54? Add ??6 equals 822
2 answers:
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Answer:
Step-by-step explanation:
I used 3 of the coordinates to solve for the a, b, and c that we need in
We have 3 unknowns so we need 3 equations. The coordinates I used are from your table:
(-2, 12), (-1, 6), (0, 2). Start with (0, 2). Sub in a 2 for y and a 0 for x in the standard form of the quadratic:
which simplifies very nicely to
c = 2. We will use that value now when we do this again using (-2, 12):
and
12 = 4a - 2b + 2 and
4a - 2b = 10 (1)
Do it again with the third coordinate (-1, 6):
and
6 = 1a - b + 2 and
a - b = 4 (2)
Now we have a system of equations, (1) and (2) that we will combine and solve for a:
4a - 2b = 10
a - b = 4
Multiply the second equation by -2 to get a new system:
4a - 2b = 10
-2a + 2b = -8
Add to get
2a = 2 so
a = 1
Now sub in 1 for a in (2):
1 - b = 4 and
-b = 3 so
b = -3
Now we have all that we need to write the equation:
Check the picture below.
so, the diameter of the sphere, is the same as a side's length of the cube, bearing in mind that all sides in a cube are the same length.
since all sides in the cube are "d", then its volume is V = d*d*d or V = d³.
![\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ V=972\pi \end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies 2916\pi =4\pi r^3 \\\\\\ \cfrac{2916\pi }{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20sphere%7D%5C%5C%5C%5C%0AV%3D%5Ccfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D~~%0A%5Cbegin%7Bcases%7D%0Ar%3Dradius%5C%5C%0A-----%5C%5C%0AV%3D972%5Cpi%20%0A%5Cend%7Bcases%7D%5Cimplies%20972%5Cpi%20%3D%5Ccfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D%5Cimplies%202916%5Cpi%20%3D4%5Cpi%20r%5E3%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2916%5Cpi%20%7D%7B4%5Cpi%20%7D%3Dr%5E3%5Cimplies%20729%3Dr%5E3%5Cimplies%20%5Csqrt%5B3%5D%7B729%7D%3Dr%5Cimplies%20%5Cboxed%7B9%3Dr%7D)
since the diameter is twice as much as the radius, thus d = 2r, or namely d = 18.
therefore, the volume of the cube will be V = 18³.
so, the diameter of the sphere, is the same as a side's length of the cube, bearing in mind that all sides in a cube are the same length.
since all sides in the cube are "d", then its volume is V = d*d*d or V = d³.
since the diameter is twice as much as the radius, thus d = 2r, or namely d = 18.
therefore, the volume of the cube will be V = 18³.