Daisy works at an ice-cream parlor. She is paid $10 per hour for the first 8 hours she works in a day. For every extra hour she
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Answer:
$1210
Step-by-step explanation:
Let x be total amount
First John spent $110 on a radio and 4/11 of what was left on presents for his friends so he was left with
Then he put 2/5 of his remaining money into a checking account
Rest he donated to charity
Hence total amount of money John originally had was $1210
A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F
B)
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
Which implies that:
, which means that 30 minutes have passed after the conditioner has started to cool the house
, 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:
where
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:
which means that the temperature decreases by 0.4°F every minute. So, the function can be written as