Answer:
<h2>4</h2>
Step-by-step explanation:
<em>Look at the picture.</em>
<em />
<em>At the beginning we have to calculate what part of the angle 360° is the given angle 75°.</em>
<em />
<em />
<em>The same part of the circumference of the circle is the arc defined by this central angle.</em>
The circumference <em>C = 20</em>.
Therefore

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:
a. 
b. $225
Step-by-step explanation:
Let Mr. Scruggs got money for his birthday be 'a'
He spent
of it on dog treats = a × 
= 
remainder amount would be = a - 
= 
Then he divided the remainder money equally among 3 favorite charities.

= 
a. Each charity receive
b. If he donated $60 to each charity.


a = $225
Mr. Scruggs received $225 for his birthday.