Which expression is equivalent to
1 answer:
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Answer:
A. 4x + h
B. 4x + h = 78
V = x²h
Step-by-step explanation:
1. The length plus girth
X +x+x+x +h
= 4x +h
2. Constraint equation
4x + h = 78 ----(1)
Objective function
Volume = v = x*x*h
V = x²h ----(2)
3. Quantity as function of x
From equation 1 in answer part b
4x+h = 78
We make h subject
h = 78-4x
We put values of h in equation 2 in part b
V = x²h
V = x²(78-4x)
V = 78x²-4x³
To get values of x and h
V = 78x²-4x³
Dv/dx = 0
= 156x - 12x²
156x = 12x²
Divide through by 12x
156x/12x = 12x²/12x
x = 13
h = 78-4x
h = 78 - 4(13)
h = 78 - 52
h = 26 inches
Answer:
Proved
Step-by-step explanation:
Given
--- sides of hexagon
--- side length
Required
Prove that for 7 points picked from the interior, 2 points are at most 1 unit apart
1. Draw a hexagon (see attachment)
2. Divide the hexagon into 6 triangles
3. Select 7 points on the hexagon
You will notice that at least 2 points will be in one of the triangle.
The maximum distance between these two points is 1 unit. This is because
1. The triangle is equilateral (all sides equal)
2. The length of each is 1 unit (in other words, the distance between points, cannot exceed the side length)
