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
Step-by-step explanation:
Since the first coordinates are both (0,0) it implies that the line passes through the origin.
The slope of the line is therefore 5/8
The equation:
y-0=5/8(x-0)
y=5/8x
<span>-28ab-35ab+12b^2-42b^2
add similar element=-</span>28ab-35ab=-63ab
so that..
=-63ab+12b^2-42b^2
add similar element=12b^2-42b^2=-30b^2
=-63ab-30b^2
Statements Reasons
1. M lies on AB Given
2. AM+MB=AB Definition of midpoint
3. 2x+2+4x-4 = 16 Segment Addition Postulate
4. 6x-2 = 16 Combining like terms
5. 6x = 18 Addition Property of equality
6. x = 3 Division Property of equality
7. AM=2(3)+2 and MB=4(3)-4 Substitution property of equality
8. AM=8 and MB=8 Definition of midpoint
9. M is a midpoint Hence, proved.