I'm having a hard time trying to comprehend this. How do I even start on proving the shape?
35884
I know that matrix multiplication in general is not commutative. So, in general:  $A, B \in \mathbb{R}^{n \times n}: A \cdot B \neq B \cdot A$  But for some matrices, this equations holds, e.g. A = Identity or A = Null-matrix $\forall B \in \mathbb{R}^{n \times n}$.  I think I remember that a group of special matrices (was it $O(n)$, the ?) exist, for which matrix multiplication is commutative.  For which matrices $A, B \in \mathbb{R}^{n \times n}$ is $A\cdot B = B \cdot A$?
9060
I'm having some difficulties continuing this problem. I get that $b^2\mid a$ and $c\mid a$ but I am not sure where to go from there.
95230
From the given figure, prove that      $$\cot\ \theta=\cot\ A+\cot\ B+\cot\ C$$     I could not even start to the first point. Please help me to solve this.  Thanks in advance
44119
Prove that three points are enough to draw/define one and only one circle, how would this be done?
122758
I tried looking it up but many websites just state it without proof and without intuition.  I'm hoping to learn it a little bit better so that I don't forget how to compute the Jacobian when working with surface integrals where the divergence theorem is not applicable.  If you have a good online reference instead, please feel free to provide it :-)  Thanks,
92014
Consider the parabola $x^2=4ay$. Two focal chords are constructed, and   the interval that the chord makes with the parabola are diameters of   two circles.       Prove that that the common chord of the two circles passes through the   origin (vertex of the parabola).    I am having trouble finding a purely geometric way of proving this result.
71832
I've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful.
105006
I saw this question here:-   This looks so much like a vandermonde identity, I know we can give a counting argument for Vandermonde. However much I try I am not able to come up with a counting argument for this.
2958
Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$? How can we find the RHS if we don't know what it is? (instead of proving the identity itself) I could find a geometric solution in , but is there any solution that doesnt require drawing something? Edit: I now saw some nice proofs using $e$ and Euler's identity. I would appreciate anything NOT using them too, as a change. Out of curiosity, Is there a proof that says you actually "can't" prove the identity using only other simple 1-variable identities like $\sin^2\alpha+\cos^2\alpha=1$?
34259
I think I have found the final answer $\left(4 \left[\frac{2t \cosh(4t) - \sinh(4t)}{t^2}\right]\right)$ but need to verify it.
48888
$$S_1=\left\{z:Im\left(\frac{z-z_1}{z-z_2}\right)=0, z_1,z_2 \in \Bbb C\right\}$$  $$S_2=\left\{z:Re\left(\frac{z-z_1}{z-z_2}\right)=0, z_1,z_2 \in \Bbb C\right\}$$  Can someone help me with the geometric description of the above two sets. I have no clue as to where I should start. Thank You!
83559
In my graph theory book exercise, I found a problem that:     Prove that the World is not flat using Mathematics     This picture is used in the exercise, but no idea of applying it.  I would have used the angles don't add to $180^\circ$, but the author is using a fourth city.
62382
I'm less than a novice in analysis, I don't even know how to approach this. Thanks in advance.
87145
Do you see any nice way to prove that $$\arctan\frac{\pi}{2}\ge1 ?$$  Thanks!  Sis.
3060
Don't let the simplicity of this diagram fool you. I have been wondering about this for quite some time, but I can't think of an easy/smart way of finding it.  Any ideas?    For reference, the Area is:  $$\bbox[10pt, border:2pt solid grey]{90−18.75\pi−25\cdot \arctan\left(\frac 12\right)}$$
116030
I know how to prove this using an element and subset proof but that's not what I'm being asked to do. I'm suppose to prove it using the distributive law and the associative law but I'm just not seeing how to do this. Can you give me some advice on how to start this. I figure the first thing would be $$((A \cup B) \cap A) \cup ((A \cup B) \cap B^c))$$ But I'm not sure where to go from there.
114549
How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto the cardioid $R=2(1+\cos \theta)$?