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A farmer is transferring 800 kilograms of grain from a truck into a silo (a building for storage of grain). The silo initially contains 40 kilograms of grain. The machine used to transfer the grain does so at a constant rate, and after 15 minutes only 200 kilograms of grain remain in the truck. However, the machine is faulty and 1 out of every 10 kilograms of grain removed from the truck falls onto the ground instead of going into the silo. Let S(t) be the amount of grain in the silo and T(t) be the amount of grain in the truck (in kilograms) at time t (in minutes). (a) At what time E has the truck been emptied? (b) When the truck is empty, how much grain is in the silo and how much is on the ground? (c) Show that T(t) = 800 1 - 40t and S(t) = 40 + 36t for t€ [0, E.

A farmer is transferring 800 kilograms of grain from a truck into a silo (a building for storage of grain). The silo initially contains 40 kilograms of grain. The machine used to transfer the grain does so at a constant rate, and after 15 minutes only 200 kilograms of grain remain in the truck. However, the machine is faulty and 1 out of every 10 kilograms of grain removed from the truck falls onto the ground instead of going into the silo. Let S(t) be the amount of grain in the silo and T(t) be the amount of grain in the truck (in kilograms) at time t (in minutes). (a) At what time E has the truck been emptied? (b) When the truck is empty, how much grain is in the silo and how much is on the ground? (c) Show that T(t) = 800 1 - 40t and S(t) = 40 + 36t for t€ [0, E.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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A farmer is transferring 800 kilograms of grain from a truck into a silo (a building for storage of grain). The silo initially contains 40 kilograms of grain. The machine used to transfer the grain does so at a constant rate, and after 15 minutes only 200 kilograms of grain remain in the truck. However, the machine is faulty and 1 out of every 10 kilograms of grain removed from the truck falls onto the ground instead of going into the silo. Let S(t) be the amount of grain in the silo and T(t) be the amount of grain in the truck (in kilograms) at time t (in minutes). (a) At what time E has the truck been emptied? (b) When the truck is empty, how much grain is in the silo and how much is on the ground? (c) Show that T(t) = 800 - 40t and S(t) = 40 + 36t for t = [0, E1. (d) At what time is there equal amounts of grain in both the truck and the silo? (e) Sketch both of the curves y = S(t) and y = T(t) on the same set of axes, for t = [0, E]. Include in your sketch the coordinates of where these curves intersect.
Transcribed Image Text:A farmer is transferring 800 kilograms of grain from a truck into a silo (a building for storage of grain). The silo initially contains 40 kilograms of grain. The machine used to transfer the grain does so at a constant rate, and after 15 minutes only 200 kilograms of grain remain in the truck. However, the machine is faulty and 1 out of every 10 kilograms of grain removed from the truck falls onto the ground instead of going into the silo. Let S(t) be the amount of grain in the silo and T(t) be the amount of grain in the truck (in kilograms) at time t (in minutes). (a) At what time E has the truck been emptied? (b) When the truck is empty, how much grain is in the silo and how much is on the ground? (c) Show that T(t) = 800 - 40t and S(t) = 40 + 36t for t = [0, E1. (d) At what time is there equal amounts of grain in both the truck and the silo? (e) Sketch both of the curves y = S(t) and y = T(t) on the same set of axes, for t = [0, E]. Include in your sketch the coordinates of where these curves intersect.
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