last qu on 1986 paper (1 Viewer)

[currysauce]

new question, last one from the paper.

see attached, i have the answers written down

 

[shafqat]

where exactly are you stuck?
to find the area of trapezium you need the length of both parallel sides
one is given, the other is found using trig on the two triangles on the sides

the max part is dont my differentiating area with respect to theta

 

[currysauce]

i can't do the first part..... second i would be able to do

 

[shafqat]

the shorter side is l
split the trapezium up into 2 triangles and a rectangle
so the longer side consists of the bases of the 2 triangles plus l
the bases are l cos @ from trigonometry
from the same triangles the perpendicular height is lsin@
so area = 1/2. . (2l + 2lcos@). lsin@
= l^2 sin@(cos@ + 1)

damn its hard to explain without a diagram

 

[acmilan]

To go with the above explanation, here is a crappy drawing:

http://www.pbuzz.com/data/f0fcf351df4eb6786e9bb6fc4e2dee02/full_2025_p18902.jpeg

hmm it doesnt seem to work from here. If you copy the url and paste it into an address bar it should work.


And my explanation going by that pic:

Sin @ = C/l --> C = l sin@

Cos @ = A/l --> A = l cos@

Cos @ = B/l --> B = l cos@

Upper Side length = A + B + l = l cos@ + l cos@ + l = l (2cos@ + 1)

Lower side length = l

Area
= ½*C*(upperside+lowerside)
= ½*l sin@ * (l + l(2cos@ + 1))
= ½*l²sin@*(2cos@ + 2)
= l²sin@(1 + cos@)

 

[currysauce]

thankyou
very
much!

 

[KFunk]

Area
= ½*C*(upperside+lowerside)
= ½*l sin@ * (l + (2cos@ + 1))
= ½*l²*(2cos@ + 2)
= l²(1 + cos@)

I think you lost a sin@ somewhere towards the end there.

 

[acmilan]

Haha yeah i did. Fixed

 

[JamiL]

u can also use the genral formual for area of a trapz = (a+b)h/2
then let a(larger side) equall to l + 2m (where m is lcos@) and h=lsin@
the sub in and u get A=l^2 * sin@(1-cos@)
find first n second dirivative.
when A' = 0
ie cos@ + cos2@=0
ie cos @= -cos2@
let 2@ = #
ie cos@= -sin (90 - #)
ie cos@= sin(#-90)
ie #-90 + @=90
ie 2@+@=180
ie 3@=180
ie@=60 (or pi/2 siut urself, i like degress better on the net, easyer, but u must use radians)