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I did say that as a joke, so thank you for your reply.

Bob

Yes, I'm very pleased too.

But there's nothing wrong with local matters being decided locally in any democracy, so let's hope this is good for all parts of the UK.

Bob

Yes,

Bob

No, it was really hard. But I'm a brilliant teacher so it now seems simple.

Bob

Tricky thing 'adding zero'.

Bob

hi NightHawk

Welcome to the forum.

So for part a, you did something like 80 - 10% of 80.

For part b: this could mean get 5% and take it off twice. You'll get the same answer as part a.

So the questioner probably means:

First step answer = 80 - 5% of 80.

Then (first step answer) - 5% of (first step answer).

This won't reduce the price by so much as the second step is working out 5% of a smaller amount.

Hope that helps.

Bob

hi pokemonmaster101

Welcome to the forum.

hi Stefy,

I make it the same as bobbym.

Bob

hi Niharika,

Same method as the earlier one:

horizontally

vertically

+ as we want to measure downwards.

If you substitute in that expression for t, cancel an 'n', and re-arrange, it comes out in a few lines.

Bob

Oh right. 4D space. That should have been obvious.

Poor redheadcaliforniagirl. This may be more than she wanted.

I'll give it some thought, but you may have to wait for her input first.

Bob

hi Stefy,

Well, personally, I don't. As the surface of a sphere is not flat, I wouldn't try to find such a thing.

In 3D geometry, any plane has 'two degrees of freedom'. That's what lambda and mu do. They can be independently chosen. A line has just one degree of freedom.

On the surface of a sphere, the surface has two degrees of freedom already:

You can (with some restrictions) choose say x and y, but then z is determined.

So if you are determined to define a plane in spherical geometry, I suggest its the entire surface.

Bob

hi redheadcaliforniagirl

Welcome to the forum.

As this is a math website, I'm gunna guess you mean in geometry.

Two lines that cross will make a plane. If the directions of those lines is given by vectors a and b, and they cross at a point with position vector c, then the equation of the plane is:

where lambda and mu are variable scalars.

In fact this equation will define a plane if c is in the plane and a and b are any vectors in the plane. (but come to think of it, that means they will cross somewhere. So what I'm really trying to say is that c doesn't have to be the crossing point; just any point in the plane.)

In Cartesian terms this can be shown to be equivalent to:

It can also be shown that

is perpendicular to the plane so yet another form for the plane is

where n is a vector normal to the plane and s is a constant.

That's all I can think of for the moment, but I'm sure there are more.

Bob

Good luck with the exam.

Bob

hi cyerra

Welcome to the forum.

Do I detect questions from Compuhigh ?

In Q7 I think they are asking for the sin(90-x), in which case B 0.6 looks good to me.

And Q8, cos(90-x) = 0.8 is right too.

For Q9, tan(90-x) you need the opposite to that angle and then divide that by the adjacent.

(bobbym. they cannot want tan(x) because none of the answers will give that. I'm guessing that was in questions 1-6. After all, we wouldn't want them to go to all the expense of making a fresh diagram.

Q10 sec(90-x) = 1 over the cos of 90 -x so go back to Q8 and find 1/(that answer)

I suggest you post back answers for those two and then we can look at the rest.

Bob

Alpha is the angle in the left hand triangle so tan alpha = h/a

Beta is the same for the right hand triangle so tan beta = h/b

Theta is the angle to the horizontal at which the projectile is launched.

Bob

hi Niharika,

I haven't had a chance to follow this through yet, but here's how I'd begin:

horizonally

vertically

So now you have a quadratic in x. You can substitute in (0,0) ; (a,h) and (a+b,0) where

h = a.tan(alpha) = b.tan(beta) and aim to eliminate a, b, g and v. Although that's four unknowns and only three equations, you can think of g/2v^2 as a single variable, so you should be left with an expression connecting the three tangents.

EDIT: Whoops the first equation would be 0 = 0 which doesn't help much. I'd better try this properly.

FINAL EDIT:

It does work. From the (a,h) equation re-arrange to make k (=g/2v^2) the subject and substitute this into the (a+b,0) equation.

Use the a and b equations to remove a and b from the equation. Bonus: the h terms all cancel.

Simplify what's left to get the required result.

Bob

hi harrychess,

The formula you need is here:

http://www.mathisfunforum.com/viewtopic.php?id=17799

post #7

That makes angle ACD = angle ABC

[note: The wording doesn't say which way round to put D and E. I've put D closer to A and E closer to B, on my diagram.)

Bob

hi demha

-1t(3.9t - 15.6)

I've corrected the sign mistake here.

This is enough to solve this problem. h = 0 at two places; the start and the finish.

so 3.9t - 15.6 = 0 will give you the time of flight.

Bob

hi

Yes, I make it 78 too.

Sorry, I slipped up with my internal angle formula. Good to see it didn't stop you getting it right. I've edited it now.

Bob

hi GreatSandy

Is there a welcome?

There sure is: **Welcome to the forum!!**

My favorite is red too, but ganesh beat me to it today.

Bob

hi SolarDevil

OK. That makes sense.

With A as centre a circle radius AB will also go through C and D.

Work out the internal angles for each (180 - 360/n) and hence CAD.

This triangle (CAD) is isosceles so you can calculate ACD.

Also ABC is isosceles so you can calculate ACB.

Together these will give you BCD.

Bob

hi Nico van Os

Welcome to the forum.

is a geometric series and there's a formula for that.

If you make b^n the subject of the equation (and it's not obvious what n is) then take logs to make n the subject.

eg.

Hope that helps,

Bob

hi SolarDevil

Welcome to the forum.

It's tricky without knowing which points are C and D. I've labelled the centres as C and D but I doubt that's the points you mean.

You can work out ACB with 360/15, and as it's an isosceles triangle, you can then get CAB.

Similarly, ADB = 360/7 and then get DAB.

If that's not enough to get the angle you want, you'll have to post back, describing which points you mean in words.

Bob

Agnishom wrote:

How do I convince people that the sum of all natural numbers isn't -1/12?

(1) Prove that:

(2) Prove that

Bob

hi chooipian

I think we're better off together too. And that goes for the EU as well.

I'm South of the border so if the Scots leave, then I'm saddled with Cameron and his chums for ever. Please Scotland take the wider viewpoint.

There is also the question of whether the EU would even admit an independent Scotland. Several EU states also have independence seeking regions and would be unhappy about setting a precedence.

It's right that regional matters should be agreed locally but there are too many business and economic ties for an estrangement to work.

And whatever will happen to the Union Flag ?

Sob sob!

Bob