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)`

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

The circumference = 14 inches. But circumference = 2πr, where r is the radius and π = 22/7. Therefore:

14 = 2(22/7)× r

14 = (44/7)×r

r= 14 × 7 / 44 = 2.23 inches

Diameter = 2r = 4.45 inches

`W=b_o+b_1(4.45^2*120)\\W = b_o+2381b_1\\Let\ us\ assume\ b_o = -34.671,b_1=1.859.\\Therefore\\W = -34.671+2381(1.859)\\W=4392 \ tons`