7-8
6-9
5-10
4-11
3-12
2-13
1-14
Length of the box = 25 - 2x
Width of the box = 14 - 2x
Height of the box = x
a.) Volume of the box = x(25 - 2x)(14 - 2x) = x(350 - 50x - 28x + 4x^2) = 4x^3 - 78x^2 + 350x
Therefore, the function that models the volume of the box is V(x) = 4x^3 - 78x^2 + 350x
b.) 4x^3 - 78x^2 + 350x ≥ 240
4x^3 - 78x + 350x - 240 ≥ 0
x = 0.834, 5.438
The values of x for which the volume is greater than 240 in^3 is 0.834 ≤ x ≤ 5.438
c.) For maximum volume, dV/dx = 0
dV/dx = 12x^2 - 156x + 350 = 0
x = 2.882910931
Therefore, maximum volume = 4(2.882910931)^3 - 78(2.882910931)^2 +350(2.882910931) = 453.798 in^3
Answer:
We let x 1 = 13, y 1 = 8, x 2 = 9, y 2 = 6, x 3 = 4, y 3 = 2, x 4 = 8, y 4 = 4 and the area is given by The absolute value of the cross product of two vectors a →, b → ∈ R 3 spanning the parallelogram is its area:
Step-by-step explanation:
Answer: 16 units
Step-by-step explanation:
