Melody

I should have said that acceleration is change in velocity / change in time

If the train is travelling at a constant 90mph then the acceleration is 0.

The instantaneous velocity has nothing to do with the acceleration at that point.

The acceleration is a measure of the change in velocity.

33)

\((x-4)^2+(y-1)^2=(6\sqrt3)^2\\ (x-4)^2+(y-1)^2=108\)

The centre looks like  (-2,3)   and the radius looks like 4

so

The equation would be

\((x+2)^2+(y-3)^2=16\)

Mmm Interesting

27.   Mmm

Well it has to be more than 3 because the two tangents to a circle subtended from a point will be equal.

(I not sure how I should word that) 

I can't be 9 either.  For the same reason.

So it has to be between 3 and 9.

What about 8 ......

No, it'll have to be less than that.

OK I don't think it can be any of those but I would like someone to give a more mathematical precise......

25.

<POD is 180 degrees,  

<POA=41

so <AOD=139

triangle AOD is isoceles so 

<OAD= 0.5*(180-139)=0.5*41=   20 degrees and 30 minutes

This is not a diophantine equation because ther is no suggestion in the question that the answers have to be integers. :)

It is however a linear equation :)

By 4th term, I assume you mean that n=4

What is the fourth term in this multiplication pattern? multiplication pattern using the formula 2 • 6n – 1

2*6*4-1=  47

I assume that 6 is the radius.

Let the centre be O

The longer interval from O to the line AB is 6+5=11cm long

6,8,11 is not a pythagorean triad so angle OAB is not a right angled triangle so

AB is not a tangent to the circle.

The tangent to a circle is at right angles to the radius that it touches :)