Multiply & Divide Rational Numbers Unit Test

Question

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Question
A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane’s altitude. Give your answer to the nearest hundredth, and remember the plane is descending.(1 point)
The quotient that best represents the rate of change in the plane’s altitude is
feet/minute.

Answer 1

To find the rate of change in the plane's altitude, we need to divide the total change in altitude by the time taken for that change.

In this case, the plane is descending 4,000 feet in 3.5 minutes.

The calculation would be:

\[ \text{Rate} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{-4000 \text{ feet}}{3.5 \text{ minutes}} \]

Now, let's perform the division:

\[ \text{Rate} = -\frac{4000}{3.5} \approx -1142.8571 \text{ feet/minute} \]

Rounding this to the nearest hundredth, we get:

\[ \text{Rate} \approx -1142.86 \text{ feet/minute} \]

So the quotient that best represents the rate of change in the plane’s altitude is approximately -1142.86 feet/minute (indicating descent).

Answer 2

That an awfully big number, are you sure its correct?

Answer 3

Let’s double-check the calculations step by step for accuracy.

We need to find the rate of descent when a plane descends 4,000 feet in 3.5 minutes.

1. Change in altitude: This is -4000 feet (because it’s descending).
2. Time taken: 3.5 minutes.

The rate of change in altitude (which will be a negative number because it’s descending) can be calculated as follows:

\[ \text{Rate} = \frac{\text{Change in altitude}}{\text{Time}} = \frac{-4000 \text{ feet}}{3.5 \text{ minutes}} \]

Now, let's perform the division accurately:

\[ \frac{4000}{3.5} = 1142.8571 \]

Thus,

\[ \text{Rate} = -1142.8571 \text{ feet/minute} \]

When we round this to the nearest hundredth, we do indeed get:

\[ \text{Rate} \approx -1142.86 \text{ feet/minute} \]

So, the calculation seems correct. This is the correct rate of descent for the airplane. The value is quite large because descending 4,000 feet in just 3.5 minutes is a significant change in altitude, which translates to a steep descent rate.

Answer 4

Alright well I got five questions wrong from this websites AI so most of it is stupid but I'm proud of you. You where one of the few who got a question right. Thanks! SOrry I doubted you

Answer 5

Thank you for your understanding, and no need to apologize—questions about calculations can sometimes be confusing! I'm glad I could help clarify the rate of descent for you. If you have any more questions, whether they're about math or anything else, feel free to ask. Good luck with your studies!