Answer:
θ = 60°
Step-by-step explanation:
The cross sectional area of the trapezoid shape will be that of a trapezoid with bases of 10 cm and (10 cm + 2·(10 cm)·cos(θ)) and height (10 cm)·sin(θ).
That area in cm² is ...
A = (1/2)(b1 +b2)h = (1/2)(10 + (10 +20cos(θ))(10sin(θ)
A = 100sin(θ)(1 +cos(θ))
A graphing calculator shows this area to be maximized when ...
θ = π/3 radians = 60°
_____
<em>A</em> will be maximized when its derivative with respect to θ is zero. That derivative can be found to be 2cos(θ)² +cos(θ) -1, so the solution reduces to ...
cos(θ) = 1/2
θ = arccos(1/2) = π/3
The measure of the angle R is 
Explanation:
It is given that the lengths of the triangle are PQ = 8 and QR = 3
To find the angle of R using the opposite and adjacent side, we shall use the tangent formula.
where opp = 8 and adj = 3
Thus, substituting these values in the formula, we get,
Multiplying both sides by 
, we get,
Dividing, we get,
Rounding off to the nearest tenth, we have,
Thus, the measure of the angle R is
27 1 27 10
---- x ---- = ---- OR 1 ----
1 17 17 17
You haven't posted the answer choices, but I think I've run across this question before and remember the answer. The answer should be whichever letter says as follows: "Smoking damages cilia in the trachea and more particles enter the lungs. Hope this helps!~
Its basically 6 times 96 I think
hope this helps ;)
