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: The answer is A.
Step-by-step explanation:
As a ratio, 5:86 represents students to teachers
We can set up the equation as 5/86=x/9460
Multiply 9460 to both sides
5x9460/86=x
47300/86=x
x=550
There are 550 professors
Table
<span> In favor Opposed Undecided
Grade 9 5 3 9
Grade 10 8 12 9
Grade 11 15 16 10
Grade 12 12 6 11
Probability = number of positive outcomes / number of possible outcomes
Probability that a student in grade 9 is in favor of extending the school day =
number of students in 9 grade in favor / number of students in grade 9
number of students in 9 grade in favor = 5
number of students in 9 grade = 5 + 3 + 9 = 17
Probability = 5 / 17
Answer: 5 / 17
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