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nata0808 [166]
3 years ago
15

A standard showerhead in Sonia's house dispenses 12 gallons of water per minute. Sonia changed this showerhead to an energy-savi

ng one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x How much water does Sonia save each day with the change in showerheads if she uses the shower for 8 minutes each day?
Mathematics
1 answer:
diamong [38]3 years ago
7 0

Sonia saves a lot of water. To figure this out, you plug the number 8 into the equation, replacing it with the variable x. y = 3(8). Therefore, y=24. To find out how much water she saves, you have to also figure out how much water she was using for 8 minutes with the other shower head, the one that wastes the water. Since it dispenses 12 gallons per minute, you multiply that by 8 minutes and get 96. Subtract 24 from 96 and get 72. Which I think is your answer. Then again, I'm in high school so I most likely am wrong.

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Phantasy [73]
Ah, this is an infinite sum question, or a sum of geometric sequence
when will the sum reach 1cm of the edge or about 1.99m
so

2m=200cm
within 1cm means at least 1.99m
so
we will use m and not cm for consitancy

sum of geometric sequence is
S_n= \frac{a_1(1-r^n)}{1-r}
a1=first term=initial jjump=1
r=common ratio=1/2
n=?, we ar solving for that

so
we want it to equal 1.99 so

1.99= \frac{1(1- (\frac{1}{2})^n)}{1-\frac{1}{2}}
1.99= \frac{(1- (\frac{1}{2})^n)}{\frac{1}{2}}
1.99= 2(1- (\frac{1}{2})^n)
divide both sides by 2
\frac{1.99}{2} = 1- (\frac{1}{2})^n
times -1
\frac{-1.99}{2} = (\frac{1}{2})^n-1
add 1 or 2/2 to both sides
\frac{0.01}{2} = (\frac{1}{2})^n
take the ln of both sides
ln(\frac{0.01}{2}) = ln((\frac{1}{2})^n)
ln(\frac{0.01}{2}) = n ln(\frac{1}{2})
divide both sides by ln(1/2)
\frac{ln(\frac{0.01}{2})}{ln(\frac{1}{2})} =n
use your calculatro to find that n≈7.64386
so on 7th jump, it is not yet at 1cm to the edge but at 8th jump, it is past
so 8th jump
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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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(10⁰x 10¹ x 1¹⁰)

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