Given:
A circle of radius r inscribed in a square.
To find:
The expression for the area of the shaded region.
Solution:
Area of a circle is:
Where, r is the radius of the circle.
Area of a square is:
Where, a is the side of the square.
A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.
So, the area of the square is:
Now, the area of the shaded region is the difference between the area of the square and the area of the circle.
Therefore, the correct option is (a).
This is hard in mathematical language, but there is only this way to present it. Let us denote by A the consentration of the substance and by A' its rate.
We have that b/A= t+c where c is a constant.
Hence A=b/(c+t)
By differentiating, we get that A'=-b/(C+t)^2
Then, we have that -(A)^2=A'/b
Hence at any point, we have that if we make the concentration 17 times, we have that there is a 17 times bigger , the rate will become bigger by 17*17, hence 289 times faster.
Huh, well the sum is just adding the numbers together, so the answer is 4905.
Suppose that this person drives at r mph going to the mountains, and gets there in 12 hours. Returning, this person drives at (r+20) mph and gets home in 8 hours. We don't know the distance yet, but can solve for the initial speed, r, by setting
d = 12r = (r+20)(8). Solving for r, r=40 mph (going) and (40+20)mph = 60 mph (returning. Since d=12 r, d = (12 hrs)(40 mph) = 480 miles (answer).
