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sertanlavr [38]
3 years ago
15

Put the following equation of a line into slope-intercept form, simplifying all fractions

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
5 0

Answer:

y = 2x - 5

Step-by-step explanation:

Slope intercept form: y = mx + c

3y - 6x = -15

3y = 6x - 15

\frac{3y}{3}=\frac{6x}{3} -\frac{15}{3}\\\\y =2x - 5

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12 to 13 is the ratio.
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3 years ago
ricardo purchased a bunk bed for his children fora sale price of $276.25. The sale price was 65% of the original price. Calculat
nikklg [1K]

Use the formula S=P-PD

S is sale price, original price is P, and PD is discounted percent,

276.25=P-P(.65), I turned the percent into a decimal.

276.25=P(1-.65)

276.25=P(1-.65)

276.25=P(.35)

Now cross multiply.

\frac{276.26}{.35}=\frac{P(.35)}{.35}\\\\P=\frac{276.26}{.35}=789.31

Hope this helps, now you know the answer and how to do it. Stay healthy and safe and HAVE A BLESSED AND WONDERFUL DAY! :-)  

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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).
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Answer:

24 mouths have passed

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