Melody

One question per post, thank you.

This is not really a trig question. It is an understanding question.

dH/dt will be 0 when the tangent to the circle is horizontal.  That is at the top and bottom.   (say 12oclock and 6oclock)

If is starts horizontal to the axis that is at  3oclock or 9 oclock.

So it must travel a quarter of a rotation to get to the top or the bottom,

45/4 = 11.25 seconds  then again at  11.25+22.5k  seconds      (where k is a positive integer)

Yes, it does look like it. 

mm

experiment

1) How many times does 3 go into 10!

3*6*9      3 3 3 3  four times

10/3 = 3 and a bit

3 and a bit/3 = 1 and a bit

3+1=4

-------------------------------------------------

1234/7 = 176.2857142857142857

176.2/7 = 25.1

25.1/7 = 3 and a bit

3+25+176 = 204

So I think    204

You can do some of this GM

Factorize each of the 4 bits separately.

and

To divide by a fraction you invert and multiple (the second one)

Your turn now  

Where is your pic?

\(\frac{3x+12}{x+4} = \frac{4x^2 + 8x + 8x^2}{2x}\\ \frac{3(x+4)}{x+4} = \frac{12x^2 + 8x }{2x}\\ \frac{3(x+4)}{x+4} = \frac{4x(3x + 2 )}{2x}\\ 3= 2(3x + 2) \\ \frac{3}{2}= 3x + 2 \\ -\frac{1}{2}=3x\\ x=-\frac{1}{6}\)

I don't really understand the wording of the question but if it means

\(xy - \frac{x}{y^2} - \frac{y}{x^2} = 3.\\~\\ and\\~\\ (x-1)(y-1)=k \)

Find all possible values of k  then this graph indicates that there are no possible values of k.

I will look later but it looks very tricky. ..... 

Thanks Alan