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MakcuM [25]
3 years ago
8

Can someone just help me out I’m bad at doing homework

Mathematics
1 answer:
jeka57 [31]3 years ago
8 0

Answer:

You forgot to attach

Step-by-step explanation:

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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
Question Find the slope of the line. (-1,3) (3,3)
navik [9.2K]

Here’s the answer is m=0
4 0
3 years ago
I need help 6+2 plz answer for brain
Pavel [41]

Answer:

8

Step-by-step explanation:

i have 6 apples + 2 peers

4 0
3 years ago
Read 2 more answers
line passes through the point (-3,-4) and its y-intercept is (o, -9). What is the equation of the line that is parallel to the f
12345 [234]

Answer:

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

Step-by-step explanation:

The first line has a slope of -5/3 found using the points in the slope formula.

m=\frac{y_2-y_1}{x_2-x_1} =\frac{-9--4}{0--3}=\frac{-9+4}{0+3}=\frac{-5}{3}

Parallel lines have the same slope. So -5/3 is the slope of the second line. Write its equation using the point slope form y-y_1=m(x-x_1).

y--7=-\frac{5}{3}(x-3)\\y+7 = -\frac{5}{3}(x-3)\\y=-\frac{5}{3}x + 5 -7\\y=-\frac{5}{3}x-2

7 0
3 years ago
Change 1.4 to a fraction. <br> 1/4<br> 1 1/4<br> 1 1/2<br> 1 2/5
dusya [7]
1.4
= 1+ 0.4
= 1+ 4/10
= 1+ (4/2) / (10/2)
= 1+ 2/5
= 1 2/5

The final answer is 1 2/5.


3 0
3 years ago
Read 2 more answers
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