Math Problems

[Radagast The Brown]

You turn 2 on, then turn one of them off. Then if you enter the room you'll have one on, one warm and one off..

And it's basically just like the other one isn't it?

[Curubethion]

Correcto

[Elanor]

Ok, how many gifts did I get from my true love on all 12 days of Christmas?

On the first day, I got one partridge in a pear tree (one gift, even though there's a partridge and a pear tree)
On the second day, I got two turtledoves and another partridge in a pear tree (three gifts)
On the third day, I got three french hens, two more turtletoves, and one more partridge (six gifts).

Oh, sure it's easy to add them up, but can you give me a formula for the number of gifts if n is the number of days that this pattern continues?

Then if you want another challenge, find out how many gifts it is if you count the partridge and the pear tree separately, along with the eggs the geese are laying, the drums the drummers are drumming, the cows the maids are milking, etc.

[Curubethion]

Ok...12+1 is thirteen, 11+2 is thirteen...There are 6 such thirteens. 6x13=um...78 gifts. That's the 12th day...oh man...I'm stuck.

[Count Comfect]

day n - sigma (j=1 to j=n) of (sigma[k=1 to k=j] k) (I think... without actual symbols I get a bit confused) because you get (sigma 1 to n) gifts on day n And you have the sum of those from day 1 to day n total gifts. Overall you have 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 gifts. That's 364 gifts? Ironically 1 fewer than the days in the year.

[Curubethion]

Darn...I forgot about using sigma.

[Rconsole]

I'm not sure I understand the question completely...you want how many presents you would have after 12 days?
so the series would go 1+2+4+5+6+....right?
this doesn't match up with Count Comfect answer though, but i can't figure out what I'm doing wrong,,,,

this is the only way I know to do it
ok you'll have to bear with me here, everything in red should be in Subscript (ya I know it looks kinda weird)
the formula to use is

Sn = n(t1+tn) / 2 where Sn is the sum of the series you are trying to find t1 is the first term tn is the last term so applied to this situation it would be S12=12(1+12)/2 so... S12=156/2 Sn=78 so you would have 78 gifts

[Elanor]

Count Comfect got it. Another formula is

1(n) + 2(n-1) + ... + n-1(2) + n(1) or sigma(i = 1 to i = n) of i(n + 1 - i)

[Rconsole]

Originally Posted by Rconsole

I'm not sure I understand the question completely...you want how many presents you would have after 12 days?
so the series would go 1+2+4+5+6+....right?
this doesn't match up with Count Comfect answer though, but i can't figure out what I'm doing wrong,,,,

this is the only way I know to do it
ok you'll have to bear with me here, everything in red should be in Subscript (ya I know it looks kinda weird)
the formula to use is

Can somebody tell me what I did (or didn't do) wrong?

[Elanor]

Oh, you just did the 12th day. I (hypothetically) got 1+2+...+12 presents on the 12th day, 1+2+...+11 presents on the 11th day, etc.

[Rconsole]

Wasn't that the point though...? calculate how many presents you would have on the 12th day? am I missing something?

[Count Comfect]

Total presents by the twelfth day, not presents received on Just the twelfth day.

You got the latter.

[Elanor]

Does anyone know anything about computational theory? Automata, regular/context-free languages, etc? I'm frustrated with it.

[Mercutio]

Theory of comp? (shudders) My brother recently took that course for his masters degree...I think it was the hardest course he took up to that point.


There isn't a physics thread, and I'm not going to start one. I'll post my question here.
I have to do a 5-10 page physics research paper (+ model/poster/etc.) I need a topic. My dad first jokingly suggested String Theory; but seriously said semiconductors or radio.

Any ideas on something particularly fascinating and not too difficult to understand? (It needs to be pretty focused, too).

[Janny]

Well you don't get help off Janny without posing a math(s) problem first. Perhaps a study into if becoming a physicist is a cause of baldness or if it's only an unrelated but strong correlation. [/mathematician]

I always found quantum physics quite interesting. I don't know quite how far you can get into it, but there is certainly a wealth of information about particles and I'm sure you can go into what determines whether a reation is allowed or not. It's pretty interesting and also really quite fundamental.

Now gimme a maths problem!

[Mercutio]

Hmmm.


Right now in calculus we are studying inverse functions - about to get to differentiating/integrating exponential functions.

A question? I'll actually be at a math team meet this Monday, and if I remember the questions (or bring home an extra copy of some) I'll post them here for all to enjoy

[Janny]

Hooray for competative maths!

[Mercutio]

Without calculator:

Simplify
squareroot(5 + squareroot(21)) - square root(5 - squareroot(21))


If f(x) = x^2 + 7x + k
and f(k) = -16
find f(6)

A triangle with sides 4, 13, 15. Find the tangent of the angle between sides 4 and 15. (A picture would help.....but I can't do one easily). [Draw a short horizontal line (4). On the left endpoint, add a longish (13) line that makes an obtuse angle. Complete triangle with longest (15) line.]

A concave pentagon. No interior angles are congruent. The smallest angle is 38 degrees. Except the smallest and biggest, each angle is the average of the two other angles nearest to it. Find the biggest angle.

3^(2x^2 -7x +3) = 4^(x^2 -x -6) Find the rational value for x.

With calculator:

A wedding cake has five graduated circular tiers, each 8 cm high. The tiers have diameters 10 cm, 20 cm, 30 cm, 40 cm, and 50 cm. What is the surface area to be frosted? There is no frosting between layers. Express your answer in terms of pi.

If x^2 + 1/(x^2) and x is greater than 0,
find x^5 + 1/(x^5)

[Janny]

Originally Posted by Mercutio

Without calculator:

Simplify
squareroot(5 + squareroot(21)) - square root(5 - squareroot(21))


If f(x) = x^2 + 7x + k
and f(k) = -16
find f(6)

{(squareroot(5 + squareroot(21)) - square root(5 - squareroot(21)))^2}^1/2 {5 + root (21) + 5 - root(21) -2root(5^2 - 21)}^1/2 {10 - 4}^1/2 root 6 -16 = k^2 + 8k 0 = k^2 +8k +16 0 = (k+4)^2 k= -4 => f(x) = x^2 + 7x - 4 f(6) = 36 + 42 - 4 = 74

Must... rational... self. Thanks

[Count Comfect]

With calculator:

A wedding cake has five graduated circular tiers, each 8 cm high. The tiers have diameters 10 cm, 20 cm, 30 cm, 40 cm, and 50 cm. What is the surface area to be frosted? There is no frosting between layers. Express your answer in terms of pi.

Well...

each layer has: 2(pi)(r)(h) of surface area on its side (pi)r^2 - [the (pi)r^2 of the one above] of surface area on its top, except the top which has its full pi(r)^2 Top layer: side=2(5)(8)pi=80pi; top=25pi = 105 pi Next: side = 2(10)(8)pi=160 pi; top= 100pi-25pi=75pi = 235 pi Next: side = 240 pi, top =225-100=125 pi =365 pi Next: side = 320 pi, top=400-225=175 pi =495 pi Next: side = 400 pi, top =625-400=225 pi =625 pi Total is 1825 pi (cm^2 of course).

Alternatively,

we're adding 80pi (from the sides, which grow by adding 8*10 each time) and 50 pi (from the top, which adds because each increment of 5 would be 25 and so an increment of 10 is 50*), so 130 each time, 105*5+(130)*(1+2+3+4)= 525+1300=1825. *That's the best way I can put it, even though it isn't actually precisely correctly phrased.