Ducky Havok

Well my friends math teacher gave him this list of 50 math puzzles, and he passed it along to me (since he knows I like them more). Out of the 50 I haven't solved 7 (I just got them this morning and worked on them through school), so I figured I'd post them on here for you guys to try. If you really want I'll put up all 50 later. 1. Use three 5's to make 115 2. Use four 8's to make 100 3. Use two 4's to make 24 4. Use four 7's to make 70 5. Use three 4's to make 50 6. Use three of the same number to make 28 7. Use three of the same number to make 13 I think most have done these kind of things before, but just in case I'll give some examples. For instance, Use six 9's to make 100: [math]\frac{(999-99)}{9}=100[/math] The only rule is you are only allowed to use that one digit, but you can use any mathematical symbols you want (such as exponents or factorials, even decimal (like .5)) Have fun!

Why does it have to be something we understand? Semag is his name so maybe he was just curious if we all liked it.

(this is just what I have so far but my sister is kicking me off so I can't finish). Since the first word and the third word are backwards, and since Callipygous mentioned screen name, I think it goes something like "Semag is games spelt backwards (he might have messed this up), is it a (not sure) screen name?" I don't have much time to finish though so I figured I'd post that to see if it helps anyone else get it.

Dandelions

I was going to answer this, but then I realized it was just like the other one I got in the word puzzle thread so I figure I'll let someone else get it.

Aren't those the conversions to polar coordinates? I'm just going off memory, we haven't gotten to those yet. So do you get something along the lines of [math]-\frac{\sqrt{R^2-U^2}}{{R^2}U}[/math] with [math]U=RCos(x-\phi)[/math] ? I think I confused myself worse there actually...

Well, on the bright side, my first answer and that answer are the exact same, that one is just super simplified compared to mine. On the dim side (because if there's a bright side there has to be a dim), I still don't get how to do it even with your hint. What is [math]R[/math] and [math]\phi[/math]? At first I thought [math]\phi[/math] was just theta but I put my mouse over it and it said phi. I haven't seen either of those symbols yet, but I'm still in baby calc. One of my friends just asked me this question because they couldn't get it.

One small thing, in my problem the bottom part is squared. [math]\int \frac{1}{{(a\sin(x) + b\cos(x))^2}} \, dx[/math]

Yes, and now I feel stupid for messing that up twice in the same post I'll go back and fix that though

How would you solve the following problem? [math]\int \frac{1}{{(asin{x}+bcos{x})^2}}, dx[/math] with a and b being constants. I'm pretty sure the answer is [math]\frac{2tan{\frac{x}{2}}}{(-btan{\frac{x}{2}}+\sqrt{2ab+1}+a)(btan{\frac{x}{2}}+\sqrt{2ab+1}-a)}+C[/math], but I want to know how to do it.

For the first one, you can find K really easily. Plug in -1 for x and set it equal to 0 and you K=3. Then you have [math] 3X^2-3X-6 [/math] You already know one factor of this, so if you divide you get [math] (3X-6) [/math] as the other. Once you divide by 3 you get it in the form given above, so M=-2

For number 2, first you multiply each equation by 3, y, and x. That'll give [math]6Y=Y^2X=3X^2[/math] By just looking at the 2nd part, you get [math]Y^2X=3X^2[/math], and [math]Y^2=3X[/math] so [math] Y=\sqrt{3X}[/math] so now you have the equation [math] 6Y=3X^2 [/math] after dividing by 3 and substituting in for y, you get [math]2\sqrt{3X}=X^2 [/math] and when you solve for x, [math]X=(2\sqrt{3})^\frac{2}{3}[/math] when you cube that you get [math]X^3=12[/math]

Yes, its easy to do it using arithmatic or common sense. The most area is of course going to be a square. But the point was to use calculus I think

Want a really simple, cool experiment? Take a beaker with some table sugar in it, and pour sulfuric acid on top. First it'll just bubble a little, and then a giant black foam will form, which looks pretty cool. It does get extremely hot though and smells like sulfur though. Extremely simple and fun to watch.

Okay, early Dave you said you couldn't think of dy/dx as fraction, but don't you have to do it to do implicit integration (actually I don't think that's what it's called, I think I just made that up)? example: [math]\frac{dy}{dx}=\frac{x}{y}[/math] [math]ydy=xdx[/math] [math]\int_a^by\,dy=\int_a^bx\,dx [/math] [math]\frac{y^2}{2}=\frac{x^2}{2} [/math] I understand that dy/dx isn't really a fraction, but how would you do something like that without treating it as one?

dan19 83, wouldn't you have to delete the first column though, not the 3rd? Since it started off with 1, then 4 and so on. I suck at using excel though so I wouldn't know how to do it

you could still use differentials to approximate it pretty close though. Like [math]\sqrt{23}[/math], you could say [math]x=25, dx=-2[/math], then [math]\frac{1}{2\sqrt{x}}dx+ \sqrt{x}[/math], which would give you [math]-1/5+5 [/math], which is 4.8. That's pretty close to the square root of 23. I'm only saying this because I don't understand how to use the binomial formula though. Can you please explain it some? (I might know it, just not know that that's what it is. Most likely I don't though)

I didn't write EVERY number out... most though. What I did was started until about 50, then started crossing out until I found a pattern. Then I found a pattern that went 5,3,4,2,4,3,5,1 and then repeated (those numbers being the gap between the numbers. Ex. 5, 8, 12, 14, 18, 21, 26, 27). I also did it in columns on 27 lined paper, so instead of having to go through and mark every single one out, I could just do entire rows at a time.... I just hope I didn't miss a number there somewhere.... I think I would die.

1,860 ..... and god damn my hand hurts

Usually its all luck . I just try to find popular endings, like -tion or -sation, then I just work from there.

Mobilisation? I think I spelt that right... yup! I just grabbed a dictionary and checked, it means to make movable, to put into motion.

I think to use spoilers, you type in the word hide (where you put spoiler). Also, Flareon was right (its possible for there to be more than one answer). Here's an explanation. [hide]20 minutes before 7:25 is 7:05. When you take the mirror image of 7:05, you get 4:55. 4:55 is exactly 2 and a half hours before 7:25.[/hide] Your answer is also right, for the same reason. I'm pretty sure those are the only two answers though.

drat, I guess it was too simple of a question for too smart of a forum.