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°
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<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
Answer:
z=7
Step-by-step explanation:
If z represents 1/2 of 14, then z=14*1/2=14/2=7
Answer:
Step-by-step explanation:
x1 = 0.5 x2 = -0.4 y1 = 1.3 y2 = -1.3
=2.75
Answer:
121
Step-by-step explanation:
A calculator can answer this for you.
_____
Following the steps of the <em>order of operations</em>, you evaluate inner parentheses first. The exponents are the first to be evaluated there.
11[6^2/(5^2-4^2)+7]
= 11[6^2/(25 -16)+7]
= 11[6^2/9 +7]
Then you do the exponent ...
= 11[36/9 +7]
Now you do the division ...
= 11[4 +7]
And finally, you can finish up the outer parentheses ...
= 11·11
= 121
3/7= 0.428571
3/6= 0.5
3/5= 0.6
So 3/5 is the greatest of all of them.
