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1) (Graphing Calculator OK) At a certain height h, a tree trunk has a circular cross-section. The radius R(h) of the tree at certain heights is given below: h 10 15 18 21 28 35 R(h) 3.1 4.0 3.3 3.6 3.8 3.2 4.1 where R(h) is measured in feet, as is h. The tree is 35 feet tall. Sue and Benjie have a logging company that chops down trees and uses the wood to build affordable housing. To protect the logging equipment, they chop down trees by making a cut 5 feet above the ground. Only the tree trunk is considered usable wood (not branches, bark, or anything else). a) From the data from the table, use a midpoint sum with three intervals, please approximate the volume of usable wood contained within this tree. Please include units.

1) (Graphing Calculator OK) At a certain height h, a tree trunk has a circular cross-section. The radius R(h) of the tree at certain heights is given below: h 10 15 18 21 28 35 R(h) 3.1 4.0 3.3 3.6 3.8 3.2 4.1 where R(h) is measured in feet, as is h. The tree is 35 feet tall. Sue and Benjie have a logging company that chops down trees and uses the wood to build affordable housing. To protect the logging equipment, they chop down trees by making a cut 5 feet above the ground. Only the tree trunk is considered usable wood (not branches, bark, or anything else). a) From the data from the table, use a midpoint sum with three intervals, please approximate the volume of usable wood contained within this tree. Please include units.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) (Graphing Calculator OK) At a certain height h, a tree trunk has a circular cross-section. The radius R(h) of the tree at certain heights is given below: 5 10 15 18 21 28 35 R(h) 3.1 4.0 3.3 3.6 3.8 3.2 4.1 where R(h) is measured in feet, as is h. The tree is 35 feet tall. Sue and Benjie have a logging company that chops down trees and uses the wood to build affordable housing. To protect the logging equipment, they chop down trees by making a cut 5 feet above the ground. Only the tree trunk is considered usable wood (not branches, bark, or anything else). a) From the data from the table, use a midpoint sum with three intervals, please approximate the volume of usable wood contained within this tree. Please include units. The radius can also be modeled by the function: G(h) = 3 + sin? (E) b) Use G(h) to approximate, to three decimal places, the volume of usable wood contained within this tree. Please include units. c) Since Sue and Benjie are partners, they agree to split the usable wood in half. After they cut the tree down, they are going to make one more cut the split the wood. Before they cut the tree down, they want to make a mark at h = k, where k represents where they will make that last cut. Of course, k must be between 5 and 35. Please set-up, but do not solve, an equation to find the value of k.
Transcribed Image Text:1) (Graphing Calculator OK) At a certain height h, a tree trunk has a circular cross-section. The radius R(h) of the tree at certain heights is given below: 5 10 15 18 21 28 35 R(h) 3.1 4.0 3.3 3.6 3.8 3.2 4.1 where R(h) is measured in feet, as is h. The tree is 35 feet tall. Sue and Benjie have a logging company that chops down trees and uses the wood to build affordable housing. To protect the logging equipment, they chop down trees by making a cut 5 feet above the ground. Only the tree trunk is considered usable wood (not branches, bark, or anything else). a) From the data from the table, use a midpoint sum with three intervals, please approximate the volume of usable wood contained within this tree. Please include units. The radius can also be modeled by the function: G(h) = 3 + sin? (E) b) Use G(h) to approximate, to three decimal places, the volume of usable wood contained within this tree. Please include units. c) Since Sue and Benjie are partners, they agree to split the usable wood in half. After they cut the tree down, they are going to make one more cut the split the wood. Before they cut the tree down, they want to make a mark at h = k, where k represents where they will make that last cut. Of course, k must be between 5 and 35. Please set-up, but do not solve, an equation to find the value of k.
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