A car gets 35 miles per gallon. How many gallons do you need to go 700 miles?
2 answers:
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Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.
For the annually rate we have that:
Where
= initial investment.
= annually interest rate in decimal form.
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
= initial investment.
= quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
![\sqrt[4]{1.07} =1+ i_{q}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B1.07%7D%20%3D1%2B%20i_%7Bq%7D%20)
![i_{q} = \sqrt[4]{1.07} -1](https://tex.z-dn.net/?f=%20i_%7Bq%7D%20%3D%20%5Csqrt%5B4%5D%7B1.07%7D%20-1)
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
For the annually rate we have that:
Where
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
The equations we get are
l = 6 + 2w (We get this from "The length of the rectangle is 6 more than 2 times the width.")
and
2l + 2w = 140 (We get this from the perimeter. Two times the length plus two times the width equals the perimeter of a quadrilateral.)
The first equation can be written as
l - 2w = 6
So now we have
2l + 2w = 140
l - 2w = 6
____________
Add the two equations.
We get 3l = 146
Divide by 3 on both sides.
l = 48
Your answer is 48.
l = 6 + 2w (We get this from "The length of the rectangle is 6 more than 2 times the width.")
and
2l + 2w = 140 (We get this from the perimeter. Two times the length plus two times the width equals the perimeter of a quadrilateral.)
The first equation can be written as
l - 2w = 6
So now we have
2l + 2w = 140
l - 2w = 6
____________
Add the two equations.
We get 3l = 146
Divide by 3 on both sides.
l = 48
Your answer is 48