BobbyChalfont said:
Don't worry Ali, I have been working on the problems myself! I'm not foolish enough to expect to learn algebra by having other people tell me the answers!
From your avatar, signiture and location, I would hazard the guess that you yourself are quite profficient with Mathematics. May I ask what you do for a living and how far you took Maths in education? (A-Levels, degree level?)
Perhaps you yourself have some interesting Mathematical problems for the good people of HairLossTalk.com to solve!!
PS: "I can solve them without using pen and paper" - show off :tongue:
I'm an engineer. The last time I studied maths was 10 years ago when I was at uni. I haven't used maths ever since. I still solve the occasional maths puzzle and I like reading books on the history of maths. One of my favourite authors of all time is Simon Singh.
I'm fed up with software development, I'm thinking of going back to my roots and getting a job that requires me to write algorithms as opposed to software architectures.
BobbyChalfont said:
Here's a few more for you mathematics, then.
1) A = h(a+b) / 2
a) find h when A=40, a=10 and b=6
b) find a when A=36, h=9 and b=6
2) The final velocity (v) of a body is related to the initial velocity (u), the constant acceleration (a) and the distance (s) for which the acceleration acts, by the formula:
v^2 = u^2 + 2as
a)If a body starts with a velocity of 10m/s and is accelerated at 2m/s^2 for a distance of 11m find the value of v^2 and hence find the final velocity.
b) Find the value of s when v = 30m/s, u=5m/s and a=1om/s^2.
c) Find the value of u when v=20m/s, a=2m/s^2 and s=10m
OK, I'll give you the solutions.
Problem (1) is a simple replacement problem, where you replace the variables with the given numbers.
1.a: A = h(a+b) / 2 where A=40, a=10 and b=6 would become:
40=h*(10+6)/2
40=h*16/2
40=h*8
h=40/8
h=5
1.b: A = h(a+b) / 2 where A=36, h=9 and b=6
36=9*(a+6)/2
36*2/9=a+6
8=a+6
a=8-6
a=2
(2). this is the same as (1), but requires using square and square root
2.a: for v^2 = u^2 + 2as, find v if u=10m/s, a= 2m/s^2, s=11m
v^2=10^2+2*2*11
v^2=100+44
v^2=144 => 144 is the solution for the first part of the problem
sqrt(v^2)=sqrt(144) => to find v apply square root to both sides of the equation
v=12m/s
2.b: v^2 = u^2 + 2as find s if v = 30m/s, u=5m/s and a=10m/s^2.
30^2=5^2+2*10*s
900=25+20*s
900-25=20*s
875=20*s
s=875/20
s=43.75m
2.c: v^2 = u^2 + 2as find u when v=20m/s, a=2m/s^2 and s=10m
20^2=u^2+2*2*10
400=u^2+40
u^2=400-40
u^2=360 => to find u square root both sides
u=sqrt(360) => there is no real number square root of 360, so you could either use a calculator to find the solution or leave it as it is.
Alternatively, you could think of 360 as 36*10 and the solution would be:
u=6*sqrt(10)
the calculator tells me that u=sqrt(360)=18.97