Question

Find the weight of a pine tree that has a circumference of 14 inches and a height of 120 feet. Use the equation: W = b0 + b1(D2H)

Answer 1

The answer is below

Step-by-step explanation:

The weight of trees is calculated using the equation:

`W=b_o+b_1(D^2H)`

W is the tree weight in tons, D is the diameter of the tree in inches, H is the height of the tree in feet and
`b_o \ and\ b_1` are constants.

The circumference is given by:

Circumference = 2πr

Where r is the radius and 2r is the diameter

Therefore:

14 = 2(22/7)× r

14 = (22/7)×2r

2r= 14 × 7 / 22

Diameter = 2r = 4.455 inches

`W=b_o+b_1(4.45^2*120)\\W = b_o+2381.643b_1\\Let\ us\ assume\ b_o = -35,b_1=1.9.\\Therefore\\W = -35+2381.643(1.9)\\W=4490 \ tons`