We appreciate your visit to While Sam was at work his house lost electrical power By the time the power was restored the temperature inside the house was 88 F. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
After 30 minutes that the air conditioner started to cool Sam's house, the temperature was 76°F.
A linear equation is given by:
y = mx + b;
where m is the rate of change, y, x are variables and b is the y intercept
Let f(x) represent the temperature, in degrees Fahrenheit, of Sam’s house x minutes. the temperature inside the house was 88°F, hence b = 88
f(x) = mx + 88
Since f(30) = 76:
This means that after 30 minutes that the air conditioner started to cool Sam's house, the temperature was 76°F.
hence:
76 = m(30) + 88
m = -0.4
f(x) = -0.4x + 88
Find out more at: https://brainly.com/question/13911928
Thanks for taking the time to read While Sam was at work his house lost electrical power By the time the power was restored the temperature inside the house was 88 F. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F
B) [tex]f(x)=-0.4x+88[/tex]
Step-by-step explanation:
A)
In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.
So we have:
x = minutes after the air conditioner started to cool the house
f(x) = temperature
Here we want to find what is the meaning of
[tex]f(30)=76[/tex]
Which implies that:
[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house
[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F
So, the interpretation of f(30) =76 is that:
"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"
B)
Here we want to write explicitely a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.
We know the following information:
- At time x = 0, the temperature inside the house is 88°F
- At time x = 30 min, the temperature inside the hosue is 76°F
We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:
[tex]f(x)=mx+q[/tex]
where
[tex]q[/tex] is the value of the temperature at x = 0, so q = 88
m is the rate of change of the temperature
The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:
[tex]m=\frac{76-88}{30-0}=-0.4[/tex]
which means that the temperature decreases by 0.4°F every minute. So, the function can be written as
[tex]f(x)=-0.4x+88[/tex]
