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Write an inequality that represents `t`, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning

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MrRoyalidn

Question:

At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.

Write an inequality that represents t, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning.

Answer:

[tex]t > 4.5[/tex]

Step-by-step explanation:

Given

Let T = temperature and t = hours past midnight

So, we have:

[tex](t_1,T_1) = (0,5)[/tex] --- at midnight

[tex]m = -2[/tex] --- rate (it is negative because the temperature drops)

Required

Determine the inequality when the temperature is colder than -4 degrees

First, we calculate the hours when the temperature at -4 degrees

This is represented as:

[tex](t_2,T_2) = (t,-4)[/tex]

[tex](t_1,x_1) = (0,5)[/tex]

Using the slope formula, we have:

[tex]m = \frac{T_2 -T_1}{t_2 - t_1}[/tex]

[tex]-2 = \frac{-4-5}{t -0}[/tex]

[tex]-2 = \frac{-9}{t}[/tex]

Solve for t

[tex]t = \frac{-9}{-2}[/tex]

[tex]t = 4.5[/tex]

This implies that: at 4.5 hours, the temperature is at -4 degrees Celsius.

So, the inequality is:

[tex]t > 4.5[/tex]

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