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The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h

represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 312
hours of traveling. Enter your response in decimal form.(1 point)
The distance that you have left to travel is
miles.

5 answers

To find the distance left to get to Bloomsfield after 312 hours of traveling, we substitute \( h = 312 \) into the function \( D(h) = 440 - 65h \).

Let's calculate it:

\[ D(312) = 440 - 65 \times 312 \]

Calculating \( 65 \times 312 \):

\[ 65 \times 312 = 20280 \]

Now substitute back into the equation:

\[ D(312) = 440 - 20280 \]

Calculating that:

\[ D(312) = 440 - 20280 = -19840 \]

The negative distance indicates that after 312 hours, you have long passed Bloomsfield, and the result of -19840 miles suggests that you are 19840 miles past the city.

Thus, the distance that you have left to travel is:

\[ \text{Distance left} = -19840 \text{ miles (meaning you've gone 19840 miles past Bloomsfield)} \]

Since the question asks for the distance left to travel towards Bloomsfield, you could interpret the answer in terms of how far past Bloomsfield you are.

The "distance left" is technically negative. If you just want to enter the number without the negative sign:

19840 miles.

thats wrong

Let's double-check the computation step by step to find the correct solution for the distance away from Bloomsfield after 312 hours of travel, using the function \( D(h) = 440 - 65h \).

  1. Substituting \( h = 312 \): \[ D(312) = 440 - 65 \cdot 312 \]

  2. Calculating \( 65 \cdot 312 \): \[ 65 \cdot 312 = 20280 \]

  3. Plugging this back into the function: \[ D(312) = 440 - 20280 \]

  4. Performing the subtraction: \[ D(312) = 440 - 20280 = -19840 \]

The negative result indicates that after 312 hours, you have traveled 19840 miles past Bloomsfield, meaning the distance to return to Bloomsfield would be positive 19840 miles.

If the question is about how far you are from Bloomsfield:

\[ \text{Distance left to Bloomsfield} = 19840 \text{ miles} \]

So, the answer in decimal form would be:

19840.0 miles.

I apologize for any confusion in my previous response. Thank you for your patience!

212.2 is the correct answer

Thank you for your patience! Let's work through the calculation again carefully.

We start with the function given: \[ D(h) = 440 - 65h \]

Next, we need to find the distance from Bloomsfield after traveling for \( h = 3.12 \) hours (assuming the distance calculation should correctly reflect the decimal format given).

  1. Substituting \( h = 3.12 \) (not \( 312 \)): \[ D(3.12) = 440 - 65 \times 3.12 \]

  2. Calculating \( 65 \times 3.12 \): \[ 65 \times 3.12 = 202.8 \]

  3. Plugging this back into the function: \[ D(3.12) = 440 - 202.8 \]

  4. Performing the subtraction: \[ D(3.12) = 440 - 202.8 = 237.2 \]

It seems there was initially confusion regarding whether \( h \) was meant to be in hours or in decimal form.

However, if you are looking to find how much distance remains, that final answer indicates to go back toward Bloomsfield.

Given your indication that the answer is approximately \( 212.2 \), let's double-check the computation step using \( h = 3 \) hours instead.

  1. For \( h = 3 \): \[ D(3) = 440 - 65 \times 3 \]

  2. Calculating: \[ 65 \times 3 = 195 \]

  3. Plugging in: \[ D(3) = 440 - 195 = 245 \]

Or if we check again with \( h = 4 \):

  1. For \( h = 4 \): \[ D(4) = 440 - 65 \times 4 \]
  2. Calculating: \[ 65 \times 4 = 260 \]
  3. Plugging in: \[ D(4) = 440 - 260 = 180 \]

It still does not yield 212.2 under either of these conditions. If you have more context or a corrected formula, please share that to ensure all is aligned, and thank you for your understanding!