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LimpNoodle
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#1
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#1
Stuck on that vintage maths problem no one can possibly do?
Equations getting you down?
Look no further, i aim to get people who need help the aid they deserve!
(sounds like a cheesy American ad!)

This is not just for the people who need help this is also for the people who can turn over maths problems in minutes, to lend their support and discuss things.


Few things to make this thread easier:

-Use caps for unknowns, like X (becasue of the one below!)
-Use x - / + =
-When wanting to put squared or cubed make the number font size 1 for example: X2
-Explain your problem thoroughly, longer posts the better! Well as long as you explain what you need.
-I can help you up to A2-Level standard, i hope we can get some Uni mathematicians helping out.

Enjoy
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sazzles
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Excellent idea!
Can you proof that the maximum area of a sector of a circle=area of a square of the same perimeter using a simple method? And the angle of the sector?
I can do it but only using ln and diffn.
Thanx
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me!
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wohoo!
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theone
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(Original post by sazzles)
Excellent idea!
Can you proof that the maximum area of a sector of a circle=area of a square of the same perimeter using a simple method
What do you mean by this "The maximum area of a sector"?
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LimpNoodle
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(Original post by sazzles)
Excellent idea!
Can you proof that the maximum area of a sector of a circle=area of a square of the same perimeter using a simple method? And the angle of the sector?
I can do it but only using ln and diffn.
Thanx
Yeah given the direct problem.

U can use Radians too i think, need to brush up on them.

I see a couple of people still posting maths problems as new topics, look save space wack em all in here!
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sazzles
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(Original post by theone)
What do you mean by this "The maximum area of a sector"?
Sorry that it wasn't clear.
If you have a set perimeter length for a shape and make a sector out of it, you can make an infinite number of different sectors and so there are many different possible areas. I'm talkin about the maximum area of a sector with a given perimeter (obviously not including a circle).
Does that clarify?
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sazzles
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(Original post by LimpNoodle)
U can use Radians too i think, need to brush up on them.
My ridiculously complicated method didn't because I wasn't integrating trig functions, that's the only time I can think of when radians are useful.
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LimpNoodle
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yeah sorry i was confused, saw sectors segments dnt bloody know! oh well. yeah or in physics when doing centripetal force
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sazzles
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(Original post by LimpNoodle)
yeah or in physics when doing centripetal force
That's only because the equations are derived from differentiation trig functions
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LimpNoodle
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#10
oh well i'm not as advanced as you it would be nice of you to sick around so you can help with the more challenging questions
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meepmeep
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#11
(Original post by LimpNoodle)
Few things to make this thread easier:

-Use caps for unknowns, like X (becasue of the one below!)
-Use x - / + =
-When wanting to put squared or cubed make the number font size 1 for example: X2
-Explain your problem thoroughly, longer posts the better! Well as long as you explain what you need.
-I can help you up to A2-Level standard, i hope we can get some Uni mathematicians helping out.

Enjoy
Certainly agree with this. Would be great to have some ground rules so posts can be more easily understood.
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sam1111_9
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#12
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#12
Its me again, just realise i had more work set, and as our teacher is worse than useless, i would really appreciate any help you can give.

I really have tried my hardest, and i've managed to do some of the questions, but here are those that i can't do.

2. A boy of mass of 60kg is standing in a lift that has an upward acceleration of magnitude 0.5ms-2. Describe the forces acting on the boy, and find their magnitudes.

4. A balloon of total mass 420kg is descending with a constant acceleration of 0.4ms-2. Find the upthrust acting on the balloon. When the balloon is moving at 1.5ms-1, enough ballast is released for the balloon to fall with a deceleration of 0.2ms-2. Calculate
a) how much ballast was released
b) the time for which the balloon continues to fall before it begins to rise.

7. A stone of mass m is released from rest on the surface of a tank of water of depth d. During the motion, the water exerts a constant resisting force of magnitude r. The stone takes t seconds to reach the bottom of the tank. Show that r=m(g- 2d/t squared)

8. An acrobat of mass m slides down a vertical rope of height h. For the first three quaters of her decent she grips the rope with her hands and legs as to produce a frictional force equal to five ninths of her weight. She then tightens her grip so that she comes to rest at the bottom of the rope. Sketch a (t,v) graph to illustrate her decent, and find the frictional force she must produce in the last quater. If the rope is 30 meters high, calculate
a) her greatest spees
b) the time she takes to decend.

