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s2008m [1.1K]
3 years ago
7

A circular pizza has a diameter of 12 inches and is cut into 10 congruent slices. What is the area of each slice, to the nearest

tenth?
Group of answer choices

14.4 straight pi inches squared

3.6 straight pi inches squared

2.4 straight pi inches squared

12.4 straight pi inches squared
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
5 0
  • Diameter=12in
  • radius=r=12/2=6in

\\ \sf\longmapsto Area=2\pi r

\\ \sf\longmapsto Area=2(3.14)\times 6

\\ \sf\longmapsto Area=2(18.84)

\\ \sf\longmapsto  Area=37.68in^2

Now area of each slice

\\ \sf\longmapsto \dfrac{37.68}{12}

\\ \sf\longmapsto 3.6in^2

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Zina [86]
The answer to this question is b 

3 0
3 years ago
You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod
lorasvet [3.4K]

Answer:

a. y=830*(0.87)^x

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

13\%=\frac{13}{100}=0.13

Upon substituting our given values in exponential decay function we will get

y=830*(1-0.13)^x

y=830*(0.87)^x

Therefore, the exponential model y=830*(0.87)^x represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

y=830*(0.87)^2

y=830*0.7569

y=628.227\approx 628.23

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be \frac{830}{2}=415.

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

415=830*(0.87)^x

Upon dividing both sides of our equation by 830 we will get,

\frac{415}{830}=\frac{830*(0.87)^x}{830}

0.5=0.87^x

Let us take natural log of both sides of our equation.

ln(0.5)=ln(0.87^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.5)=x*ln(0.87)

\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}

\frac{ln(0.5)}{ln(0.87)}=x

\frac{-0.6931471805599}{-0.139262067}=x

x=4.977286\approx 4.98

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

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