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s344n2d4d5 [400]
3 years ago
11

If a+b+c=16 and a^2+b^2+c^2=90 then find the value a^3+b^3+c^3-3abc

Mathematics
1 answer:
grin007 [14]3 years ago
3 0

(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\\(16)^2=90+2(ab+bc+ca)\\256-90=2(ab+bc+ca)\\166/2=ab+bc+ca\\83=ab+bc+ca\\a^3-b^3-c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)\\(a+b+c)(a^2+b^2+c^2-(ab+bc+ca))\\16(90-(83))\\16(7)\\=112

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Answer:

Number one the base is 24 and the Volume is 120

Number two the base is also 24 and the Volume is 240.

Step-by-step explanation:

For #1:

For the first one the area of the base is 8x3 which equals 24 so for base Number 1 its 24.

All we got to do to figure out the volume is multiply by 10 *the height* and then divide by 2 because we are finding the volume of a pyramid. 24x10 = 240/2 = 120. So the volume for Number 1 is 120.

For #2:

It has the exact same number except we are dealing with a rectangular prism which means at the end we don't have to divide by 2. For the base its  8 x 3 = 24 the same as the pyramid.  For the volume-  8 x 3 = 24 x 10 = 240 which means the volume is 240. And of course don't forget the unit yards³

Hope I was able to help!

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