Melody

Hi Jenny,

It is nice to see you back again.

No.2

\(log_3(x^2-22)=3\\ 3^{log_3(x^2-22)}=3^3\\ x^2-22=27\\ x^2=49\\ x=\pm7 \)

Can you please check the the first one is inputed correctly. 

And next time put them on a seperate posts.  (1 post = 1 question)

Ok, 13 units     

Here is the great circle of the sphere  (The equator if you like)

CA will be the longest possible distance, in a straight line from A to C

Method:

1) Use the cosine rul to find angle alpha (keep it exact)

2) Find DX (exact)

3) find XC Pythagoaras's theorem (exact)

4) CA = 2* CX

I have not an arc distance, it is the straight distance.)

If you want the longest possible arc distance then you can find it afterwards easily enough. 

Welcome to the forum,

but please next time proof read your question and get rid of meaningless dollar signs.

Points A,B and C are on a sphere whose radius is 3. 

If AB=BC=10 what is the longest possible value of AC?

No 2 points on the sphere can be more than 6 units apart. (in a straight line). 

If you are talking the arc distance then the greatest distance is half of  9pi   (half the circumference of the great circle)

4.5pi is approx 14.13 units.

I would think that the points could be at most 4.5pi  units apart.

If the number of friends is  F

and the number of shells is H

then 10F-30 = H

and    8F-6 = H   

Now solve simultaneously.                                                                                                                                            

There is not enough infomation here.

A suppose you are supped to assume that it starts at is mean temperature.

So it starts in the middle which is 12 degrees  at time 0 minutes

it goes up to 18 degrees in 2 minutes.

At 4 minutes it will be back to its centre line

At 6 minutes it will be at its minimum (which is the same distance from the centreline as the max is)

At 8 minutes it will be back to the centre and so on.

You can draw it.

Please proofread your qwuestions before you post them

choose a point, from there 9 lines can be draw

go clockwise to the next point. 8 new lines will be able to be drawn

etc until only one new line can be drawn

so that would be    9+8+7+6+5+4+3+2+1