The absolute value function, f(x) = |x + 2|, is shown.
2 answers:
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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.
Answer:
26 years
Step-by-step explanation:
Given:
The mean age of 9 women = 27 years old
The mean age of 7 men = 25 years old
Question asked:
What is the mean age (nearest year) of all the people in the office?
solution:
By using, mean = sum of observations divided by number of entities
The mean age of 9 women = 27 years old
=
The mean age of 7 men = 25 years old
=
Total sum of ages of men and women in the office = 243 + 175
= 418 years
Total number of people in the office = 9 women + 7 men = 16
The mean age of all the people in the office = Total sum of ages of men and women in the office divided by Total number of people in the office
=
Therefore, the mean age (nearest year) of all the people in the office = 26 years