Assignment:
A company is constructing guttering to carry water. The cross section of the guttering is below:
Each side is the same length and the angle between each side and the hosizontal are equal. That is, the cross section is symmetrical about the vertical line through the mid point of its base.
Denote the width of the material used to make the guttering as w.
Denote the length of each side as x.
Denote the ration of w/x as k.
Denote the angle of inclination of the sides as Θ.
Q1. If Θ=90o , find the value of k to maximise the volume of water that the guttering can transport.
Q2. If k = 2 ,find the value of Θ to maximise the volume of water that the guttering can transport..
Q3. If Θ=60o , find the value of k to maximise the volume of water that the guttering can transport.
NOTES
Use calculus to find all values of all the tasks listed above.
Show all workings and use both graphs and numbers to denote workings along with diagrams of the guttering where necessary.
Provide complete and step by step solution for the question and show calculations and use formulas.