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The Math Game :D
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| ninja |
Posted on 08/17/2013 20:38:23
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Super Admin
Posts: 4174
Joined: 15.11.10
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ODST wrote:
let u = (tan x)^3
du= 3 (tan x)^2 (sec x)^2 dx
dv = sec x tan x dx
v = sec x 
so
uv - the integral of v du
so that is
(tan x)^3 (sec x) - integral of 3(sec x)^3 (tan x)^2 dx
(sec x) (sec x)^2 (tan x) ^2
(sec x)^2 = 1+ (tan x) ^2
I think I've filled in your missing 3 in red. Funny to post a question to which you don't have the answer - how would you know if we were right?!
I started by parts as you did but didn't fancy integrating 3 sec^3 x tan^2 x dx, even after playing a little with trig identities. Sounds like a lot of slog, so I'm glad I didn't persevere - we don't memorise things like the integral of sec^3 x.
We ought to get LaTeX for this thread!
Since noone's set a new question yet ...
Give the next term in the sequence: 5, 7, 11, 13, 17, 19, 23, ...
and explain your choice.
My brain is open.
- Paul Erdős |
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| BuhBiggieback |
Posted on 08/17/2013 21:52:29
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Wanker
Posts: 582
Joined: 18.07.13
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29 would be next because the others are all prime numbers.
What isn't 2+2? |
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| Dudeman |
Posted on 08/18/2013 01:15:18
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Super Admin
Posts: 1277
Joined: 03.01.12
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BuhBiggieback wrote:
29 would be next because the others are all prime numbers.
What isn't 2+2?
Lies it's going +2, then +4, then +2, then +4 so wouldn't It be 25.
2+2 isn't 3
What is sin of pi/4 in radical form (not decimal)
P.S. Get those unit circles out 
Edit: I just realized both are correct. You tricky ninja 
Edited by Dudeman on 08/18/2013 01:16:42
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| ninja |
Posted on 08/18/2013 08:23:05
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Super Admin
Posts: 4174
Joined: 15.11.10
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Dudeman wrote:
What is sin of pi/4 in radical form (not decimal)
Edit: I just realized both are correct. You tricky ninja
Yea, I deliberately chose an ambiguous sequence. Was wondering if anyone would pick up on the primes, but I was expecting the +2, +4 interpretation.
sin(pi/4) = 1/sqrt(2) = sqrt(2) / 2
Let's see who can do this ...
Find the absolute value of 'a' such that the quadratic equation x^2 + 2a - 3(a^2) = 0 has two real roots for x which differ by 8.
My brain is open.
- Paul Erdős |
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| Revenge |
Posted on 08/18/2013 17:12:06
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Super Admin
Posts: 1297
Joined: 28.06.12
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I tried that problem on paper.. I would probably get it if I was fresh with quadratics. Good thing school is in two weeks.
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| BuhBiggieback |
Posted on 08/18/2013 18:17:21
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Wanker
Posts: 582
Joined: 18.07.13
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How about a hint if I got a negative repeating decimal for the first subproblem am I on the right track? |
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| ninja |
Posted on 08/18/2013 18:49:53
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Super Admin
Posts: 4174
Joined: 15.11.10
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BuhBiggieback wrote:
How about a hint if I got a negative repeating decimal for the first subproblem am I on the right track?
Which sub-problem?
A hint for my last question: try to express the two roots in terms of a.
My brain is open.
- Paul Erdős |
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| BuhBiggieback |
Posted on 08/18/2013 20:39:31
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Wanker
Posts: 582
Joined: 18.07.13
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ninja wrote:
BuhBiggieback wrote:
How about a hint if I got a negative repeating decimal for the first subproblem am I on the right track?
Which sub-problem?
A hint for my last question: try to express the two roots in terms of a.
(-3a + -1x)(a + -1x) = 0 <--- is what I get after factoring
(-3a+ -1x) <-- when solved I get a negative repeating decimal.
-3a + -1x = 0
-3a + -1x + x = 0 + x
-3a + 0 = 0 + x
-3a = 0 + x
-3a = x (divide by three)
since solving the second sub would give me the same answer a= -0.3333333333x, x ????? |
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| ninja |
Posted on 08/19/2013 06:32:13
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Super Admin
Posts: 4174
Joined: 15.11.10
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BuhBiggieback wrote:
(-3a + -1x)(a + -1x) = 0 <--- is what I get after factoring
(-3a+ -1x) <-- when solved I get a negative repeating decimal.
-3a + -1x = 0
-3a + -1x + x = 0 + x
-3a + 0 = 0 + x
-3a = 0 + x
-3a = x (divide by three)
since solving the second sub would give me the same answer a= -0.3333333333x, x ?????
Your factorisation is correct: (x +3a)(x - a) = 0.
There are two values of x for which the equation above is true - they're known as the roots of the equation.
You've found one of them: x = -3a.
(Notice that if you substitute this into the factorised quadratic, the left bracket is 0 making the product 0.)
First you'll need to find the other root (/solution), so you can work out the difference between them and hence find the value(s) of a for which this difference is 8.
My brain is open.
- Paul Erdős |
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| ninja |
Posted on 08/22/2013 07:41:54
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Super Admin
Posts: 4174
Joined: 15.11.10
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Okay, since no-one understands quadratics, I'll post a different (hopefully easier) question, so this thread doesn't die.
First, the solution, in case you're interested.
