3 years ago

Factor using given common factor. Assume all variables represent real positive numbers. (Y^-5)-(3y^-3); y^-5

Mathematics

1 answer:

stellarik [79]3 years ago

6 0

Divide the expression by the factor y^-5
y^-5(1 - 3y^2)

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5 times marys age is the same as 28 less than 7 times her age. Find her age

Gnom [1K]

setup a simple algebraic equation and solve.

5x = 7x-28

-5x -5x

0=2x-28

+28 +28

28=2x

Now divide both sides by 2 and you get that she is 14

3 0

2 years ago

Read 2 more answers

WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"

Feliz [49]

Recall Euler's theorem: if $\gcd(a,n) = 1$ , then

$a^{\phi(n)} \equiv 1 \pmod n$

where $\phi$ is Euler's totient function.

We have $\gcd(9,32) = 1$ - in fact, $\gcd(9,32^k)=1$ for any $k\in\Bbb N$ since $9=3^2$ and $32=2^5$ share no common divisors - as well as $\phi(9) = 6$ .

Now,

$37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6$