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Andrei [34K]
3 years ago
14

Two similar parallelograms have areas of 18in^2 and 32in^2. find the ratio of their perimeters

Mathematics
1 answer:
raketka [301]3 years ago
3 0
   
\displaystyle\\
k =  \frac{P_1}{P_2} =  \sqrt{ \frac{A_1}{A_2} }=\sqrt{\frac{18}{32}}=\sqrt{\frac{9\times2}{16\times2}}=\sqrt{\frac{9}{16}}=\frac{\sqrt{9}}{\sqrt{16}}= \boxed{\bf \frac{3}{4}}



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Answer:

Part A)

Chorus:

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Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

c(t)=a(r)^t

Where <em>a</em> is the initial population and <em>r</em> is the rate of change.

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c(t)=15(1.12)^t

This represents the number of people in the chorus after <em>t</em> years.

We are given that 2 new people join the band each year. So, it increases linearly.

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And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

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Part B)

We want to find the number of people in the chorus and the band after 9 years.

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There will be approximately 41 people in the chorus after 9 years.

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Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for <em>t</em>. So:

15(1.12)^t=2t+30

Unfortunately, it is impossible to solve for <em>t</em> using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

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