/sci/ - Science & Math

find length AB

>>10178004
find f(x)

find f(x)

>>10178039
That's just sin(ax)*exp(bx) for some a, b which I certainly can't be arsed to solve from your picture.

>>10178020
slowly but surely, these 3 circles get me pissed off

>>10178100
that b isn't in the exponent but in front of e, but I'm not sure if it matters

find the radius of the circle which passes through A(0,0), B(1,4) and C(5,1).

If you pass the last person in a race which place will you be?

>>10178020
[math]3\sqrt{6}[/math]

>>10178123
still first

This is the graph of f(x,y) = 0. Find f(x,y).

Find length AB

>>10178162
true
>>10178253
u wot nigger

>>10178253
AB=OE/3
easy

solve for radius in terms of a,b and c

>>10178380
Prolong b, connect it to c on both points, big right triangle. Connect prolongation of b to other point of a, big right angle, thus diameter.

>>10178123
Anything from first to second to last

>>10178253
[eqn]AB=\frac{4}{87}OE\sqrt{2+19\sqrt{7}}[/eqn]

>>10178211
>>10178410
you can't overtake the last person, because that person wouldn't be last then

>>10179533
overtake =/= pass
lapping is a thing

find the area of all the grey circles
also why isn't anyone solving the questions

>>10179621
I don't have a compass on me, so solving geometry is a huge pain. And these >>10178004 >>10178253 along with the one you just posted are the only ones worth solving.

>>10178499
correct

>>10179621
$$ \pi \frac{R^2}{2} $$

stop posting geometric problems, you fucking brainlets

>>10179621
i mean \pi \frac{R^2}{2}

>>10178004
>interesting

>>10179655

[math] \displaystyle\pi\cdot\frac{R^2}{2} [/math]

here you go

>>10178241
I really want to know this

>>10179667

>>10178112
gotta be kidding me

>>10179659
thank you, was too lazy to look it up

>>10179674
how do people come up with this shit?

>>10179753
wolfram alpha

>>10179659
>>10179655
Where was the mistake? I can't math tags to display correctly, either.

>>10179763
*can't get

>>10178004
does anybody know the solution to this problem?

>>10178294
I'm pretty sure you are fucking right. If the answer is anything else than this, based on the information provided, this question is retarded.

>>10180984
That's kind of the joke/trick of the question.
At first glance it looks like it should just be the diameter of the circle, but it's actually >>10178499, which is ever so slightly less (~0.3324OE).

>>10180984
If you assume that OE goes through the centers of the circles, that OD is tangent to the top-right circle, and that every circle is identical, then that answer would be wrong. AB would actually be 0.9972 times the radius of each circle. See >>10178499

>>10178039
Amortiguated oscillation, flipped around and with the Y axis moved a bit around?

>>10181031
Fuck, that makes sense. Good point, anon. Cheers. How would one solve without numbers then? Or even values of R? I would assume to let R equal the diameter of a circle, which is equal to OE/3

>>10179674
We should broadcast this in the direction of the Wow! signal at full power

geometry is the worst math subject
t math major

>>10178004
>>10180858
I think it's [math]R=\frac{144}{23}[/math].

>>10180858
Sure enough.
See the points where the two smaller semicircles touch the big circle? If you connect them, the line passes through the point in the triangle, and is parallel to the hypothenuse.
Mark the midpoint in the line, and trace a line at a ninety degree angle. It passes through the hypothenuse. Mark this midpoint. Big circle's center.
The rest is trivial, I just really don't feel like applying Pythagoras fifteen times over. And again, no compass, so I'd have to draw things on fucking Paint.

There's no thread for this and I feel like a fucking retard for not remembering this but it's been a very long day of working on assignments so my brain is burnt out.
What statistical test do you use to show that the mean of one group is significantly larger than the mean of another

>>10181222
that line and the hypotenuse aren't parallel but almost are. Or if they are prove it

