/SQT/- STUPID QUESTIONS

it should be
integral_{-1 to 0} x^3/4-x
= ((1/4)x^4/4-(1/2)x^2)_{-1 to 0}
=((1/4)0-(1/2)0)-((1/4)(1/4)-1/2(1))
=-1/16+1/2

Do you mind simplifying further please.

I'm pretty retarded.

It is negative. Looks like they omitted a '0' which might have made it more clear. The evaluated integral is negative since you're evaluating from 0 to -1. You subtract the value of the integral at -1 from the value at 0 -- which of course is zero. So the answer is: 0 - (what you said) = negative(what you said).

Does it make sense that the following must be co-prime for all k ?
[math] (2k+1, 2k+3, 2k+5, 2k+7) [/math]
If so, how could I prove it?

I see, thanks.

i assume you mean coprime as a 4-tuple, since otherwise 2k+1 and 2k+7 are not coprime when k is 1

if n divides all four then n divides (2k+7)-(2k+5)=2, so n is either 1 or 2

n can't be two since all of them are odd, so they're coprime

for

Thanks for that!

Memorization, really. Memorizing associations between things for example powers of 2, etc. Working on textures for vidya gave me instant calculation for powers of 2 from constantly seeing things like 128x128, 256x256, 1024x1024, etc

Would being suspended in fluid help withstand more than 1g constant acceleration? Assume the force is perpendicular to the human.
I personally don't see how it will help keep blood circulating to the brain, although you'll feel buoyant?

Consider the language of math expressions, with an alphabet S = A ∪
{(,), [, ]}, where A denotes all legal math symbols except for the round and
square brackets. Design a pushdown automaton with a single state that
parses strings formed of symbols from S and accepts these strings if and
only if the opening and closing brackets match correctly.

How would I start this/What would be the first 3 states so I could work out the rest.

Thanks

Does specialization in EE undergrad really matter for finding a job? Want to get into defense or aerospace company and not sure which electives would be best

If f is continuous, then x being "close" to x0 means that f(x) will be "close" to f(x0). More precisely, for any given positive "distance" ε, there's always some non-empty neighbourhood around x0 where all f(x) are within that distance of f(x0), i.e. f(x0)-ε |x[n]-x0|1/ε.

You're being asked to prove that
> yn = f(x0+1/n) converges to f(x0)
I.e. (from the definition of convergence) that
∀ε>0, ∃N∈N, ∀n∈N, n>N => |f(x0+1/n)−f(x0)|0, ∃δ>0, ∀x∈R, |x−x0| |f(x)−f(x0)|0, ∃δ>0, ∀x∈{x0+1/n : n∈N}, |x−x0| |f(x0+1/n)−f(x0)|0, ∃δ>0, ∀n∈N, |(x0+1/n)−x0| |f(x0+1/n)−f(x0)|0, ∃δ>0, ∀n∈N, |1/n| |f(x0+1/n)−f(x0)|0, ∃δ>0, ∀n∈N, n>1/δ => |f(x0+1/n)−f(x0)|0, ∃δ>0, ∃N∈N, ∀n∈N, n>N => |f(x0+1/n)−f(x0)|0, ∃N∈N, ∀n∈N, n>N => |f(x0+1/n)−f(x0)|

If you were in equilibrium (i.e. same average density as the fluid), then acceleration wouldn't change that. As the acceleration increases, the fluid pressure would increase.

The reason why you lose blood flow to the brain under upward acceleration is that the forces accelerating you upward tend to be applied more to your skeleton than to your blood. So the forces are basically lifting your brain upward, out of your blood supply

If the forces were applied via a fluid in which you were (barely) floating, that wouldn't be the case; they'd affect all of your body equally.

Is it possible to make a box such that all 3 side lengths and all 4 diagonals (one on each face, and one from bottom left front corner to top right back corner) are integers?

So it would "sorta help"?

Practice more. You'll see patterns eventually.

mathworld.wolfram.com/PerfectCuboid.html

very very open and hard problem

mast.queensu.ca/~kani/lectures/cuboids-b.pdf
mast.queensu.ca/~kani/lectures/cuboids2-b.pdf
^ some slides from a talk I saw once that went through some of the history of the problem, gets into hardcore arithmetic geometry very quickly

I'm struggling with the fundamentals of sets.
For instance, the line:
({7, 14, 21, 28, ....} ∩ {5, 10, 15, 20, 25, ....})
Is this the one set where the sets {7,14,21...} and {5,10,15...} intersect?
And also, how would you specify this set?
"The set of the multiples of 7 intersecting with the multiples of 5"?

