Hi guys, ive been staring at this question for a while now and im hitting a brick wall every time. Some help would be fantastic.
I have this trapezium, the question is, "The cross section of an open channel is a trapezium, with base 6cm and slopping sides each 10cm long. calculate the with of the open top so that the cross sectional area shall be a maximum"
Here is my working so far up until my brick wall.
x2+h2=102[br]h2=102−x2[br]h=102−x2​
The area of a triangle = hx/2 The area of a rectangle = 6h
Total area = 22hx​+6h = hx+6h = (x+6)h
using h=102−x2​ in total area calculation
total area = (x+6)∗102−x2​
And this is were i hit a brick wall, i know that i need to differentiate this (x+6)∗102−x2​ and then set the differential to zero to get an answer that i can use to calculate x, but not sure how to do it.
Hi guys, ive been staring at this question for a while now and im hitting a brick wall every time. Some help would be fantastic.
I have this trapezium, the question is, "The cross section of an open channel is a trapezium, with base 6cm and slopping sides each 10cm long. calculate the with of the open top so that the cross sectional area shall be a maximum"
Here is my working so far up until my brick wall.
x2+h2=102[br]h2=102−x2[br]h=102−x2​
The area of a triangle = hx/2 The area of a rectangle = 6h
Total area = 22hx​+6h = hx+6h = (x+6)h
using h=102−x2​ in total area calculation
total area = (x+6)∗102−x2​
And this is were i hit a brick wall, i know that i need to differentiate this (x+6)∗102−x2​ and then set the differential to zero to get an answer that i can use to calculate x, but not sure how to do it.