Math Is Fun Forum

Thanks for the reply.

Can you see this image?

And what about this?

The first looks small and a bit blurred for me.

The second is larger and much sharper.

Both have the img /img format.

I'll repeat what I said in post 4.  The y axis is the line of symmetry. The red and green lines are at 90 degrees to the axis and are bisected by it.

Bob

I'm so sorry this is proving so hard for you. My new image site offers the following possibilities. I'll number them so you can say which works for you.

(1) https://postimg.cc/4KJ9rhFk

(2) https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif

(3) [symmetry_on_parabola.gif](https://postimg.cc/4KJ9rhFk)

(4)

(5) <a href="https://postimg.cc/4KJ9rhFk" target="_blank"><img src="https://i.postimg.cc/4KJ9rhFk/symmetry_on_parabola.gif" alt="symmetry_on_parabola"></a>

(6)

(7) <a href="https://postimages.org/" target="_blank"><img src="https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif" alt="symmetry_on_parabola"></a>

(4) is the one they says should work for forums.  That's what used when I changed post 4.

If none then what?

What device are you using?  Does your own image show ok?

Maybe Phrontister will have some ideas for you. He has been a great help in sorting out the image problem for me.

Bob

Many thanks Phro,

I knew you had said that before but I was in a hurry to get the picture up. I've corrected it now.

I can access Imgur if I I use a VPN.  I've chosen Australia for this purpose. 

The UK's Ofgov site has a checking device, according to which the forum is not subject to the new law. So I've kept a copy of their statement about this and I'll just carry on for now and hope the police don't come knocking. 

Bob

hi,

I've read and re-read your post and I don't understand what you mean.  Pretend I'm an 'old man' who isn't familiar with social media and spell it out in simple terms.  I should add that, although I have administrator status,  I don't have access to the underlying code for the forum, so I probably cannot make the change you are seeking anyway.

Best wishes,

Bob

hi criticalCat

Both answers correct.

The first and last functions are invertable, so you could construct a similar function definition for 
x in terms of f(x).  The middle has no inverse because many values of x lead to the same f(x); so there is no one formula that gives x when you know f(x).

Bob

hi Phro, Thanks for the info. I was totallly unaware of this. I've followed the news about the UK Government's Online Safety legislation; I hadn't picked up on this side effect.

I've checked all my posts and I'm blocked from viewing every Imgur image!  There's loads of them. I have copies on my computer but I haven't got the time or enthusiasm to switch them all.  If asked by a poster I'll attempt to find my copy and get it on the site.

I haven't had a chance to check yet, but as I read it, I won't be able to log in to Imgur either.

What site are you now using?

And how long before that bans the UK too.

I'll give VPN a try when I get a moment.

Bob

ps. This could destroy us once the regulator gets to hear about us.

hi Phrzby Phil

In that case, there's more.

A fraction either terminates or it recurs. A decimal that terminates can be shown to be a fraction, and the above shows that a recurring one can too.

So the set of all fractions (the rationals) is also the set of all terminating or recurring decimals.

So what else could there be?

Well it's fairly easy to construct a decimal that neither terminates nor recurs.

eg. 0.10010001000010000010000001.....................  I'm adding an extra zero in each group of zeros before another 1.

It's possible to show that pi neither terminates nor recurs.  I was shown the proof at University but I didn't really follow it then and I don't know how now.

e and the golden ratio are also such numbers.  They are called the irrationals.  Between every two rationals you can construct another; and also an irrational.

Between every two irrationals you can construct another and also a rational.  So there are an infinite number of rational and irrationals.

But Cantor showed that the infinity of irrationals is bigger than the infinity of rationals.  Whoops; that's a bit weird isn't it. But I do know his proof if you're interested.

Bob

OK I've got it.

If one grade gets 3, then there are 3 ways to achieve this so 3 x 5!. But some possibilities are repeated.  I am counting vwx, vxw, wvx, wxv, xvw, xwv so I need to divide by 6.

If 2 grades get 2 each, again 3 ways, so 3 x 5!, but this time I'm counting vy and yv in one grade and wz and zw in a second grade so I need to divide by 2! and 2! again.

So I should have calculated thus:

Bob

I only get 30 for that first group

Calling the equipment types V W X Y Z and giving three to 1st grade we have

VWX        Y       Z
VWX        Z       Y
____________________
VWY        X        Z
VWY        Z        X
____________________
VWZ        X         Y
VWZ        Y         X
____________________
____________________
VXY         W         Z
VXY         Z           W
____________________
VXZ          W         Y
VXZ          Y          W
____________________
____________________
VYZ          W          X
VYZ          X         W
____________________
____________________
WXY         V            Z
WXY         Z            V
____________________
WXZ         Z            Y
WXZ         Y            Z

WYZ          V           X
WYZ          X           V
____________________
XYZ           V           W
XYZ          W           V
____________________

That makes 10 ways. Then multiply by 3 for 2nd and 3rd grades getting the three. 30 + 90 = 120

Bob

Oh.  Don't know why that is.

I have emailed MIF and I am awaiting a reply.

Bob

Oh, I thought you had cracked it. Longer standing Members with existing avatars continue to have them after the upgrade. More recent members find nothing happens when they follow the instructions.

Bob

Test post.

https://www.google.com/
https://www.mathsisfun.com/data/function-grapher.html
https://www.bbc.co.uk/
math
math
https://www.google.com/ https://www.mathsisfun.com/data/function-grapher.html https://www.bbc.co.uk/
https://www.google.com/https://www.mathsisfun.com/data/function-grapher.htmlhttps://www.bbc.co.uk/

I can stop multiple posting if the hyperlinks are all on one line but not if there's a newline between them.

Actually I cannot stop them even then as the last two show.

Bob