How do I stay motivated to study for my finals.

1 week left...

yup, you got it

if you don't study you'll be more of a failure than you are now.

I'll be blunt; how the fuck do I into linear programming? Pic related is an example problem that I got the answers to only because myomlab is retarded

can someone tell me what the 3x3 matrix does geometrically.

cos(a) -sin(a) 0
sin(a) cos(a) 0
0 0 1

There is this exercise that while I know the answer, I don't know how to get to it:
Find a linear function f(x) = ax+b that the graphic intercept the quadratic function g(x) = x^2 in only one point (1,1).
The answer is f(x) = 2x - 1. I can find it using the derivative, but this is from a pre-calculus book and the book didn't even teach derivative. So how do I go in finding it?
There is also this one:
Find a linear function f(x) = ax+b that the graphic intercept the quadratic function g(x) = x^2 in only one point (p, p2).
And this one I don't know how to do even using derivative.

the intersection is 'the set of multiples of 35'

picture the x-y-z 3d space

the matrix rotates the entire space counterclockwise around the z-axis by 'a' radians

graph* and intersect*

What about this kind of sequent?
{x ∈ N : 7x = x2} ∪ {x ∈ N :6+ x = x2} =
I'm somewhat confused as to what to make of the 'such that' symbol when there's more than just a single symbol to the left of it. I also don't see what I'm meant to deduce from this. The question wants me to specify something from this set but I don't know what to make of it.

The answer was:
{35, 70, 105, 140, ....} = {35n : n ∈ N}
I have no fucking clue how this works.

Someone mind telling me what this means & what the transition rules would actually be + how it would achieve binary addition?

Thank you.

So I needed to build an energy extraction device for a system of baking soda and vinegar and i need to be able to calculate the work output. I used a U-tube filled with water to measure the work. One end of the tube is connected to a reaction chamber/valve system, the other is open to the air. How do i calculate the work if I measure the change in height of the water?

Talk to a tutor

Taking notes.

Rewrite notes you made in class - yes or no?
What's your opinion on it? Seems like a huge time waste to me

How do I find/describe the area over which we are integrating?

Sets make no sense to me.
Specifically, A ∩ B ⊆ A ⊆ A ∪ B
So if AuB is {1,2,3,4,5,6}, and A is {1,2,3}, how the fuck can A∩B contain A? Where is it ever explicitly stated that A∩B contains every element that's within A?
This kind of math just seems like the most illogical concept ever. It feels less like it makes sense and more like I'm learning some ancient rules that someone came up with off the top of their head.

rewriting them reinforces them

also you might come across something you took for granted and learn something new while filling in that gap

>how the fuck can A∩B contain A? Where is it ever explicitly stated that A∩B contains every element that's within A?
it doesn't, that's why you wrote A ∩ B ⊆ A, which means A contains A∩B

you can think of ∩ as 'and' and ∪ as 'or'

Consider the regions described by each integral starting from the inner most one. Ignoring the first two integrands for the moment, the first one's limits indicate that the region is half an infinite cylinder of radius 3 of which the x-axis goes straight through, the half of which constitutes the region is of course the half where y is positive, since y is only positive in the integral. Now it shows that given a fixed z, x varies from 0 to z. Consider the plane defined by x=z. To visualize this, look at the xz plane and the like x=z, basically the identity line. That line is the edge of the plane. This plane will intersect the infinite half cylinder. Clearly we only consider the plane that is in the first octant, because only in this octant will x, y, and z all be positive. The intersection will split the cylinder into two pieces, only one will be finite. Lastly we only vary z from 0 to 2. This part is easy, just "erase" the figure past z=2 and below z=0 (The figure would terminate after z=3 anyways)

I'm confused as to the fundamentals of sets.
So is A∩B the set that contains EVERY element in A and EVERY element in B? Or is it the set that contains the elements that are ONLY shared by A and B?
If it's the forner then I can't really see a difference between A∩B and AUB, since they both seem to encompass both sets in Venn diagrams.

