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Answer is 7/2...anyone else?

A rubber washer is being compressed. At a certain time, the outer diatmeter is found to be 3cm, the inner diameter is 1cm, the thickness of the washer is decreasing at a rate of 1/4 cm/min and the outer diameter is increasing at a rate of 1/2 cm/min. If the volume remains pi cm^3, at what rate...

. y = 0, when x = 22.5 and y = 11.25 You can say this because you are projecting it from ground level, noting that 22.5 is half of 45 meaning that y = 11.25 must be the maximum height

Hmmm..i thought there was supposed to be something different with tan^-1 compared to sin^-1 and cos^-1 Thx for the clearup

y = tan^-1 f(x) y' = ? Whats the general equation when it comes to inverse tan?

Ok thx Riviet...i also understand Q29 now

Questions are from Fitzpatrick - 25a) Q18 and 29 Q18 Two straight roads meet at an angle of 60 degrees. A starts from the intersection and travels along one road at 40km/hr. One hour laater B starts from the intersection and travels along the other road at 50km/hr. At what rate is the distance...

i) Since y=f'(x) is drawn, stationary points occur when f'(x)=0, so that would be when x = 0 and 3 ii) There is an inflexion point when x = 1 and a horizontaly point of inflexion when x = 3 (anyone confirm? im rusty at graphs) iv) y=f(x) is concave down when the gradient changes from positive to...

Could you can say that 'θ' determines the sign of cosθ, so a ± is not necessary?

With y=sinx and y=cosx around the x axis, just use the 3U formula When its around the y axis, you'll have to use by parts when integrating (i think)

1) tan 3x = sin3x/cos3x =(3sin x - 4 sin^3 x) / (4cos^3 x - 3 cos x)....divide both sides by cos^3 x =(3tanx.sec^2x - 4tan^3x) / (4 - 3sec^2x) =[3tanx(1+tan^2x) - 4tan^3x] / [4 - 3(1+tan^2x)] =(3tanx - tan^3x) / (1 - 3tan^2x) 2) (2 sin^3 x + 2 cos^3x) / (sinx + cosx) = 2(sin^3x + cos^3x) /...

As Riviet said, you can use LIATE...but its really just common sense. e.g. if you have sinxlnx, you know you cant integrate lnx, so you let u = lnx When it comes to reduction involving by parts, always look at what the answer looks like. If it has n+1, you know you have to integrate something...

Just a basic thing...if it looks stuffed, use by parts :)

Sucks to wake up at 6:00 for 4U morning classes on mon/wed/fri that start at 7:45

Eng Adv - 85% Math 3U - 95% Math 4U - 95% Economics - 72% Physics - 78% As you can see, eco and physics needs a kicking

I never fell asleep. However, i was day dreaming half the time

4 periods of 4U, 50mins each...

You will lose one mark for not changing it back to 'I' from '2I'...unless the question specifically asked for 2I which i highly doubt

I = ∫[pi/2-->0] (cosx)dx/(cosx + sinx)....(1) = ∫[pi/2-->0] [ (cos (pi/2 - x)dx ] / [ cos(pi/2 - x) + sin(pi/2 - x) ] = ∫[pi/2-->0] (sinx)dx/(sinx + cosx)....(2) (1) + (2) 2I = ∫[pi/2-->0] (sinx + cosx)/(sinx + cosx)dx = ∫[pi/2-->0] 1.dx = x | [pi/2-->0] = pi/2 I = pi/4

Just a general question about Q3, how can you get factorials from doing integration involving reduction?