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2 years ago

A store sells pool floats.

Mathematics

1 answer:

Andrei [34K]2 years ago

6 0

Step-by-step explanation:

the original retail price was 120% of the manufacturer price (100% manufacturer price + 20% markup).

now, the whole retail price is reduced by 12%.

that means we have to subtract 12% from the 120%.

but careful, we cannot just do 120-12=108.

that is simply because these 120% are now for this calculation the new basic amount and therefore 100%.

we actually need to calculate and subtract 12% of 120 to get the new percentage over the manufacturer price.

we do this by multiplying 120 by (100-12)/100 = 88/100 = 0.88 :

120 × 0.88 = 105.6%

so, the new retail price is now only 5.6% over the manufacturer price.

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2 years ago

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9514 1404 393

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Step-by-step explanation:

We assume your falling-distance formula is supposed to be ...

s = 16t²

So, the time required to fall distance s is ...

t = √(s/16) = (1/4)√s

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s = 1100t

t = s/1100

Then the sum of the time for the ball to fall and the time for the sound to travel back is ...

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275√s = 22000 -s . . . . . multiply by 1100 and subtract s

75625s = s^2 -44000s +484,000,000 . . . square both sides

s^2 -119,625s +484,000,000 = 0 . . . . put in standard form

s ≈ (1/2)(119,625 ±√12,374,140,625) = {4192.943, 115432.057}

Only the smaller of these two solutions makes any sense in this problem.

The hole is about 4192.9 feet deep.

_____

<em>Additional comment</em>

The distance equation for the falling object presumes a vacuum. The sound transmission presumes the presence of air, so the question setup is self-contradictory.

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3 years ago