Slope: Y-Intercept: Equation:

Which number has more than two factors? A. 19 B. 23 C. 25 D. 29

Whitepunk [10]

The answer would be 25 because all of the others are prime numbers, meaning they can only be divided by themselves and 1. So it would be C.

4 0

3 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

Whats 15-b=4b-5(5-3)

Gala2k [10]

15-b=4b-5(5-3)

Multiply the bracket by -5

(-5)(5)=-25

(-5)(-3)=15

15-b=4b-25+15

15-b=4b-10

Move 15 to the other side

Sign changes from +15 to -15

15-15-b=4b-10-15

-b=4b-25

Move 4b to the other side.

-b-4b=4b-4b-25

-b-4b=-25

-5b=-25

divide both sides by -5

-5b/-5=-25/-5

Answer: b=5

5 0

2 years ago

Your beginning balance on your lunch account is $55. You buy lunch for 1.75 everyday and sometimes buy a snack for $0.85 after 2

Agata [3.3K]

Multiply 1.75 with 25 because you bought snacks everyday and then you’re left with 11.25

Now subtract .20 because you were left with that on day 26 and you get 11.05

Lastly you divide 11.05 with .85 to see how many snacks you bought

ANSWER IS 13 snacks

3 0

3 years ago

The computer store pays its employees $150 per day plus a commission of 15% of their sales. Teagan wants to make at least $450 t

Savatey [412]

The equation 0.15 x + 150 ≥ 450 will help Teagan determine how much he has to sell today ⇒ A

Step-by-step explanation:

The given is:

The computer store pays its employees $150 per day plus a commission of 15% of their sales
Teagan wants to make at least $450 today

We need to find which equation will help Teagan to determine how much he has to sell today

Assume that he has to sell by $x today

∵ The store pays $150 per day plus a commission of 15%

of their sales

∵ Teagan's total sales = x

- Multiply 15% by x, then add the product by 150

∴ Teagan makes = 15% × x + 150

∵ 15% × x = $\frac{15}{100}$ × x = 0.15 x

∴ Teagan makes = 0.15 x + 150

∵ Teagan wants to make at least $450 today

- At least means ≥

∴ Teagan makes ≥ 450

- Substitute Teagan makes by 0.15 x + 150

∴ 0.15 x + 150 ≥ 450

The equation 0.15 x + 150 ≥ 450 will help Teagan determine how much he has to sell today

Learn more:

You can learn more about the linear inequality in brainly.com/question/6703816

#LearnwithBrainly

6 0

3 years ago

Read 2 more answers