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
A dekameter is ten times a hectometer
There are two solutions
AG =BG
mesDBG = mesEBG
Answer and Step-by-step explanation:
This is the correct matching:
1. Coefficient: The number in front of a variable in a term.
2. Constant: A number; a term containing no variables.
3. Arithmetic sequence: A set of numbers where the difference is the same between any two consecutive terms.
4. Closed circle: A circle filled in to show that the point is a part of the solution set.
5. Algebraic expression: An expression involving one or more variable terms.
6. Common ratio: The ratio of a term to the previous term in a geometric sequence.
7. Common difference: The difference between any two consecutive terms of an arithmetic sequence.