Respuesta :
Answer:
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 [tex]c(x)=(0.5)^{x-7}[/tex] , where x is measured in hours and then a cooling device id added that aids in cooling according to the function [tex]h(x)=-x-2[/tex]
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, [tex]w(x)=[c+h](x)\\\\w(x)=(0.5)^{x-7}+(-x-2)\\\\[/tex] , where x is measured in hours.
Thus, after two hours that is when x = 2
the temperature of metal is given by w(2)
[tex]w(x)=(0.5)^{x-7}+(-x-2)\\\\ w(2)=(0.5)^{2-7}+(-2-2)[/tex]
Solving , we get,
[tex]w(2)=(0.5)^{2-7}+(-2-2)\\\\ w(2)=(0.5)^{-5}+(-4)\\\\ w(2)=32-4=28[/tex]
Thus, the temperature of the metal after two hours is 28 Celsius.
Hence, Option (b) is correct.
Answer:
Option B is correct.
28 Celsius
Step-by-step explanation:
As per the statement:
A heated piece of metal cools according to the function
[tex]c(x) = (0.5)^{x-7}[/tex] 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:
[tex]f(x) = c(x)+h(x)[/tex]
Substitute the functions:
[tex]f(x) = (0.5)^{x-7} +(-x-2)[/tex] ......[1]
We have to find the temperature of the metal after two hours.
⇒x =2 hours
Substitute the value in [1] we have;
[tex]f(2) = (0.5)^{2-7} +(-2-2)[/tex]
[tex]f(2) = (0.5)^{-5} +(-4)[/tex]
⇒ [tex]f(2) = 32 -4 = 28[/tex]
Therefore, the temperature of the metal after two hours will be 28 Celsius
