If the simple interest on $6000 for 9 years is $2160, then what is the interest rate?
1 answer:
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Answer:
B.
Step-by-step explanation:
To simplify something that looks like you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:
.
If you had , then you would multiply top and bottom the conjugate of
which is
.
The conjugate of a+b is a-b.
These have a term for it because when you multiply them something special happens. The middle terms cancel so you only have to really multiply the first terms and the last terms.
Let's see:
(a+b)(a-b)
I'm going to use foil:
First: a(a)=a^2
Outer: a(-b)=-ab
Inner: b(a)=ab
Last: b(-b)=-b^2
--------------------------Adding.
a^2-b^2
See -ab+ab canceled so all you had to do was the "first" and "last" of foil.
This would get rid of square roots if a and b had them because they are being squared.
Anyways the conjugate of is
.
This is the thing we are multiplying and top and bottom.
In case you're not already aware, the expression is called the "difference quotient" and represents the average rate of change of a function
over an interval
.
For the function , by substituting
we get
Then the difference quotient is
where the last equality holds as long as .