Mathematics Question Thread

[g98]

In what sense? But probably not a good idea

I tend to use when i sub points into a line...
find the tangent at (1,0) and the gradient equation was m=x-2
then I would write:
@ x=1 m=-1
...I also use it in stationary point questions..I guess i'll try not to in the exam though

[RuiAce]

 Yeah might want to write "At" for those. The symbol doesn't really leave a good impression.

Of course if you really forget to then don't stress over it when you come out of the exam either.

[dtinaa]

Please help!!

[lha]

Well if you need to describe the motion based off what you have.

Suppose you have the graph of the displacement.

Velocity is the first derivative of the displacement
Therefore if the graph is increasing, velocity is positive
If graph is decreasing, velocity is negative
If graph is at a stationary point, particle is at rest


Acceleration is the second derivative of the displacement
Therefore if the graph is concave up, acceleration is positive
If the graph is concave down, acceleration is positive
If we are at a point of inflexion, acceleration is constant (possibly 0 but we don't know).



And say we were given the graph of the velocity.
Velocity is the first derivative
Hence v > 0 means particle is travelling away from the origin (+'ve direction, to the right, however you memorised it)
v < 0 means particle is travelling in the other direction from the origin (-'ve direction, to the left etc.)



And those are just some examples. If you know what the derivatives actually MEAN then this is more intuitive than trying to rote learn a few dot points.

If velocity is positive, does that mean its going in thd positive direction?

Also if acceleration is positive, does that mean it is speeding up and if accelerstion is negative, its slowing down?

also, how do i know it has changed direction if it gives me a displacement, velocity or acceleration graph

[imtrying]

are both these formulas right for surface area of a cone?

[jakesilove]

are both these formulas right for surface area of a cone?

Yep they are both correct!

[BPunjabi]

If velocity is positive, does that mean its going in thd positive direction?

Also if acceleration is positive, does that mean it is speeding up and if accelerstion is negative, its slowing down?

also, how do i know it has changed direction if it gives me a displacement, velocity or acceleration graph

Imagine a ball thrown in the air, the exponential either moves to the right or the left. The velocity goes up but then comes to a stop. Then acceleration is applied. Apples.

Gyet Yit?

[jakesilove]

If velocity is positive, does that mean its going in thd positive direction?

Also if acceleration is positive, does that mean it is speeding up and if accelerstion is negative, its slowing down?

also, how do i know it has changed direction if it gives me a displacement, velocity or acceleration graph

Yep, that's pretty much right. However, if the velocity is negative, and the acceleration is negative, the particle is actually speeding up in the negative direction!

It changes direction if the displacement starts to decrease (ie. go back towards the origin) or the velocity changes sign (ie. goes from positive to negative).

[BPunjabi]

Yep they are both correct!

are we expected to know that?

[BPunjabi]

Good Luck Guys!! We will need it. See you in an hour.

[jakesilove]

Please help!!

Hey! I think it's easier here to take cases where he DOESN'T win in the first three throws. This would only occur if the coins read HTH, or THT. The probability of HTH is (0.5)(0.5)(0.5), as is the probability of THT. Therefore, 2(0.5)(0.5)(0.5)=0.25. The probability of WINNING is 1-P(not winning), therefore the answer to i) is 1-0.25=0.75.

Fuck Joe. Why make such a complicated game? Now, we don't want him to win on the second go (even), or on any even goes. The probability of NOT winning on an even go must be something like

P(Not winning)=HTHTHTHT...+THTHTHTHTHTHT=2(0.5)^n for n throws, where n is even. Him WINNING on an odd turn is the same as NOT WINNING on an even term (sort of? In terms of infinity, where winning is assured? I'm not actually 100% about that, but let's go with it).

Therefore, we need to sum up 2(0.5)+2(0.5)^2+...+2(0.5)^n for n=infinity. Use your sum to infinity formula to get a solution, then your answer should be 1-ans!

Let me know if this works out,

Jake

[jakesilove]

Good Luck Guys!! We will need it. See you in an hour.

Know whatever formulas you think you'll need. You won't need to know multiple variations of volume/surface area for the same shape

[lha]

Yep, that's pretty much right. However, if the velocity is negative, and the acceleration is negative, the particle is actually speeding up in the negative direction!

It changes direction if the displacement starts to decrease (ie. go back towards the origin) or the velocity changes sign (ie. goes from positive to negative).

So if velocity is negative but acceleration is positive, the particle is going in the negative direction but slowing down?

[Hua Fei]

So if velocity is negative but acceleration is positive, the particle is going in the negative direction but slowing down?

Yes. If velocity and acceleration are opposite in direction, the particle would be decelerating in the direction of the velocity (although, I'd wait for someone else to second that)

Also, I don't get how to do this Q

[ml125]

Yes. If velocity and acceleration are opposite in direction, the particle would be decelerating in the direction of the velocity (although, I'd wait for someone else to second that)

Also, I don't get how to do this Q

The displacement is equivalent to the area under the velocity curve: (8×4)/2=16. In the question, it states that at t=0, x=2. Therefore, the maximum displacement at t=4 would be x=2+16=18