Recent content by parabol

Homework Statement A motor is used to rotate a ball attached to a rope in a vertical plane. The mass of the ball is 2kg and the length of the rope is 3m. Ignoroing air resistance and the mass of the rope, calculate: a) The minimum motor speed in rpm that will maintain the ball in a...

I'm still not 100% with this question. I have been re-working on it and have now come up with this answer. \frac{dy}{dx}=\frac{\frac{2(sin2x)^2}{(cos2x)^2}+\frac{sinx}{(cosx)^2}+2}{\frac{sin2x}{cos2x}+\frac{1}{cosx}} Does this look right?

Thanks for the input. Have I started off using the method by using the chain rule? Do I just leave it as: (\frac{sin2x}{cos2x}+\frac{1}{cosx})^{-1} ?

Thanks for your help. I reckon I have it sorted now. Cheers

Homework Statement By using cos and sin subs for tan and sec, find the gradient of: ln(tan2x+secx) Homework Equations tanx=sinx/cosx secx=1/cosx The Attempt at a Solution Substituting y=ln(\frac{sin2x}{cos2x}+\frac{1}{cosx}) Using the chain rule let: z=...

Thanks for the reply. Happy with the first part. But for the 2nd. Are you saying that I have carried it out incorrectly by findging the first and second derivative and then integrating them and working out thorugh the boundary values?

Homework Statement 1st problem I'm struggling to answer this question using my calculus workbook. Find the point of intersection of the lines: y_{1}=3x+2 3y_{2}=16-x I can solve this question as a simultaneous equation, but, as it is in my calculus question paper believe it to...

Things are starting to become a bit clearer, I think/hope. In this question then, is K=3\sqrt{\theta^{2}+1}? And if it is then \frac{dy}{dx}=(3\sqrt{\theta^{2}+1})\times(-x.sin(x^{2}+2\theta)) If it is I can see why you siad I had complicated it. I just wouldn't know how to make it less so.

that would be secxtanx. I do not understand the above statement. Could you elaborate? Thanks

Thanks for your help tiny-tim. But you have completely thrown me there. The texts I am working off are, well, limited and teach the basics. They essentially cover, sum, product, chain rule and quotient rule and then some higher derivatives, so I'm not certain what techniques I should be using...

Thanks tiny-tim A touch of progress then. Utilsing the chain rule I have differentiated the denominator. let v = x2 + 2\theta, let u = cos v let y = 1/2u \frac{dv}{dx}= 2x ... \frac{du}{dv}= -sin.v = -sin(x^{2}+2\theta) ... \frac{dy}{du}= \frac{1}{2}...

Homework Statement Find the gradient of y with respect to x: y=\frac{3\sqrt{\theta^{2}+1}}{\frac{1}{2}cos(x^{2}+2\theta)} Well, I am at a complete loss where to start with this. The learning package I have in all its examples and text has no similar worded examples or utilises 2...

Thanks Mark. Its just that I tried the invert first off and got completely different colutions once I had substitued values in (why I got confused) .

Homework Statement Transpose for t, x=12(1-e^(-t/RC)) I can't get it out of my head but, the soltuion I have come up with doesn't seem right. Solution is, t=-RC ln(1-x/12) Thanks in advance, Realted, but not as important as the sanity check. For my own mind, could someone explain to me...

All sorted now. Thanks very much for the sanity checks with this.