>Where is it ever explicitly stated that A∩B contains every element that's within A?
You have it backwards. The statement A ∩ B ⊆ A means that every element in A ∩ B is an element of A. This is, of course, true, because the all of the elements in the intersection of two sets are members of both sets.

>This kind of math just seems like the most illogical concept ever. It feels less like it makes sense and more like I'm learning some ancient rules that someone came up with off the top of their head.
I suggest you read the first few chapters of How to Prove It, if you aren't reading that already. I'm sure it will clear up a lot of things. Sets are very logical.

>So is A∩B the set that contains EVERY element in A and EVERY element in B?
no, thats AUB

>Or is it the set that contains the elements that are ONLY shared by A and B?
yes

Right, thanks.
Is it safe to ignore the sizes of the Venn diagrams then? I feel like I'm approaching this wrong.

Thanks

A∩B (intersection) is the set of all elements that are shared by both sets. In logical terms, if an element is in A∩B, then that element is in A AND B.

AUB (union) is the set of all elements in both sets. In logical terms, if an element is in AUB, then it is either in A OR B (or both).

Ey buddy, appreciated. Thank you very much.

They're the same set
[math] \{35n: n\in N\}=\{7,14,21,...\}\cap \{5,10,15,...\} [/math]

Saying two sets are equal is the same as saying that each is contained in the other. So to see they're equal, you have to show that the left side is contained in the right side, and vice versa.

Let's show the left is contained in the right. To do this, we need to show that every element of the left set is also an element of the right set.

Take any element x of the left side. By definition, it is of the form x=35n for some integer n. But also x=7(5n), and since 5n is an integer, we conclude [math] x\in \{7n: n\in N\} [/math]. Similarly, x=5(7n), and since 7n is an integer, we have [math] x\in \{5n: n\in N\} [/math]. Therefore, [math] x\in\{7,14,21,...\}\cap \{5,10,15,...\} [/math] since the intersection is by definition all elements in both sets.

We've shown that every element of the left side is also an element of the right side. i.e.
[math] \{35n: n\in N\}\subset\{7,14,21,...\}\cap \{5,10,15,...\} [/math]

To finish up, you also have to show that every element of the right side is also an element of the left, which it would behoove you to try yourself.

Not a question but a request to believers in the almighty God. I currently have a 79.8% percent in my College Trigonometry class. I just took the final today. Pray that I at least got a 40%. I will at least pass the class then. I'm also taking a Pre-cal final Friday. I'm not too worried about that one as I find Pre-cal a lot simpler even though it's considered slightly higher on the totem poll.

Is there any difference between something that can't be known and something that can't be proven?

define 'know'

Like, say I look up at the sky, I know in my mind that it is blue. But I might not have the means on hand to prove it in any exhaustive way.

So I'm taking a first topology class, and so far it's gone pretty good. Covers from metric spaces to fundamental groups. Everything makes perfect sense, except last test there was a question on a topic we spent no time on, only went over the definition. It asked if there could be an open map from [math]S^n\to\mathbb{R}^n[/math]. I would assume, "no", and this had something to do with compactness, but I couldn't manage to figure it out within test time, and I'm still having trouble figuring it out after the fact, because 99% of the work we had done involved continuous functions. Anyone able to tell me what I'm not seeing? The class was not well versed in properties of open maps, and even after consulting the text further, it's not clear.

Define "prove"

You need to calculate the change in potential energy, which is equal to the weight (i.e. mass multiplied by gravitational acceleration) of the water multiplied by the change in mean height.

For a U-tube, you can ignore the water in the U portion and consider only the water which moved. I.e. if the water level dropped by H on one side and increased by H on the other (so the difference changed from zero to 2*H), a cylindrical section of water of height H moved up by H.

The mass of that section is H*area*density, its weight is H*area*density*g, and the change in potential energy is H^2*area*density*g. The density of water is ~1e3 kg/m^3, g is 9.81 m/s^2. H and area should be in m and m^2 to get energy in Joules.

Would it be difficult to get my doctor to prescribe me HGH? I'm fairly sure poor nutrition stunted my growth
(mentally ill parents, i was never allowed to eat much, weighed 52 kilos or 114.64 pounds at 18, and i'm around 4 inches shorter than all of my cousins on both sides)
Would HGH even help? I'm 19 now and my economic situation is vastly different, I have plenty of money for food but i'm fairly sure my growth spurts have ended.

