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.
Step-by-step explanation:
Morning is 4 hr 15 min
afternoon is 4 hour 15 min
together is 8 hour 30 min
8.5*14 = 119 dollars
Answer:
33.5
-by-step explanation:
8.5 + (12 + 4) × 2 - 7
Use PEMDAS ( I think this is right hope it helps!)
Answer:
Each student gets 2 1/3
Step-by-step explanation:
So you would divide 7 by 3, which you can't...so 6 divided by 3 is 2, and when you split the last one into thirds you can each have 1/3. Add the sections together, and each person gets 2 1/3