The cubic function is f(x) = x^3
You need to perform three transformations to the cubic function to obtain
f(x) = - (x + 2)^3 - 5.
Those transfformations are:
1) Shift f(x) = x^3, 2 units leftward to obtain f(x) = (x + 2)^3
2) reflect f(x) = (x + 2)^3 across the x-axis to obtain f(x) = - (x + 2)^3
3) shift f(x) = - ( x + 2) ^3, 5 units downward to obtain f(x) = - (x + 2)^3 - 5
Given/equations formed from text:
I: l=w+3
II: A=l*w
III: new area B=(l-2)*w
IV: B=A-30
substitute l in II with I to remove l:
II': A=l*w=
(w+3)*w=
w^2+3w
substitute l in III with I to remove l:
III': B=(l-2)*w=
(w+3-2)*w=
(w+1)*w=
w^2+w
substitute A and B from II' and III' into IV:
B=A-30
w^2+w=w^2+3w-30
30=2w
w=15
insert w=15 into I:
l=15+3=18
->
A) dimensions of full size rectangle are width 15 and length 18
dimensions of reduced size rectangle are width 15 and length 16
B) full size: 15*18=10*18+5*18=180+90=270cm^2
reduced size: 15*16=10*16+5*16=160+80=240cm^2
A heptagon has 7 sides, so 7-2=5
To get the answer, divide 3852 feet by 4 days. That will give you an average of 963 feet per day as your answer.