Without much context, is this plot irredeemably shitty? I was thinking of differentiating some of them with different styles(dots, dashes, etc.), but it seems to just make them busy. It's supposed to represent 5 different sets of data - for each one, an upper (red) curve, a lower (blue) curve and an average(green) of those two's asymptotes

silly me

i don't know your doctor, but if you're exceptionally short for your height, then there is a case to be made. my brother was very short and skinny for his age, and his doctor suggested putting him on hgh (although he didn't take it and now is over 6 feet lol)

Can anyone help please?

Trig identities question:
Simplify: tanx csc^2x - tanx

What does the matrix geometrically:
-1 0 0
0 -1 0
0 0 -1

youre a fucking retard

its the diagonal of a unit cube in the octant of negative x,y,z

> tanx csc^2x - tanx
tan = sin/cos
csc = 1/sin

tanx csc^2x - tanx
= ( sinx / cosx ) ( 1/sin^2x - 1)
= ( sinx / cosx ) ( (1 - sin^2x) / sin^2x)
= ( cosx / sinx)
= cotx

Scale by -1, i.e. reflection in the origin.

number theory fags, help me out here

suppose g is a primitive root mod p( a prime) and we want to solve the discrete log problem, g^x = a (mod p). Critique this approach, ie what are the pros and cons(if any) of this method.

First, find a LEGENDRE p (a/p) and therefore, the parity of x.

If x is even (a LEGENDRE p) == 1, rewrite x as 2x and take a square root on both sides and go back to step 1.

If x is odd, (a LEGENDRE p) == -1, multiply both sides by g, rewrite x+1 as 2x, take a square root on both sides, and go back to step 1.

What about if p = 1(mod 4)?, p=3(mod4)?

why do you still not have anything that actually outputs the x you want?

this is theoretical, if i wanted to solve a discrete log i'd use an index calculus, but just for this question, how does it help anyone find a discrete log? is there anything about this that would aid in someones quest to find x?

I just need a random person's opinion on this, if it's readable by an outsider

maybe pick a less offensive shade of green, mark each trio of data lines by a letter

What jobs can I get with a Bachelor's in Mathematics?

your employability will be unequivocally related to the brand of knee pads you invest in

Is this a blowjob joke?

it means if you happen to have great connections, you can expect literally 200k+
if you don't, then you won't come close

I know, but is it a reference to sleeping your way to the top?

If you further assume the map to be continuous, then f(S^n) will be compact and open in R^n, so by Heine Borel open and closed. Since R^n is connected you get a contradiction

Yes, that would be the case under a continuous map, and we've covered many such similar cases, however the map was not assumed to be continuous, which is why I'm having difficulty moving forward.

He's talking about IT. 'Cause they climb ladders and are generally datacenter monkeys and shit like that.

do it by induction

I know how to write in LaTeX.

How do I input LaTeX in a post on Veeky Forums?

put it between a [math]
and a
[/math]

[math] testing [/math]

Please help, in telling me exactly what the transition rules would be from this example of a Turing machine.

Thanks

What's the necessary condition on [math] f [/math] for a solution [math] x: \mathbb{R} \to \mathbb{R}^n [/math] to exist for a given autonomous differential equation:
[eqn] \dot{x} = f(x) [/eqn]

Also why do you have to specify the standard basis for [math] \mathbb{R}^n [/math]. Why isn't it just that [math] \mathbb{R}^n [/math] is defined by induction on the Cartesian product?
[math] \mathbb{R}^1 = \mathbb{R} [/math]
[math] \mathbb{R}^{n+1} = \mathbb{R}^n\times \mathbb{R} [/math]

Why is thermodynamics so confusing? Why are the Kelvin and Clausius statement of the second law equivalent? How to make sense out of the Clausius theorem? Why does S always increase? Why does the maximization of S imply the minimization of the internal energy?

What is the geometrical interpretation of complex integrals?

What exactly are branch points and why there is a discontinuity between two "sides" of a cut line but not discontinuity between two "sides" of a countour line?

Yes, it would sorta help, dependant on the density of the fluid and the severity of acceleration

why does pussy feel so good?

Please someone answer this is an emergency.

Why is w perpendicular to [math]w^Tx + b = 1[/math]?