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2 years ago

What is the domain of the function f(x) = (-5/6)(3/5)superscript x

Mathematics

1 answer:

Georgia [21]2 years ago

5 0

Answer:

$-\infty < x < \infty$

Step-by-step explanation:

Given

$f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x$

Required

The domain

There are no undefined points such as denominator of x or square roots.

Hence, the domain is:

$-\infty < x < \infty$

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Answer:

Part A)The amount of water in the tank is changing at -2/3 gallons per minute. 

Part B) it will take 7.5 minutes for the tank to drain completely.

Part C) The water tank was completely full 4.5 minutes before Jada arrived.

Step-by-step explanation:

Information fetching:

Tank of water can hold up-to 10 gallons.

When it is active, a drain empties water from the tank at a constant rate.
7 gallons of water present in the tank when Jade first saw
5 gallons of water left after 3 minutes

Part A) At what rate is the amount of water in the tank changing?

As the gallons were decreased from 7 to 5 in three minutes. It means in three minutes, 2 gallons were decreased.

So, gallons per minute change would be -2/3 gallons per minute. Hence, the amount of water in the tank is changing at -2/3 gallons per minute. 

Note: negative sign indicates the number of gallons of water are decreasing.

Part B) How many more minutes will it take for the tank to drain completely.

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As Jada arrived when the tank had left 7 gallons.

Let 'm' be the number of minutes before Jada arrived when the water tank was completely full.

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= 4.5 minutes

So, the water tank was completely full 4.5 minutes before Jada arrived.

Keywords: time rate of change, time

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