Posted on 01 April 2017 - 04:48 PM
SipinOnSumSizurp wrote
A = [5 6]
- - - [1 3]
to encode the message "DO YOUR BEST"
Plain: - - - -A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Cipher: - - D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
(The dashes are used in places of space, because Badlion excludes multiple spaces)
Sorry, I forgot to respond to this.
My best guess is the following:
Assign numbers to each letter: A = 1, B =2, C =3, etc.
Then we use the cipher to switch that around, so that D = 1, E = 2, F =3, etc.
Now, we transcribe "DO YOUR BEST" into numbers, letting spaces be zeroes: 1, 12, 0, 22, 12, 18, 15, 0, 25, 2, 16, 17.
Use the enciphering matrix to transcribe each group of two letters/numbers into the encoded form.
[5 6] [1,12]^T = [5 + 72, 1 + 36]^T = [77, 37]^T. Then, we follow it up on each other pair of numbers to finally obtain
[1,3]
the encoded sequence: 77, 37, 132, 66, 168, 66, 75, 15, 137, 31, 182, 67.
Then you can use the inverse matrix of the encoding matrix and the cipher to regain "DO YOUR BEST."
Last edited on 20 April 2017 - 05:32 PM by whitpillow
teach me how to solve solve these inequalities pls-1 < I 2x-3 I < 7 and II x-4 I -2 I < 3 and I 0.2x+3.5 I > 1.7 and I 8y/3 - 2y/4 I < -13
I is absolute value by the way xd
Posted on 20 April 2017 - 05:45 PM
whitpillow wrote
-1 < I 2x-3 I < 7 and II x-4 I -2 I < 3 and I 0.2x+3.5 I > 1.7
I is absolute value by the way xd
Recall that the definition of the absolute value function is f(x) = |x| = x for x >= 0; -x for x < 0.
Thus, if |x| < 1, we have to have x < 1 and -x < 1, or x > -1. Thus, -1 < x < 1.
So basically we solve two inequalities for each.
a.) Positive: -1 < 2x - 3 < 7. Add 3 to all sides to get 2 < 2x < 10, or 1 < x < 5.
Negative: -1 < 3 - 2x < 7 (took the negative of what's inside of the inequality), or -4 < -2x < 4, or 2 > x > -2.
Now we take the union of these two intervals (everywhere that holds true): -2 < x < 5.
b.) Now we have to do this twice.
Positive: |x-4| - 2 < 3, so |x-4| < 5.
Negative: -|x-4| + 2 < 3, so -1 < |x-4|.
Thus, we need -1 < |x-4| < 5.
Positive: -1 < x - 4 < 5, or 3 < x < 9.
Negative: -1 < 4 - x < 5, or -5 < -x < 1, or 5 > x > -1.
Thus, -1 < x < 9.
You can do the last one!
Posted on 20 April 2017 - 07:30 PM
for problems that have the greater than sign like these not sure what to do but I can do the problems with the less than sign.I 2x+5 I > 0.5 and I x+5 I > -1
Last edited on 22 April 2017 - 01:23 PM by AlbertEinstein
whitpillow wrote
I 2x+5 I > 0.5 and I x+5 I > -1
Same idea. Just solve two inequalities: one with positive inside the absolute value bars, and one with negative. It doesn't matter what the sign is. Just remember to flip the signs if you multiply by a negative number.
|2x+5| > 1/2
+: 2x + 5 > 1/2, or 2x > -9/2, or x > -9/4.
-: -2x - 5 > 1/2, or -2x > 11/2, or x < -11/4.
Thus, -9/4 < x or x < -11/4. Note that we have to separate these, since -11/4 < -9/4.
The other one can be done in the same way.
Posted on 28 April 2017 - 06:59 PM
The length of a side of a rectangle is 6 cm. What should the length of the other side be so that the perimeter of the rectangle is smaller than the perimeter of a square with a side of 4 cm?these problems are aids so have fun!
Posted on 29 April 2017 - 12:37 AM
SporkHandles wrote
these problems are aids so have fun!
Call the other side of the rectangle x. Then the perimeter of the rectangle is 2(6) + 2x = 12 + 2x.
The perimeter of a square of side length 4 is 4(4) = 16. Thus we need to solve an inequality for x.
perimeter of rectangle < perimeter of square
12 + 2x < 16
2x < 4
x < 2.
Since side lengths have to be greater than zero, the side length x of the rectangle must satisfy 0 < x < 2 cm.
Posted on 09 May 2017 - 10:52 PM
Your task is to construct a building which will be a pile of n cubes. The cube at the bottom will have a volume of n^3, the cube above will have volume of (n-1)^3 and so on until the top which will have a volume of 1^3.You are given the total volume m of the building. Being given m can you find the number n of cubes you will have to build?
