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A circle is characterized by radius, arc, sectors and circumference
- The length of the major arc is
- The radius of the circle is 15
- The area of the shaded sector is
The given parameters are:
--- the circumference
-- the center angle
The length of the major arc is calculated using:
So, we have:
Evaluate
Hence, the length of the major arc is
The circumference is given as:
So, we have:
Divide through by 2pi
Hence, the radius of the circle is 15
<h3>The area of the shaded sector</h3>The area of a sector is:
So, we have:
Evaluate
Hence, the area of the shaded sector is
Read more about circumference at:
Answer:
x = 2
Step-by-step explanation:
The relevant rule of logarithms is ...
log(a/b) = log(a) -log(b)
This lets us combine the logs on the left to get ...
log((6 +7x)/(3x -2)) = log(5)
Taking anti-logs gives ...
(6 +7x)/(3x -2) = 5
6 +7x = 5(3x -2) . . . . . multiply by (3x -2)
7x +6 = 15x -10 . . . . . eliminate parentheses
8x = 16 . . . . . . . . . . . add 10-7x to both sides
x = 2 . . . . . . . . . . . . . divide by 8
The solution is x = 2.
_____
The graph shows the left side of the equation is equal to the right side for x=2.
