All categories

2 years ago

Give the prime factorization of the number. use exponents when possible 126

Mathematics

1 answer:

nataly862011 [7]2 years ago

3 0

Answer:

=2*3^2 *7

Step-by-step explanation:

Prime factorization means to simplify 126 down to prime numbers

126 = 2*63

= 2* 9*7

= 2*3*3*7

Since 2 3 and 7 are prime numbers, we rewrite these with exponents

=2*3^2 *7

You might be interested in

PLEASE HELP!!

user100 [1]

(8/-4) / (-3/9)=

(8/-4) * (9/3)=

72/-12=

-6

6 0

2 years ago

Mikkel pays a 4 percent state income tax on his earnings. If he earns $1,867, how much state income tax can he expect to pay? $4

lisabon 2012 [21]

Answer:

$74.68

Step-by-step explanation:

Convert the percent to a decimal.

4% = 0.04

Multiply his income by the percentage to find the tax.

$1,867 × 0.04 = $74.68

He can expect to pay $74.68.

3 0

2 years ago

Read 2 more answers

If Q is the midpoint of PR, and PQ = 2x + 3 and QR = 3x– 2, find x, PQ, QR, and PR.

leva [86]

Since they tell us that Q is the midpoint you now understand that the line is split evenly.
PQ=QR
2x+3=3x-2
2x+5=3x
x=5.

8 0

2 years ago

The volume of a Cylinder is given by the formula v=pir2h, where are is the radius of the cylinder and H is the height. Suppose a

faust18 [17]

You just need to plug those expressions inside the formula: it doesn't matter if they're expressions involving a variable instead of plain numbers: the formula becomes

$V = \pi (x+8)^2(2x+3)$

If you want, you can simplify it by expanding the square and then multiply the two parenthesis:

$V = \pi (x^2+16x+64)(2x+3) = \pi (2 x^3 + 35 x^2 + 176 x + 192)$

6 0

2 years ago

How to know if a function is periodic without graphing it ?

zhenek [66]

A function $f(t)$ is periodic if there is some constant $k$ such that $f(t+k)=f(k)$ for all $t$ in the domain of $f(t)$ . Then $k$ is the "period" of $f(t)$ .

Example:

If $f(x)=\sin x$ , then we have $\sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x$ , and so $\sin x$ is periodic with period $2\pi$ .

It gets a bit more complicated for a function like yours. We're looking for $k$ such that

$\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5$

Expanding on the left, you have

$\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2$

and

$1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5$

It follows that the following must be satisfied:

$\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}$

The first two equations are satisfied whenever $k\in\{0,\pm4,\pm8,\ldots\}$ , or more generally, when $k=4n$ and $n\in\mathbb Z$ (i.e. any multiple of 4).

The second two are satisfied whenever $k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}$ , and more generally when $k=\dfrac{10n}7$ with $n\in\mathbb Z$ (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when $k$ is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

$\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2$

$\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5$

More generally, it can be shown that

$f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))$

is periodic with period $\mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n)$ .

4 0

2 years ago