The height of a tree trunk is 20 meters and the base diameter is 0.5 meter. a. the wood has a density of 380 kilograms per cubic meter. find the mass of the trunk to the nearest kilogram. the mass of the tree trunk is about kilograms. question 2 b. the trunk puts on a growth ring of 4 millimeters and its height increases by 0.2 meter this year. how many cubic meters of wood does the tree trunk produce? round your answer to the nearest hundredth. the tree trunk produces about cubic meters of wood this year.

Originally,
h = 20 m, the height of the tree trunk
d = 0.5 m, the diameter of the trunk

Because the density is 380 kg/m³, the mass of the trunk is


1492.3 kg

After one year:
After the tree puts on a growth ring, the new diameter is
  d = 0.5 + 2(4 x 10⁻³ m) = 0.508 m
The tree grows by 0.2 m, s the new height is
  h = 20 + 0.2 = 20.2 m

The increase in volume is


The volume produced  is 0.17 m³ (nearest hundredth) 

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12