Answer:
r = (ab)/(a+b)
Step-by-step explanation:
Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).
Using the Pythagorean theorem, we can write the relation ...
((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2
a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2
-4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab
r = ab/(a+b) . . . . . . . . . divide by the coefficient of r
The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).
_____
The graph in the second attachment shows a trapezoid with the radius calculated as above.
The minimum of this graph is the focus of the parabola. I'm not sure with the maximum though but I think it doesn't have a maximum because the y value of the parabola will extend infinitely upward.
Answer:
It's C
Step-by-step explanation:
Because the angle measurements are the same on rectangles and they have the same side lengths but the one on the right is a smaller rectangle which its only half the side of the bigger one.
Answer:
62.8
Step-by-step explanation:
the circumference is equal to the radiusx2xpi
it gives us the diameter but not the radius
to find the radius from the diameter we just divide it by 2 so the radius is 10
then we just do 10x2x3.14 which is 62.8
Answer:
Distance traveled by Sierra in h hours at a rate of 2x miles per hour = 2xh
Explanation:
Distance traveled by a body = Velocity of the body * Time taken by the body
Here velocity of Sierra = 2x miles per hour
Time taken by Sierra = h hours.
Distance traveled by Sierra = 2x * h = 2xh
So distance traveled by Sierra in h hours at a rate of 2x miles per hour = 2xh
