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2 years ago

Find the diagonal of the rectangular prism.

Mathematics

1 answer:

KiRa [710]2 years ago

3 0

Answer:

First diagonal: 7.874

Second diagonal: 8.3666

Step-by-step explanation:

We use the Pythagorean Theorem to find these.

First diagonal = 5²+6²=c²

25+36=c²

61=c²

√61=c

c=7.874

Then we use that to find the second diagonal.

7.874²+3²=c²

61+9=c²

70=c²

√70=c

c=8.3666

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If x+1/x= 3, then prove that m^5+1/m^5= 123

alina1380 [7]

9514 1404 393

Explanation:

We can start with the relations ...

$\displaystyle\left(x+\frac{1}{x}\right)^3=\left(x^3+\frac{1}{x^3}\right)+3\left(x+\frac{1}{x}\right)\\\\\left(x+\frac{1}{x}\right)^5=\left(x^5+\frac{1}{x^5}\right)+5\left(x^3+\frac{1}{x^3}\right)+10\left(x+\frac{1}{x}\right)\\\\\textsf{From these, we can derive ...}\\\\x^5+\frac{1}{x^5}=\left(x+\frac{1}{x}\right)^5-5\left(\left(x+\frac{1}{x}\right)^3-3\left(x+\frac{1}{x}\right)\right)-10\left(x+\frac{1}{x}\right)$

$\displaystyle x^5+\frac{1}{x^5}=\left(x+\frac{1}{x}\right)^5-5\left(x+\frac{1}{x}\right)^3+5\left(x+\frac{1}{x}\right)\right)\\\\x^5+\frac{1}{x^5}=3^5 -5(3^3)+5(3)\\\\=((3^2-5)3^2+5)\cdot3=(4\cdot9+5)\cdot3=(41)(3)\\\\=\boxed{123}$

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3 years ago

HELPPP!! DUE NOWWWW!

Colt1911 [192]

Answer: C

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1 year ago

What are the factors of rty

algol13

The factors of rty are

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3 years ago

Answer please.........

kozerog [31]

I think it’s the third option

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2 years ago

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Gwar [14]

Yeah Imao you usually do these type of questions on a calculator but I've tried writing it on a calculator and it keeps on saying "error" so I'm gonna guess the question is wrong or sth

but if you type out the question without the bracket before the 12 you'll get 6.63

anyway hope this helps- have a good day bro cya)

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2 years ago