Answer:
The car's average 18 number of miles per gallon
Step-by-step explanation:
The car has different efficiencies depending if its used on highway or city streets.
The efficiency on a highway is:
The efficiency for city driving is:
We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.
Then, we can calculate how many miles makes the car on average as:
Here we have a system of equation like this:
from the first equation we get:
Substitute in the second equation we get:
Substitute i the first equation again we get:
We deduce that:
A is bigger than B.
The intersection of two planes is always a line
All you have to do is plug in the given values into the given equation and evaluate.
The expression is,
But we have to analyze the problem carefully. This is a natural phenomenon that can be modelled by a decay function. The reason is that, after every hour we expect the medicine in the blood to keep reducing.
Therefore we use the decay function rather. This is given by,
where,
and
On substitution, we obtain;
Now, we take our calculators and look for the constant
,then type e raised to exponent of -1.4. If you are using a scientific or programmable calculator you will find this constant as a secondary function. Remember it is the base of the Natural logarithm.
If everything goes well, you should obtain;
This implies that,
Therefore after 10 hours 24.66 mg of the medicine will still remain in the system.
