QuestionWhat was the temperature at midnight if it dropped $0.5^{\circ} \mathrm{C}$ each hour to $11.5^{\circ} \mathrm{C}$ by $5:00$ am?

Studdy Solution

STEP 1

Assumptions1. The temperature dropped $0.5^{\circ} \mathrm{C}$ each hour from midnight to $500$ am. . The temperature at $500$ am was $11.5^{\circ} \mathrm{C}$ .
3. The temperature drop was consistent each hour.

STEP 2

First, we need to find the total temperature drop from midnight to $500$ am. We can do this by multiplying the temperature drop each hour by the number of hours.
$Total\, temperature\, drop = Temperature\, drop\, each\, hour \\times Number\, of\, hours$

STEP 3

Now, plug in the given values for the temperature drop each hour and the number of hours to calculate the total temperature drop.
$Total\, temperature\, drop =0.5^{\circ} \mathrm{C} \\times5\, hours$

STEP 4

Calculate the total temperature drop.
$Total\, temperature\, drop =0.^{\circ} \mathrm{C} \\times\, hours =2.^{\circ} \mathrm{C}$

STEP 5

Now that we have the total temperature drop, we can find the temperature at midnight. This is the temperature at $500$ am plus the total temperature drop.
$Temperature\, at\, midnight = Temperature\, at\,500\, am + Total\, temperature\, drop$

STEP 6

Plug in the values for the temperature at $500$ am and the total temperature drop to calculate the temperature at midnight.
$Temperature\, at\, midnight =11.5^{\circ} \mathrm{C} +2.5^{\circ} \mathrm{C}$

STEP 7

Calculate the temperature at midnight.
$Temperature\, at\, midnight =11.5^{\circ} \mathrm{C} +2.5^{\circ} \mathrm{C} =14^{\circ} \mathrm{C}$ The temperature at midnight was $14^{\circ} \mathrm{C}$ .

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