find the area of the octagon then subtract the area of the square
For this case we must find the area of the octagon and subtract the area from the square, in order to obtain the area of the shaded region.
P: It is the perimeter
a: It is the apothem
We have to:
On the other hand:
the answer to this is 5000,000
g = 2.38
8.17 = 2(g + 2.24) − 1.07
8.17 = 2g + 4.48 - 1.07
add or subtract like terms
8.17 = 2g + 3.41
subtraction property of equality (-3.41 on both sides)
4.76 = 2g
divide both sides by 2 to get g alone
2.38 = g
9514 1404 393
f⁻¹(x) = √((3 -x)/3)
A function gives you a y-value for each value of x.
y = f(x)
An inverse function tells you the x value that produced a given y-value. It is the solution to the equation ...
x = f(y)
So, we want to find y for ...
x = -3y² +3
x -3 = -3y² . . . . . . . . . . . subtract 3
(x -3)/-3 = y² . . . . . . . . . divide by -3
√((x -3)/-3) = y . . . . . . . take the square root.
The requirement for x > 0 in the original function means y > 0 for the inverse function. That is why we use the positive square root.
This can be simplified a little bit to remove the minus sign from the denominator.
The graph plots the function and its inverse. They are reflections of each other over the line y=x. (That's one way you can tell you have the correct inverse function.)