Aheated piece of metal cools according to the function c(x) = (.5)x − 7, where x is measured in hours. a device is added that aids in cooling according to the function h(x) = −x − 2. what will be the temperature of the metal after two hours?
-4 celsius
28 celsius
32 celsius
38 celsius

Option (b) is correct.

The temperature of the metal after two hours is 28 Celsius

Step-by-step explanation:

  Given : A heated piece of metal cools according to the function   ,  where x is measured in hours and then a cooling device id added that aids in cooling according to the function

We have to determine the temperature of the metal after two hours.

Let w(x) denotes the temperature of metal .

Thus, w(x) can be given by function c(x) + h (x) = [c + h](x)

Thus, , where x is measured in hours.

Thus, after two hours that is when x = 2

the temperature of metal is given by w(2)

Solving , we get,

Thus, the temperature of the metal after two hours is 28 Celsius.

Hence, Option (b) is correct.

Option B is correct.

28 Celsius

Step-by-step explanation:

As per the statement:

A heated piece of metal cools according to the function

where x is measured in hours.

It is also given that:

A device is added that aids in cooling according to the function h(x) = −x − 2.

then the resultant metal of function becomes:

Substitute the functions:

                   ......[1]

We have to find the temperature of the metal after two hours.

⇒x =2 hours

Substitute the value in [1] we have;

⇒

Therefore, the temperature of the metal after two hours will be 28 Celsius