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iragen [17]
2 years ago
8

B. Juan’s cell phone company charges $35 a month for phone service plus $0.50 for each text message. How many text messages does

Juan send in a month if his bill was $52?
1. Define the variable: 2. Determine the constant:$35
3. What is the rate? 4. Write the equation and solve: 35+0.50t=52

C. Friendship’s soccer team purchased uniforms and equipment for a total cost of $912. The equipment cost $612, and the uniforms cost $25 each. How many uniforms did the school purchase?
1. Define the variable: 2. Determine the constant:
3. What is the rate: 4. Write the equation and solve:


D. Long’s Coffee Shop sells a refill mug for $8.95. Each refill costs $1.50. Last month, Jalissa spent $26.95 on a mug and refills. How many refills did she buy?
Write the equation and solve:
Mathematics
2 answers:
Crank2 years ago
8 0

C. Because that is the answer my guy.

goldfiish [28.3K]2 years ago
4 0
The answer is c I’m pretty sure :)
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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
Peter wallpapered a wall that was 9 feet wide and 8 feet high. He had 27 square feet of wallpaper left over. How many square fee
ivanzaharov [21]

Answer:

99 square feet

Step-by-step explanation:

Because 8 times 9=72+27=99

7 0
2 years ago
Read 2 more answers
Help could it be any two integers?
Novosadov [1.4K]

Yes, as long as it's between the two numbers

51) -4 and 1

52) -1 and -3

53) -9 and -10

5 0
3 years ago
joe and Eric have to ship 75 packages. Joe can do the job alone in 5 hours. if Eric helps, they get it done in 4 hours. How long
Umnica [9.8K]

Eric took 20 hours to do the job alone.

<u>Step-by-step explanation</u>:

<u>Given </u>:

  • Total work = 75 packages
  • Joe took 5 hours to complete the total work.

The amount of work Joe alone can do per hour = 75/5 = 15 packages.

The amount of work Joe and Eric together do per hour = 75/4 = 18.75

The amount of work Eric alone can do per hour = 18.75 - 15 = 3.75

The time Eric took to complete the entire work = 75 / 3.75 = 20 hours.

8 0
3 years ago
Please help its due tommorrow morning!
LenaWriter [7]

Answer: $324

Step-by-step explanation:

i=prt

i=(6000)(.054)(1)

i=324

4 0
3 years ago
Read 2 more answers
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