Q: Find the absolute value of a such that x^2 + 2a - 3(a^2) = 0 has two real roots that differ by 8.
A:
Factorise the equation:
(x - a)(x + 3a) = 0
Use this to find the two roots for x:
x = a, x = -3a
Find the difference (d) between the roots:
d = a - (-3a) = 4a
Find the value of a for which d = 8:
4a = 8
a = 2
So the answer is 2.
---------------
What is the value of 1 + 2 + 3 + ... + 97 + 98 + 99 + 100?
(Explain your method if it's interesting.)
My brain is open.
- Paul Erdős |
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| BuhBiggieback |
Posted on 08/23/2013 13:52:35
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Wanker
Posts: 582
Joined: 18.07.13
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I know this one line them up like so
1 + 2 + 3 + 4 + ... + 48 + 49 + 50
100 + 99 + 98 + 97 + ... + 53 + 52 + 51
columns will all add to 101
50 columns
50 x 101 = 5050
1
11
21
1211
111221
312211
13112221
^what number goes in that blank?
Edited by BuhBiggieback on 08/23/2013 18:03:01
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| ninja |
Posted on 08/24/2013 17:25:22
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Super Admin
Posts: 4174
Joined: 15.11.10
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BuhBiggieback wrote:
I know this one line them up like so
1 + 2 + 3 + 4 + ... + 48 + 49 + 50
100 + 99 + 98 + 97 + ... + 53 + 52 + 51
columns will all add to 101
50 columns
50 x 101 = 5050
Good technique!
1
11
21
1211
111221
312211
13112221
^what number goes in that blank?
1113213211
It's describing the previous line.
Solve the equation for x:
7x - 5 = 17
My brain is open.
- Paul Erdős |
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| ninja |
Posted on 08/27/2013 15:22:44
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Super Admin
Posts: 4174
Joined: 15.11.10
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y u no like algebra?
My brain is open.
- Paul Erdős |
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| ODST |
Posted on 08/27/2013 15:38:21
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Super Admin
Posts: 2047
Joined: 11.09.12
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ninja wrote:
BuhBiggieback wrote:
I know this one line them up like so
1 + 2 + 3 + 4 + ... + 48 + 49 + 50
100 + 99 + 98 + 97 + ... + 53 + 52 + 51
columns will all add to 101
50 columns
50 x 101 = 5050
Good technique!
1
11
21
1211
111221
312211
13112221
^what number goes in that blank?
1113213211
It's describing the previous line.
Solve the equation for x:
7x - 5 = 17
I was out of town when that was posted so i didnt see the question, add 5 to either side to get 7x = 22 / 7 =
x = 22/7
First 5 terms of the sequence ((n^3)-4)/n with n starting at 0
Edited by ODST on 08/27/2013 15:40:03
�RG� (Renegade Gamers) Senior Admin
[C�R] Veteren
^Don't mess with ODST
Quis custodiet ipsos custodes? |
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| ninja |
Posted on 08/27/2013 16:07:22
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Super Admin
Posts: 4174
Joined: 15.11.10
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ODST wrote:
First 5 terms of the sequence ((n^3)-4)/n with n starting at 0
I assume you mean to take ((n^3)-4)/n as the "nth" term of the sequence.
In which case, the first term is undefined (you ought to start the sequence with n=1). It then continues: -3, 2, 23/3, 15, 121/5, ...
My question:
What is the area of a circle with a radius of 1 unit?
Edited by ninja on 08/27/2013 16:08:50
My brain is open.
- Paul Erdős |
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| ZA BrickSquad |
Posted on 08/27/2013 18:52:49
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ShawnPeezy
Posts: 5303
Joined: 12.05.11
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Pi units! lol
What is the area of a rectangle if one side is 3cm and the other 8.5cm? |
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| Sinder |
Posted on 08/27/2013 19:58:18
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I got a big blue star for posting. i must be special
Posts: 1705
Joined: 30.11.11
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ZA BrickSquad wrote:
Pi units! lol
What is the area of a rectangle if one side is 3cm and the other 8.5cm?
25.5cm²?
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| ninja |
Posted on 08/28/2013 07:07:55
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Super Admin
Posts: 4174
Joined: 15.11.10
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Sinder wrote:
ZA BrickSquad wrote:
Pi units! lol
What is the area of a rectangle if one side is 3cm and the other 8.5cm?
25.5cm²?
You need to post another question when you answer one!
I'll do it for you ...
Yesterday I drove from home to a shop/store, and then back again. My average speed on the way there was 50mph. My average speed on the way back was 70mph. What was my average speed over the whole journey?
Hint: Average Speed = (Total Distance) / (Total Time Taken)
My brain is open.
- Paul Erdős |
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| ZA BrickSquad |
Posted on 08/28/2013 12:47:26
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ShawnPeezy
Posts: 5303
Joined: 12.05.11
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ZA Code wrote:
LMFAO! This made my day omg, I'm still laughing! |
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| ninja |
Posted on 09/09/2013 05:02:05
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Super Admin
Posts: 4174
Joined: 15.11.10
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ninja wrote:
Yesterday I drove from home to a shop/store, and then back again. My average speed on the way there was 50mph. My average speed on the way back was 70mph. What was my average speed over the whole journey?
Hint: Average Speed = (Total Distance) / (Total Time Taken)
So noone understands average speeds? None of you should be driving! :P
My brain is open.
- Paul Erdős |
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