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The temperature has been dropping 2º c every hour, and the temperature at 10:00 AM was-15 °c. At what time was the temperature 0°c ?

Sagot :

Darian

Answer:

[tex]\huge\boxed{2:30 AM}[/tex]

Given Information:

  • Every hour the temperature decreases by 2ºC.
  • At 10 AM the temperature was -15ºC.
  • We need to find the time when the temperature was 0°C.

Variables and constants:

  • y is the temperature.
  • t is the time in hours.
  • m is the rate of temperature decrease per hour, which is -2°C per hour.
  • c is the initial temperature at 10:00 AM, which is -15°C.

Step-by-step explanation:

As the temperature decrease is linear, we can construct a linear equation in the format [tex]y=mt+c[/tex] using the information given, giving us [tex]y=-2t-15[/tex]. The next step is to set y, which is the temperature, to 0. This will give us the equation of [tex]-2t-15=0[/tex]. We can then rearrange this to make -2t the subject of the equation by adding 15 to both sides, giving us [tex]-2t=15[/tex]. To isolate t we would divide both sides by -2, giving us [tex]t=-7.5[/tex]. This tells us that 7.5 hours before 10AM the temperature was 0. To find the time 7.5 hours before 10:00 AM, subtract 7 hours and 30 minutes from 10:00 AM, telling us that the temperature was 0°C at 2:30 AM.

1) Identify that it is a linear decrease.

[tex]y=mt+c[/tex]

2) Construct a linear equation.

[tex]y=-2t-15[/tex]

3) Set the equation to 0.

[tex]-2t-15=0[/tex]

4) Add 15 to both sides.

[tex]-2t=15[/tex]

5) Divide both sides by -2.

[tex]t=\frac{15}{-2}[/tex]

[tex]t=-7.5[/tex]

6) Subtract 7 hours from 10:00 AM.

10:00 AM−7 hours=3:00 AM

7) Subtract 30 minutes from 3:00 AM:

3:00 AM−30 minutes=2:30 AM

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