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andriy [413]
3 years ago
8

Cal is creating a circular garden for his yard. The radius of the garden is 15 feet. He wants to put fencing around the garden t

hat costs $3.54 per foot. How much will the fencing cost? Explain your steps.
Mathematics
1 answer:
notsponge [240]3 years ago
7 0

Answer:

The fence will cost $333.64

Step-by-step explanation:

In order to calculate how much it'll cost to build the fence around his garden we first need to know the length of material he'll need to buy. To do that we must find the length of the circle that surrounds the garden and then multiply by the price of each foot. The length of the circle is given by:

length = 2*pi*r

length = 2*pi*15

length = 30*pi

length = 94.25 feet

The cost of the fence, is:

cost = length*(cost per foot) = 94.25*3.54

cost = 333.64

The fence will cost $333.64

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<span>From the message you sent me:

when you breathe normally, about 12 % of the air of your lungs is replaced with each breath. how much of the original 500 ml remains after 50 breaths

If you think of number of breaths that you take as a time measurement, you can model the amount of air from the first breath you take left in your lungs with the recursive function

b_n=0.12\times b_{n-1}

Why does this work? Initially, you start with 500 mL of air that you breathe in, so b_1=500\text{ mL}. After the second breath, you have 12% of the original air left in your lungs, or b_2=0.12\timesb_1=0.12\times500=60\text{ mL}. After the third breath, you have b_3=0.12\timesb_2=0.12\times60=7.2\text{ mL}, and so on.

You can find the amount of original air left in your lungs after n breaths by solving for b_n explicitly. This isn't too hard:

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and so on. The pattern is such that you arrive at

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which is a very small number close to zero.</span>
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