Answer:
A.) 1018 square inches
Step-by-step explanation:
The largest sphere will have a diameter equaling the length of the cube (see picture).
If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:

For this formula, we need the radius of the sphere. Divide the diameter by 2:

The radius is 9 inches. Plug this into the equation:

Simplify the equation:

Round the result to the nearest whole number:
→
The surface area is 1,018 inches².
:Done
Picture:
In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.
The given expression is ![3b^2*(\sqrt[3]{54a}) + 3*(\sqrt[3]{2ab^6})](https://tex.z-dn.net/?f=%203b%5E2%2A%28%5Csqrt%5B3%5D%7B54a%7D%29%20%2B%203%2A%28%5Csqrt%5B3%5D%7B2ab%5E6%7D%29%20)
This can be simplified as :
= ![3*b^2*(\sqrt[3]{27 *2*a}) + 3*(\sqrt[3]{2*a*b^6})](https://tex.z-dn.net/?f=%203%2Ab%5E2%2A%28%5Csqrt%5B3%5D%7B27%20%2A2%2Aa%7D%29%20%2B%203%2A%28%5Csqrt%5B3%5D%7B2%2Aa%2Ab%5E6%7D%29%20)
We know that: ![\sqrt[3]{27} = 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B27%7D%20%20%3D%203%20%20%20)
Similarly we also can simplify: ![\sqrt[3]{b^6} = b^2](https://tex.z-dn.net/?f=%20%20%5Csqrt%5B3%5D%7Bb%5E6%7D%20%20%3D%20b%5E2%20)
So our expression will look like this:
= ![3*3*b^2*(\sqrt[3]{2a}) + 3*b^2*(\sqrt[3]{2a})](https://tex.z-dn.net/?f=%203%2A3%2Ab%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20%2B%203%2Ab%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20)
= ![9b^2*(\sqrt[3]{2a}) + 3b^2*(\sqrt[3]{2a})](https://tex.z-dn.net/?f=%209b%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20%2B%203b%5E2%2A%28%5Csqrt%5B3%5D%7B2a%7D%29%20)
=![\sqrt[3]{2a}*(9b^2 + 3b^2)](https://tex.z-dn.net/?f=%20%20%5Csqrt%5B3%5D%7B2a%7D%2A%289b%5E2%20%2B%203b%5E2%29%20)
=![\sqrt[3]{2a}*(12b^2)](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B2a%7D%2A%2812b%5E2%29%20)
This can also be written as:
![12b^2(\sqrt[3]{2a})](https://tex.z-dn.net/?f=%2012b%5E2%28%5Csqrt%5B3%5D%7B2a%7D%29%20)
So the Answer is Option B
Answer:
Hi! The correct answer is x= -3 ,-5!
Step-by-step explanation:
<em>~Factor and set each factor equal to 0~</em>
Answer: 97 students
Step-by-step explanation:
Simple! We need to split 388 into four equal parts, so
388 / 4 = 97
Hope this helps!