>>10182819
https://en.wikipedia.org/wiki/Thales%27s_theorem

>>10178380
(\sqrt(a^2+b^2)+\sqrt(2c^2))/2

>>10182845
sorry I don't see how that theorem is applicable

>>10180858
Any line orthogonal to a tangent line of a circle must pass through that circle's center. Draw lines from the center of the big circle to its points of tangency with the smaller circles. Those lines must pass through the centers of the smaller circles. Split those lines at those centers. The outer lengths are simply the radii of the smaller circles, and the inner lengths are labeled a, b, c. The sum of an inner length with its outer length must be the radius of the big circle. This relation can be expressed as
[eqn]R=a+3=b+4=c+5.[/eqn]
Rearrange and square both sides to get
[eqn]a^2-9=R^2-6R,\\
b^2-16=R^2-8R,\\
c^2-25=R^2-10R.[/eqn]
Next, draw line segments orthogonally from the legs of the triangle to the center of the circle. Label these x and y. The lengths a, b, c can be expressed in terms of x, y by the Pythagorean theorem.
[eqn]\begin{alignat}{16}
a^2-9&{}={}&(3-x)^2{}&+&{}y^2{}&-&{}9&{}={}&x^2&{}-{}&6x&{}+{}&y^2&&&{}=R^2-6R\\
b^2-16&{}={}&x^2{}&+&{}(4-y)^2{}&-&{}16&{}={}&x^2&&&{}+{}&y^2&{}-{}&8y&{}=R^2-8R\\
c^2-25&{}={}&(3-x)^2{}&+&{}(4-y)^2{}&-&{}25&{}={}&x^2&{}-{}&6x&{}+{}&y^2&{}-{}&8y&{}=R^2-10R
\end{alignat}[/eqn]
This gives a system of polynomial equations which can be eliminated to obtain the relation:
[eqn]3x=2y=R.[/eqn]
This can be plugged back in to the polynomial equations. Finally, solve for R and discard the extraneous solution.
[eqn]R=\frac{144}{23}[/eqn]

>>10180858
We name the points of the triangle A, B, and C, where AB=6 and AC=8, we name the semi-circles ABD, ACE and BCF, where D, E and F are the points of tangency.
Connect DC, BE and AF. We claim that the point G where DC, BE and AF meet is the center of the large circle, and GE, GD or GF can be used for the radius.
Proof of the whole thing has been left to the reader.

For what value of a does [math]x^a=a^x[/math] have only one unique real solution?

True of False? z=y is the tangent plane to f(x,y)=e^(x^2+y) at (x,y)=(0,0)?

I got Z=Y+1 as the truest answer, but technically Z=Y is parallel to the tangent plane? Doesn't that make Z=Y the tangent plane as well? What should I put down as the answer, I am taking an Online Quiz for homework points and I dont' want to miss anything.
Also post more multivariable math problems, anons. I want to test my knowledge before finals.

>>10183842
I'll just post free multivariable calculus problems for you non uni faggot anons.

>>10183877

>>10183842
>>10183877
>>10183882
>solving multivariable calculus
>for free
Not fucking happening.

>>10183882
Good Luck.

>>10183888
I can do these, anon. I will post basic linear algebra for you to solve for your own damn practice.
I only asked for verification on the autistic problem my professor asked for the other Z=Y problem.

>>10183891
The world doesn't fly around you, I was complaining that this thread is for interesting problems. Emphasis on interesting.

>>10178004
[math]r=\frac{ \left(\frac{6+8+10}{2}\right)^2 }{ (6+8+10) -1}[/math] MOTHAFUCKA
YOU CAN'T TOUCH DIS SHIT
I'M ON FIRE NIGGAAAAAAAA

Calculate

>>10183907
wtf how?!

>>10183936
[math] \frac{1}{\sqrt{2}} [/math]
right?

>>10178004
No solution. Since tangents to the outer circles coincide with the tangents of the semicircle, every radius of the semicircles coincides with a radius of the outer circle.

All radii meet at the center and the radii would therefore meet at the halfway point of the hypotenuse.

But that point is 7 units away from the circumference for two of the radii and 5 units away from the third, and which means the point can't form a circle.

>>10183889
It's literally just an implicit differentiation Calc AB problem, but with gradient. [math]\vert\vert(\nabla z)(1,1)\vert\vert=\sqrt{29}[/math], unless if I fucked up somewhere.

>>10184012
What do you mean Calc AB? Your school must have been actually good to make it seem obvious.
All of the problems were retardedly easy besides that one. Example shown:

>>10184048
This is for those who forgot their Lagrange definitions.

>>10184069

>>10183955
How did you come up with a pattern?

the left end of an elastic rope is fixed and the right end moves away from the left one at a speed of 10cm/s, an ant is on the left end of the rope and moves to the right end of the rope at a speed of 5cm/s. How long will it take the ant to get to the right end?