7/4 - 5/3
(7/4)*(3/3) - (5/3)*(4/4)
(7*3)/(4*3) - (5*4)/(4*3)
21/12 - 20/12
= (21 - 20)/12 = 1/12
Given that x = 2 + 2^(2/3) + 2^(1/3)
so x - 2 = 2^(2/3) + 2^(1/3)
=(x-2)^3 = [2^(2/3)+2^(1/3)]^3
use (a-b)^3= a^3 - b^3 - 3ab(a-b)
and (a+b)^3= a^3 + b^3 + 3ab(a+b) formulae.
or x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)
or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)
or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12
or x^3 - 6x^2 +6x = 2
Let width = w
length = 4w/3
Area = 432 = length*width = w*4w/3
4w^2/3 = 432
w^2 = 432*3/4 = 324
w = 18
so the width of the cake pan is 18 inches.
the slope is 7 and the y-intercept is 1/2
The average rate of change is defined as the slope of the secant line and is given by the formula
[f(x+h)-f(x)]/h; where h=x₂-x₁.
[f(w+h)-f(w)]/h
= [0.11(w+h)² - 0.2(w+h) + 1.33 - 0.11w² + 0.2w - 1.33] / h
= [0.11w²+0.22wh+0.11h²-0.2w-0.2h-0.11w²+0.2w] / h
= [0.22wh + 0.11h² - 0.2h] / h
= 0.22w + 0.11 h - 0.2
w₂ = 700 g and w₁ = 400 g
0.22(400) + 0.11 (700-400) - 0.2 = 120.8 hectares/g