Last edited on 10 May 2017 - 02:26 PM by AlbertEinstein
Survive wrote
You are given the total volume m of the building. Being given m can you find the number n of cubes you will have to build?
Assuming I'm reading this correctly, we have to find the total volume of the building in terms of n, and then solve for n in terms of m.
So we have to add up each individual cube's volume and go from there (I guess they're all just stacked on top of one another).
n^3 + (n-1)^3 + (n-2)^3 + … + 2^3 + 1^3 = sum_{k=0}^{n-1} (n-k)^3 (using summation notation).
Now, when I first worked through this, I expanded that sum and evaluated each individual part, and then I realized that was a lot of work and could be done more easily.
Let's change the index on the sum by k=n-r. Then, inside the sum, we have n-k = n-(n-r) = r. And then the indices on the summation symbol change by k =0=n-r, so r=n. And k=n-1 = n-r gives r=1. Now the summation bounds are inverted (with bigger number on bottom and smaller number on top), so we simply switch them around.
Now our sum is sum_{r=1}^{n} r^3. Now, this is a sum that you can look up or that you may have learned in class. It can be expressed in terms of n, which is what we want.
The sum is [n(n+1)/2]^2. Check the sign on the (n+1) part if you want to be sure. I could be wrong on the sign or may have messed up somewhere before.
So this is the volume of the entire building in terms of n. So we can set it equal to m and solve for n.
m = [n(n+1)/2]^2, so 2*sqrt(m) = n^2 + n, so n^2 + n - 2*sqrt(m) = 0.
Now we can just use the quadratic formula to solve for n.
n = -1/2 +- (1/2)*sqrt[1-4(-2sqrt(m))]. Now, since we want n to be positive, we take the positive root, since otherwise, we'd obtain a negative n.
Thus, n = -1/2 + (1/2)*sqrt[1+8*sqrt(m)].
I implore you to go back through and check the signs on some parts, because I may have made some small sign error in between. Also, it may be instructive for you to expand my original sum and use formulas to get an explicit expression for the volume in terms of n that way.
Also, maybe try some explicit numbers with this formula, and see if they give a plausible solution. If they don't, switch around some signs until they do.
Hope this helps.
Posted on 13 May 2017 - 07:11 AM
do you have an occupation currently? (since i know you're at university)what occupation do you want, once you've finished uni?
Posted on 13 May 2017 - 03:46 PM
Survive wrote
what occupation do you want, once you've finished uni?
I'll be working on research with a physicist over the summer if I can secure funding for the project.
I'll probably be a research physicist and/or professor (though, as a professor, you usually do both research and teaching) after I go through all the steps to get a Ph.D.
Posted on 13 May 2017 - 09:56 PM
AlbertEinstein wrote
Survive wrote...
I'll be working on research with a physicist over the summer if I can secure funding for the project.
I'll probably be a research physicist and/or professor (though, as a professor, you usually do both research and teaching) after I go through all the steps to get a Ph.D.
Posted on 13 May 2017 - 11:23 PM
Survive wrote
AlbertEinstein wrote...
Big range. Professors can get paid a lot, especially at top universities, up to hundreds of thousands of dollars a year. But probably more average is around 100k dollars more or less (at least according to Google).
But even better than the cash is the cool stuff I'd get to study–literally understanding the nature of the universe itself. When you're learning stuff that people have never known before, that's gotta be a good feeling.
Last edited on 16 May 2017 - 05:41 AM by MCsteveswag9
Boi send help S = K. log WIt may seems strange but yeah… I am going to kill myself, I need to do it and we have 4 days no schlool so can't ask my teacher how to do this
Pls be a genius
Posted on 16 May 2017 - 10:59 AM
NotificationBell wrote
It may seems strange but yeah… I am going to kill myself, I need to do it and we have 4 days no schlool so can't ask my teacher how to do this
Pls be a genius
What's the question?
That looks like a way to define entropy in the microcanonical ensemble of statistical thermodynamics. W is the multiplicity of the system; K is Boltzmann's constant; and S is the entropy.
Posted on 17 May 2017 - 01:53 PM
That's what I needed, thx. Sorry if I wasn't clear enough I had something to do.Last edited on 22 May 2017 - 09:17 PM by AlbertEinstein
Closing this. Thanks for you all your questions over these last few months. I'm formally resigning from my positions as moderator and also ending this post.This Discord will still be open if you are interested in homework help: https://discord.gg/x5Z2Yqf.
I hope I helped you guys out.