7B5%7D%29%2B%5Cleft%282%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D)
Simplifying the terms, we have,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=16 \cdot 5 x^{4}+16 \sqrt{30} x^{4}+4 \cdot 6 x^{4}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D16%20%5Ccdot%205%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D%2B4%20%5Ccdot%206%20x%5E%7B4%7D)
Multiplying, we get,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=80 x^{4}+16 \sqrt{30} x^{4}+24 x^{4}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D80%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D%2B24%20x%5E%7B4%7D)
Adding the like terms, we get,
![\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=104 x^{4}+16 \sqrt{30} x^{4}](https://tex.z-dn.net/?f=%5Cleft%284%20x%20%5Csqrt%7B5%20x%5E%7B2%7D%7D%2B2%20x%5E%7B2%7D%20%5Csqrt%7B6%7D%5Cright%29%5E%7B2%7D%3D104%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D)
Thus, the product of the given expression is ![104 x^{4}+16 \sqrt{30} x^{4}](https://tex.z-dn.net/?f=104%20x%5E%7B4%7D%2B16%20%5Csqrt%7B30%7D%20x%5E%7B4%7D)
Answer:
the distance between the points is about 9.2 units
Step-by-step explanation:
It is well you should not understand it. <em>No question is asked</em>.
__
The answer choices suggest you are to find the distance between the two points. There is only one choice in a reasonable range: 9.2 units.
Each point is more than 2 units from any axis, so 2 units is clearly not the answer. The size of the graph is much less than 81 units, so clearly that is not the answer.
The difference of coordinates in the x-direction is 6; in the y-direction the difference is 7 units. The distance between the points will be more than the longest of these (7) and less than about 1.5 times that (10.5). Only one choice is in this range: 9.2 units.
__
The Pythagorean theorem is used to calculate the distance between points. The distance is considered to be the hypotenuse of a right triangle with legs of lengths equal to the differences of coordinates. Here, that means the distance (d) is ...
d² = 6² + 7² = 36 +49 = 85
d = √85 ≈ 9.2 . . . . grid squares, or "units"