Answer:
x < 20/3
(negative infinity, 20/3)
Answer:
The diameter that will reward with the largest pizza is 14 in
Step-by-step explanation:
The perimeter of a sector of a circle is:
P = 2r + l
l = rθ
P = 2r + rθ
P=28 inches
28=2r + rθ
28-2r=rθ
θ=(28-2r/r)
=(2*14 - 2*r)/r
=2(14-r)/r
Area of the sector of the circle is:
A = r²/2 * θ
A = r²/2 * 2(14 - r)/r
A = r² * (14 - r)/r
A = r(14 - r)
A = 14r - r²
For the maximum area:
A = 14r - r²
A' = 14 - 2r
Set A' = 0
14 - 2r = 0
14= 2r
r = 7 in
The diameter (D) of the circle is twice of the radius:
D = 2r = 2 * 7= 14 in
The maximum area is:
A = 14r - r²
r = 7 in
A = 14 * 7 - 7²
A = 98 - 49
A = 49 in²
Answer:
B) 6.9 cm
Step-by-step explanation:
The remaining angle is the smallest, 180° -48° -97° = 35°. The shortest side is opposite this angle. The Law of Sines tells you its length is ...
short side = (longest side)·(sin(smallest angle)/sin(largest angle))
= (12 cm)sin(35°)/sin(97°) ≈ 6.9 cm
The shortest side is about 6.9 cm.
Look at my upload to see the graph, I couldn't see the choices, so I can't give you a definite answer. But the graph below is the correct one.
Hope that helped!