Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.
1 answer:
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.
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Answer:
Step-by-step explanation:
Let p represent cost of each drink.
We have been given that the medium pizza costs two times as much as one drink, so the cost of medium pizza would be .
We are also told that the large pizza costs three times as much as one drink, so the cost of la pizza would be .
We have been given that Mary wants to buy one large pizza, one medium pizza, and three drinks.
Since the cost of one drink is p, so cost of 3 three drinks would be .
The total cost of one large pizza, one medium pizza, and three drinks would be
Mary started with $30, so amount left after all of her purchases would be 30 minus total cost of all purchases.
Therefore, Mary will have dollars left after making all of her purchases.
The number is (2√3) / 3
To find the missing number, convert what it says in words to an equation:
Divide both sides by 15:
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To find the missing number, convert what it says in words to an equation:
Divide both sides by 15:
Take the square root: