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____ [38]
3 years ago
13

The cold water faucet of a bathtub can fill the tub in 15 minutes. The drain, when opened, can empty the full tub in 20 minutes.

Suppose the tub is empty and the faucet and drain are both opened at the same time. How long will it take to fill the tub?
Mathematics
2 answers:
masya89 [10]3 years ago
8 0

Answer:

60 minutes

Step-by-step explanation:

  • faucet takes 15 minutes to fill the tub, so how much of the full tub is added per minute?
  • 15 minutes=1added/minute\\1minute=\frac{1}{15} added/minute
  • drain takes 20 minutes to empty the tub so how much of the full tub is lost per minute?
  • 20minutes=1lost/minute\\1minute=\frac{1}{20} lost/minute
  • How long it takes to fill the tub can be found by how much of it is added per minute minus lost per minute
  • totalfilled/minute=added/minute-lost/minute\\=\frac{1}{15} -\frac{1}{20}=\frac{1}{60}
  • So one sixtieth of the tub is filled a minute, so that 60 parts of the tub, each taking a minute, that's 60 minutes or 1 hour
pentagon [3]3 years ago
5 0

Answer:

10 minutes

Step-by-step explanation:

This is because if u have both the faucet and drain on at the same time, it will fill the tub faster

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Answer:

4, 2, 1, 2, 4

Step-by-step explanation:

-2 <= 0, so use the first equation, f(x) = (1/2)^x, to find f(-2).

f(-2) = (1/2)^-2 = 1^-2/2^-2 = 2^2/1^2 = 4/1 = 4

-1 <= 0, so use the first equation, f(x) = (1/2)^x, to find f(-1).

f(-1) = (1/2)^-1 = 1^-1/2^-1 = 2^1/1^1 = 2/1 = 2

0 <= 0, so use the first equation, f(x) = (1/2)^x, to find f(0).

f(0) = (1/2)^0 = 1^0/2^0 = 1/1 = 1

1 > 0, so use the second equation, f(x) = 2^x, to find f(1).

f(1) = 2^1 = 2

2 > 0, so use the second equation, f(x) = 2^x, to find f(2).

f(2) = 2^2 = 4

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1 year ago
Which expression is equivalent to x2 − x − 6 x2 + 2x − 15 ? A) x + 3 x + 5 B) x + 2 x + 5 C) x + 3 x − 3 D) x + 2 x − 3
Tema [17]

Answer:

Well, I am not sure which one is equivalent to another, but I have some information that should help you find your answer.

Step-by-step explanation:

The simplified expression to x2 − x − 6 x2 + 2x − 15 would be equal to −5 x 2 + x − 15.

The simplified expression to x + 3 x + 5 would be equal to 4x + 5.

The simplified expression to x + 2x + 5 would be equal to 3x + 5.

The simplified expression x + 3 x − 3 would be equal to 4x − 3.

The last simplified expression to x + 2 x − 3 would be equal to   3x − 3.

Hope this helps, I am really sorry if I didn't answer your question properly, or the way you asked!

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
andrew11 [14]

Differentiating both sides of

x^2 + 2xy - y^2 + x = 20

with respect to x yields

2x + 2y + 2x \dfrac{dy}{dx} - 2y \dfrac{dy}{dx} + 1 = 0 \\\\ \implies (2x-2y) \dfrac{dy}{dx} = -1 - 2x - 2y \\\\ \implies \dfrac{dy}{dx} = \dfrac{1 + 2x + 2y}{2(y-x)}

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