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Blizzard [7]
2 years ago
8

Determine the value of y when x=15 if y=6 when x=30

Mathematics
1 answer:
swat322 years ago
6 0
I THINK the answer is 12
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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
3 years ago
Constant of proportionality y = 1/4 x
Dovator [93]

Answer:

The constant of proportionality is 1/4.

Step-by-step explanation:

4 0
2 years ago
A 13-ounce box of cereal sells for $3.25. An 18-ounce box of cereal sells for $3.60. Which statement describes the difference in
prisoha [69]

Answer:Is there a answer choice?

Step-by-step explanation:

6 0
2 years ago
Plz help me-7.1(z-1.1)
Elena-2011 [213]

Answer:

<h2>-7.1z +7.81</h2>

Step by step explanation:

- 7.1(z - 1.1)

Multiply each term in paranthesis by -7.1

- 7.1 \times z - 7.1 \times ( - 1.1)

Multiply:

-7.1z + 7.81

Hope this helps...

Good luck on your assignment..

6 0
3 years ago
In triangle ACD, what is the value of X:<br> who ever show works gets brainly.
Keith_Richards [23]

Answer:

x = 7.5

Step-by-step explanation:

Given that BE is parallel to CD and intersects the 2 other sides, then it divides the 2 sides in proportion, that is

\frac{AB}{BC} = \frac{AE}{ED}, substitute values

\frac{x}{6} = \frac{10}{8} ( cross- multiply )

8x = 60 ( divide both sides by 8 )

x = 7.5

6 0
3 years ago
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