Mth163
I would Just like to know if i am doing the following problem right. The question states Obtain expressions for the following: Where value(t)=$1000(1.07)^t find for value(t+3) and value(t+3)/value of(t)When I did these problems I came out with $1000(1.07)^(t+3) and $1000(1.07)^(t+3)/$1000(1.07)^t Am I anywhere near to being correct?
Good but that expression can be simplified. The following was also posted with questions for 050914:
value(t+3) / value(t) = 1000(1.07)^(t+3)/(1000 * 1.07^t).
This can be simplified.
Recall that a^(b + c) = a^b * a^c. So
$1000 ( 1.07)^(t + 3) =
$1000 ( 1.07)^t * (1.07)^3.
So
1000(1.07)^(t+3)/(1000 * 1.07^t) =
$1000 ( 1.07)^t * (1.07)^3 / ( $1000 * 1.07^t) =
1.07^3.
Obtain expressions for the following: Where illumination(distance)=50/distance^2 for illumination(distance)/illumiation(2*distance). The answer I got is (50/distance)/(50/4distance^2)Is this correct?
Also good, but be careful of your grouping. Your expression at this point should read
(50/distance)/(50/ (4distance^2) ).
(50/4distance^2) means 50 / 4 * distance^2, or 50 distance^2 / 4, by order of operations; and that would not be right.
This is also posted under Questions for 050914:
There are two expressions in the expression illumination (distance)/illumination(2*distance).
One is
illumintation(distance)
and the other is
illumination (2 * distance).
You are given that
illumination (distance) = 50 / distance^2.
From this it follows that
illumination (2 * distance) = 50 / (2 * distance)^2.
So
illumination (distance)/illumination(2*distance) = ( 50 / distance^2 ) / (50 / (2 * distance)^2 ).
(a / b) / ( c / d) = (a / b) * ( d / c), so
( 50 / distance^2 ) / (50 / (2 * distance)^2 ) = ( 50 / distance^2 ) * (2 * distance)^2 / 50.
50 / 50 = 1 so the expression is
(2 * distance)^2 / distance^2, which is equal to
2^2 * distance^2 / distance^2. Since distance^2 / distance^2 = 1, the final result is just
2^2, or 4.