Answer:
pretty sure its -2,3 :)
Step-by-step explanation:
Answer: 5 cups 4 ounces
Step-by-step path to answer:
Pints to cups:
1 pint= 2 cups
2 pints= 4 cups
0.5 pints=1 cup
2.5 pints= 5 cups
Cups to ounces:
1 cup= 8 ounces
0.5(1/2) cups= 4 ounces
All together:
2.5pints + 0.5cups = 5cups 4ounces
The standard equation of parabola:
(y-k)²=4p(x-h), with:
a) vertex = (h,k)
b) focus = (h+p, k)
c) directrix = (x=h-p)
Since this parabola has a vertex at (0,0) that means h=k=0
Hence the equation becomes: y²=4px, let's calculate p:
focus is given (-9,0) Remember h+p = -9 & since h=0, then p= -9
===> y²= - 36x
Answer:
We verified that ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
Hence proved
Step-by-step explanation:
Given equation is
We have to prove that
That is to prove that LHS=RHS
Now taking RHS
![\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
![=\frac{a+b+c}{2}[a^2-2ab+b^2+b^2-2bc+c^2+c^2-2ac+a^2]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5Ba%5E2-2ab%2Bb%5E2%2Bb%5E2-2bc%2Bc%5E2%2Bc%5E2-2ac%2Ba%5E2%5D)
(using 
)
![=\frac{a+b+c}{2}[2a^2-2ab+2b^2-2bc+2c^2-2ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B2a%5E2-2ab%2B2b%5E2-2bc%2B2c%5E2-2ac%5D)
(adding the like terms)
![=\frac{a+b+c}{2}[2a^2+2b^2+2c^2-2ab-2bc-2ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B2a%5E2%2B2b%5E2%2B2c%5E2-2ab-2bc-2ac%5D)
![=\frac{a+b+c}{2}\times 2[a^2+b^2+c^2-ab-bc-ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5Ctimes%202%5Ba%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%5D)
![=a+b+c[a^2+b^2+c^2-ab-bc-ac]](https://tex.z-dn.net/?f=%3Da%2Bb%2Bc%5Ba%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%5D)
Now multiply the each term to another each term in the factor
![=a^3+ab^2+ac^2-a^2b-abc-a^2c+ba62+b^3+bc^2-ab^2-b^2c-abc+ca^2+cb^2+c^3-abc-bc^2-ac^2]](https://tex.z-dn.net/?f=%3Da%5E3%2Bab%5E2%2Bac%5E2-a%5E2b-abc-a%5E2c%2Bba62%2Bb%5E3%2Bbc%5E2-ab%5E2-b%5E2c-abc%2Bca%5E2%2Bcb%5E2%2Bc%5E3-abc-bc%5E2-ac%5E2%5D)
(adding the like terms and other terms getting cancelled)
=LHS
Therefore LHS=RHS
Therefore
Hence proved.