9. In a lab experiment the motion of a steel ball-bearing falling vertically in a tank containing liquid is observed.
a)state why the acceleration of the ball bearing is less than g
b)The ball bearing of mass 0.15kg is released from rest in the liquid, and after 0.60 seconds it has fallen a distance of 1.53m. Assuming that the acceleration has a constant value of a ms-2, find a and the magnitude of the force resisting the motion.

10. A lift travels vertically upwards from rest at floor a to rest at floor b, which is 20m above a, in 3 stages, as follows. At first the lift accelerates from rest at a at 2ms-2 for 2s. It then travels at a constant speed and finally it decelerates uniformly, coming to rest at b after a total time of 6 1/2s. Sketch the (t,v) graph for this motion, and find the magnitude of the constant deceleration.

The mass of the lift and its contents is 500kg. Find the tension in the lift cable during the stage of the motion when the lift is accelerating upwards.

If you can help with any i would appreciate sooooooooo much. Thankyou.

There u go, its posted in your thread now.
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sazzles
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#13
(Original post by LimpNoodle)
oh well i'm not as advanced as you it would be nice of you to sick around so you can help with the more challenging questions
I may sound clever, but don't let that fool you. If you don't mind, I'd prefer to stick, than 'sick' around (lol typos, we all make them).
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sazzles
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2. Use F=ma and resolve the forces on the boy

4.
a) Do before and after diagrams of the balloon releasing its ballast. Use F=ma again, I think or maybe momentum/impulse?
b) Not sure

7. Ahh, 'show that';
Draw a good diagram and work out the acceleration of the stone, call it x. Times by m to get the force.
u=0
t=t
s=d
a=?
s=ut+at^2/2
g-x=2d/t^2/2
x=(g- 2d/t^2)
F=ma
R=mx
R=m(g- 2d/t^2)
Show that r=m(g- 2d/t squared)

8.
a) her greatest speed occurs 20m down. consider accn due to gravity-deccn due to friction
b) the time she takes to decend;consider two parts of motion separatly0-20 and 20-30. Use equations of motion as you know her speed at top and bottom of rope and at 20m, and also distance.

Sorry, I would answer in more detail, and the other questions, but am too busy. Apologies for that and any mistakes.
Hope this is useful.
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LimpNoodle
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#15
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#15
Right i think i can help out with most, here are the equations you will need;

F=ma

s = ut + 1/2at2 (remember S is displacement/distance)

s = vt - 1/2at2 (not that important)

v2 = u2 + 2as

s = (u+v)/2 x t (the x is multiply)

v = u + at

Tension equation:
T - mg = ma (T being tension)
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LimpNoodle
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#16
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#16
any one need help in physics aswell? i take maths, physics and IT alevel so i can help with these books, P1, P2, M1, S1, (we haven't done M2 and S2 just yet so i may need help on them when we start!), Physics 1 and Physics 2.

Hope to help out some people, laters
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mikesgt2
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#17
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#17
(Original post by sazzles)
Excellent idea!
Can you proof that the maximum area of a sector of a circle=area of a square of the same perimeter using a simple method? And the angle of the sector?
I can do it but only using ln and diffn.
Thanx
Is the angle 2 radians?
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sazzles
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(Original post by mikesgt2)
Is the angle 2 radians?
yeah, how did you do?
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mikesgt2
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(Original post by sazzles)
yeah, how did you do?
If the sector is in a circle of radius r and has an angle t (in radians), then:

Area = ( tr^2 )/2
Perimeter = 2r + rt = r(t+2)

So a square with the same perimeter has sides of length r(t+2)/4; therefore, the area of this square is ( r(t+2)/4 )^2.

We require the area of the sector to be equal to the area of the square, so:

( tr^2 )/2 = ( r(t+2)/4 )^2
( tr^2 )/2 = ( r^2(t+2)^2 ) /16
8tr^2 = r^2(t+2)^2

The r^2 terms cancel, so:

8t = (t+2)^2
8t = t^2 + 4t + 4
t^2 -4t +4 = 0
(t-2)^2 = 0
t = 2
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Jonatan
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(Original post by sazzles)
that's the only time I can think of when radians are useful.
They clean up lots of equations. If you want to use degrees you very often end up with a 360/2pi factor.

Also, when you need to raise a number to a complex exponent you probably want to use radians when expressing the complex numbers in polar form. This gives rise the following beautiful equation:

e^(i * pi) + 1 = 0

Also, do you take this task (Its a physics one, but still)

At what height do you find geostationary satelites?
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