Answer:
Is the -8x2 a -8x squared? Because the answer of this problem can be different.
Step-by-step explanation:
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).
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The graph in the second attachment shows a trapezoid with the radius calculated as above.
Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Answer:
height = 78 yd
Step-by-step explanation:
<u>Formula</u>
Volume of a rectangular prism = width × length × height
Given:
- volume = 4,212 yd³
- width = 2 yd
- length = 27 yd
Substituting given values into the formula and solving for height:
⇒ 4212 = 2 × 27 × height
⇒ 4212 = 54 × height
⇒ height = 4212 ÷ 54
⇒ height = 78 yd