Answer:
Given: The radius of circle C is 6 units and the measure of central angle ACB is StartFraction pi Over 2 EndFraction radians.
What is the approximate area of the entire circle?
113 square units
What is the approximate area of the entire sector created by central angle ACB?
28 square units
What is the approximate area of the shaded region only?
22 square units
Answer:
Step-by-step explanation:
this is a set problem (mathematical set)
30 students played soccer
9 students played cricket and soccer
x students played neither cricket nor soccer
3x students played cricket only.
we can see that in the first set 21 appears and in the middle of the set 9 because it says 30 students played soccer adding x and 3x we have the following formula
30 + x + 3x = 50 where x is equal to 5 then ask us Determine the number of students who played cricket. then the value would be 3x + 9 = (3x5) + 9 = 24
Volume of the cube with side 4p = 4p x 4p x 4p = 64p³
Volume of the cube with side 2q² = 2q² x 2q² x 2q² = 8q⁶
Total Volume = 64p³ + 8q⁶
Total Volume = (4p)³ + (2q²)³
Total Volume = (4p + 2q²)( ( 4p)² - (4p)(2q²) + (2q²)²)
Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)
Answer: (4p + 2q²)( 16p² - 8pq² + 4q⁴)
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:
mid point: (4,5)
hope that helps :)
Step-by-step explanation: