Use the order of operations to find the value of the expression. 2 + 3 × 16 − 2 × 21 − 3
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Answer:
The equation to represent the amount of water that the tank contains after the pump was working for
hours can be given as:
Step-by-step explanation:
Given:
Water tank initially contained = 24 gallons of water
The pump to fill the tank was switched to fill it.
From 10:00 AM to 10:30 AM the tank contained 40 gallons of water.
By 1:00 PM the tank contained 120 gallons of water.
To write an equation which will tell the amount of water that the tank contains after the pump was working for
hours
Solution:
Initially, gallons of water in tank = 24
From 10:00 AM to 10:30 AM the tank had 40 gallons of water.
Thus, in half an hour the pump filled = = 16 gallons
Using unitary method:
If in of an hour water filled = 16 gallons
So, in 1 hour the water filled will be = = 32 gallons
In 3 hours the water filled will be = = 96 gallons
Thus, by 1:00 PM the water in the tank will be = = 120 gallons
This confirms the data given for 1:00 PM.
This shows that the rate at which the pump fills the tank is 32 gallons of water per hour.
The equation to represent the amount of water that the tank contains after the pump was working for
hours can be given as:
Because they're not inverses, not exactly. is not invertible on its entire domain because it's not one-to-one. There are infinitely many values of
such that
, for example.
The standard function has a domain of
and outputs values between
and
. This means that its inverse,
, is indeed its inverse as long as
.
is larger than
and thus does not fall in the "invertible part" of the domain of
. We have
which is a value between -1 and 1, so that
If we wanted to recover , we'd have to redefine
or define a new inverse function that works on a different branch of the domain of
.