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mestny [16]
2 years ago
11

3.2 is what percent of 80?

Mathematics
1 answer:
Rus_ich [418]2 years ago
6 0
Percent means per one hundred...

3.2/80=p/100

p=100(3.2)/80

p=4%
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Solve for k<br> k - 2/ 5 = 11j
Vikki [24]
You have to move the -2/5 by the 11j to get k by its self
K=11j+-2/5
8 0
3 years ago
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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))

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4 0
3 years ago
What is 5,841 divided by 62
baherus [9]

Answer:

The answer is 94.2096774194

5 0
3 years ago
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If the difference of a number and two is tripled, the result is six more than the number. Find the number. Round your answer to
Nataly [62]

Answer:

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8 0
2 years ago
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grigory [225]

Answer:

The equation to represent  the amount of water that the tank contains (W) after the pump was working for T hours can be given as:

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Step-by-step explanation:

Given:

Water tank initially contained = 24 gallons of water

The pump to fill the tank was switched to fill it.

From 10:00 AM to 10:30 AM the tank contained 40 gallons of water.

By 1:00 PM the tank contained 120 gallons of water.

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From 10:00 AM to 10:30 AM the tank had 40 gallons of water.

Thus, in half an hour the pump filled = 40-24 = 16 gallons

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This shows that the rate at  which the pump fills the tank is 32 gallons of water per hour.

The equation to represent  the amount of water that the tank contains (W) after the pump was working for T hours can be given as:

W=32T+24

4 0
3 years ago
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