Top new questions this week:
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I see this answer to this question and this one.
My $7$th grade son has this question on his homework:
How do you know an exponential expression will eventually be larger than any quadratic expression?...
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My son's high school teacher says his solution to this proof is wrong because it is not "the right way" and that you have to "start with one side of the equation and prove it is equal ...
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Let $a_n=(-1)^{\left\lfloor{\frac{3^n}{2^n}}\right\rfloor}$ and $$s_n=\sum_{k=1}^na_k.$$
Is it true that $s_n\le 0$ for all $n\geq 1$ ? (This is true for $n\le 100000$.)
In other words, odd numbers ...
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When you calculate what ${x}^{x^{x^{x\cdots }}}$ converges to between 0 and 1, before approximately 0.065 the graph bifurcates.
Why does this happen and is there a reason for it happens at that ...
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Let $m≥2$, $n≥2$ integers. We want to color the squares of an $m × n$ board with black and white so that each square has exactly two neighbors of the other color. Determine all the values of $m$ and ...
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It's quite easy to find a regular square prism (cube) or a regular triangular antiprism (octahedron) with vertices in $\mathbb Z^3$. Take for instance, take the convex hulls $$ \begin{align*}
&\...
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Say that the perimeter of a polyhedron is the sum of its edge lengths. What is the maximum volume of a polyhedron with unit perimeter?
A reasonable first guess would be the regular tetrahedron of side ...
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Greatest hits from previous weeks:
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My attempt to solve this problem is:
First digit cannot be zero, so the number of choices only $6 (1,2,3,4,5,6)$
The last digit can be pick from $0,2,4,6$, so the number of choices only 4
Second ...
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This is a very simple but confusing puzzle.
A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase.
The lady gives him a $1000$ ...
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I just came across this annotation in my school's maths compendium:
The compendium is very brief and doesn't explain what this means.
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What is the Jacobian matrix?
What are its applications?
What is its physical and geometrical meaning?
Can someone please explain with examples?
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Why is it that e raised to the power of negative infinity would equal 0 instead of negative infinity? I am working on problems with regards to limits of integration, specifically improper integrals ...
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$$\dfrac{1}{2}\ln(x+7)-(2 \ln x+3 \ln y)$$
Our professor let's us solve this but i do not understand how $\ln$ works. He says it has same properties with $\log$ but i still don't get it. What's the ...
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How do I find a vector perpendicular to a vector like this: $$3\mathbf{i}+4\mathbf{j}-2\mathbf{k}?$$
Could anyone explain this to me, please?
I have a solution to this when I have $3\mathbf{i}+4\...
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Can you answer these questions?
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I found in a solution that expands the following series,
$$
=\sum_{i=1}^m{\left( \alpha _{ik+1}p_{k+1}+\alpha _{ik+2}p_{k+2}+...+\alpha _{in}p_n \right) ^T\left( \alpha _{ik+1}p_{k+1}+\alpha _{ik+2}...
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Say we got this simple example
$$f(x) = \begin{cases}
p_1(x),\text{ for }5 \leq x \leq 8,\\
p_2(x),\text{ for }8 \leq x \leq 10
\end{cases}$$
Assuming $p_1(8)=p_2(8)$, is this permissable?
Arguments ...
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Given the ideal $$I=\langle x^2+2y^2-3, x^2+xy+y^2-3\rangle$$ in $ ℚ[x,y]$, how do I find the Grobner basis for $I \cap \Bbb Q[x]$ and $I\cap\Bbb Q[y]$?
I have learned to find a Grobner basis using ...
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