What is the volume of the pyramid? 8,704 ft3 1,280 ft3 34,816 ft3 4,624 ft3

Mathematics

2 answers:

Anna [14]3 years ago

6 0

The volume of a Pyramid is
$V= \frac{1}{3} Bh$
Big B means you have to multiply the base first so 16*16
to find the hight you can use the Pythagorean theorem
the length of one of the sides is 16 so we have to divide that by 2 to get one of the legs for the Pythagorean theorem which is 8 and 17 is the hypotenuse.
Pug it in and it will look like this
$8^{2} + b^2 = 17^2$
square them to get
$64+b^2=289$
subtract 64 from both sides to get
$b^2=225$
then square root it to get the height
$h=15$
then plug that into your volume formula
$V= \frac{1}{3} 256*15$
Add it up to get a volume of 1,280. Hope this helps Good luck :)

Mariulka [41]3 years ago

5 0

1st you need to find the height then you can find the volume

see attached picture

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In the equation (x^2+y)^5, what is the coefficient of the term x^4y^3? what is the coefficient of the same term in the expansion

lys-0071 [83]

$\displaystyle
(x+y)^n=\sum_{k=0}^n\binom{n}{k}x^{n-k}y^k$

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$\displaystyle
(x^2+y)^n=\sum_{k=0}^n\binom{n}{k}x^{2n-2k}y^k\\
n=5\\
k=3\\\\\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdor5}{2}=10$

It's 10.

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$\displaystyle
(3x^2+y)^n=\sum_{k=0}^n\binom{n}{k}(3x)^{2n-2k}y^k=\sum_{k=0}^n\binom{n}{k}\cdot 3^{2n-2k}\cdot x^{2n-2k}y^k\\\\
n=5\\
k=4\\\\
\binom{5}{3}\cdot3^{2\cdot5-2\cdot4}=10\cdot3^{2}=10\cdot9=90$