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AdorableApatosaurus7671

Good evening, I have trouble to get the right answer for the following question. The answer key says it’s 8 hours, but I really can’t see how to get this number even though with a graph.

Thank you so much for helping me ;)

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FerUpsilon5520

You should consider the time for this science project as

starting at 07:00 up to 19:00 as it covers a period of 12 hours.

Your function becomes

T(t) = a|t - 15| + 0 as the maximum is at (15,0)

using the other point (7, -20) one finds a = -5/2

You should be able to verify that the period during which

T(t) = (-5/2) |t - 15| < -5 for 7 ≤ t ≤ 19

is effectively 8 hours (dont forget to consider the two sides)

Ramzi Z

Hi !

There might be a mistake in the points you have taken. Since \(x\) is the number of hours and we can take 7 AM as the beginning of the recording, the points should be (0,-20) and (8,0) sinc 3 PM is 8 hours later than 7 AM. And with these points, you can go on and find the formula for the absolute value function.

https://www.alloprof.qc.ca/fr/eleves/bv/mathematiques/la-recherche-de-la-regle-d-une-fonction-valeur-ab-m1160

I hope this helped you and if you have any other questions, feel free to ask them !

Have a nice day !

ArsenicSigma5082

Hi

Let's start by figuring out the rate of change (a) For this, we can use the given information along with the formula y2-y1/x2-x1. y being the temperature (-20 and 0) and x being the time (7:00 and 15:00):

(0 - -20) / (15 - 7) = 20/8 = 2.5

Let's remember that since we want our vertex to be the maximum, we need to add a negative sign in order to flip the line upside down. We therefore know that our equation will look something like this:

f(x) = -2.5|x - h| + k

To find the rest of the formula, we just have to find the vertex, which you already wrote down (although I will convert it to 24h time to avoid errors), and put it in the formula:

f(x) = -2.5|x - 15| + 0

Now, you just have to plug the value you're evaluating (-5) into the formula as a variable (y):

-5 = -2.5|x - 15|

2 = |x - 15|

2 = ±(x - 15)

x1:

2 = x - 15

17 = x

x2:

2 = -x + 15

-13 = -x

x = 13

We now know that the temperature went above -5 at 1 pm (13:00) and went back down under -5 again at 5 pm (17:00)

Finally, we know that our experiment began at 7 am and lasted 12 hours (7:00 to 19:00). Therefore, we just have to count the hours between 7:00 and 13:00, and the hours between 17:00 and 19:00:

13 - 7 = 6 hours before

19 - 17 = 2 hours after

Total 8 hours.

Hope this helped, let me know if you have other questions