Answer:
Height = 14
Base = 8
Step-by-step explanation:
h=6+b
a=(1/2)bh
a=56
56=(1/2)bh
times 2 both sides
112=bh
h=6+b
112=b(6+b)
112=b²+6b
minus 112 both sides
0=b²+6b-112
factor
what 2 numbers multily to get -112 and
add to get 6
-8 and 14
0=(b-8)(b+14)
set to zero
b-8=0
b=8
b+14=0
b=-14
false, measures can't be negative
base=8
h=6+b
h=6+8
h=14
height=14
base=8
2x+3y=60 solve for x...
x=(60-3y)/2
p=xy^3, using x from above:
p=y^3(60-3y)/2
p=(60y^3-3y^4)/2
dp/dy=(180y^2-12y^3)/2
dp/dy=90y^2-6y^2
dp/dy=0 when:
90y^2-6y^3=0
6y^2(15-y)=0, we know y>0 so
y=15, since x=(60-3y)/2
x=7.5
(We solved it this way because otherwise you get quartic equations and cubic derivatives, yuck :P)
I believe it would multiplication because if Karim wrote 4 times as many as Aviva you would want to know what the 4times of 8 which would be 32.
