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Elza [17]
3 years ago
12

Trevon and Riggs are brothers.

Mathematics
2 answers:
Svet_ta [14]3 years ago
8 0
Let’s take T for Trevon and R for Riggs.

T = 7 years older than R which can be written as T = R + 7

Their combined age is 49.

Therefore, T + R = 49

We need to find Trevon’s age (T.)

We can substitute R + 7 for T in the equation

T + R = 49.

We have:

R + 7 + R = 49
Now solve.

2R + 7 = 49

2R = 42

R = 21

We have found Riggs’ age which is 21.

Add 7.

Trevon’s age is 28.
lord [1]3 years ago
3 0

Answer:

Trevon is 28 years old

Step-by-step explanation:

Riggs =x

Trevon =7+x

7+x+x=49

7+2x=49

2x=49-7

2x=42

x=21

Trevon is 21+7= 28 years old

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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

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

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\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.

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

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