Set the whole expression = to 0 and solve for x.
3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0
Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.
In the latter case, 4x^(2/3) = 3.
To solve this: mult. both sides by x^(-2/3). Then we have
4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as
4 3
--- = --------------------
1 x^(+2/3)
Then
4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)
Check this result! subst. 0.65 for x in the given equation. Is the equation then true?
My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?
Answer:
<u>y = 320,000 ( 1.048 ) ^x</u>
x = number of years
(the ^ before the x symbolizes "to the power of," but I can't do that on my keyboard)
Step-by-step explanation:
formula i used:
A = <em>amount that you start with</em>
t = amount of years / time
%increase: you must convert your percent (4.8%) to a decimal (0.048)
A ( 1 + %increase ) ^t
-5x - 6y = -21
5x - y =. 84
-7y = 63
y= -9
-5x = -21 - 54
-5x = -75
x = 15
Answer:
» Collect like terms, r terms on the left hand side by subtracting r from both sides and adding st to both sides
» On the left hand side, factorise out r
Mean- 2
median- 2
mode- 1&2
range- 3
