RolyPoly
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Questions Asked

RolyPoly:
Group Title
"The numbers 1, 1+1=2, 2+1=3, etc. are said to be natural; it is assumed that none of these numbers is zero".
Why do we have/need such an a…
 updated one year ago
 17 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Suppose \(E\subset R\), \(z\in R\) and \(x\le z \forall x\in E\). The upper bound \(z_0\) of the set E is called the least upper bound of E…
 updated one year ago
 15 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Let \(x:(0, \pi) \rightarrow \mathbf{R} ^2\) be the path given by \(x(t) = (\sin t, \cos t + \ln ( \tan\frac{t}{2} ) )\), where t is the ang…
 updated one year ago
 1 reply
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Suppose G is a simple undirected planar graph.
Prove that G contains a vertex with degree at most 5.
 updated one year ago
 20 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
<Graph theory>
Suppose G=(V,E) is a simple undirected graph with no selfloop; moreover, the graph G has n=V \(\ge\) 1 vertices, m=E edg…
 updated one year ago
 33 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Suppose there are m different hunters and n different rabbits. Each hunter selects a rabbit uniformly at random independently as a target. S…
 updated one year ago
 33 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Consider integer solutions to the equation:
\(x_1+x_2+x_3+x_4+x_5=10\)
How many nonnegative integer solutions are there such that \(x_1>x_2…
 updated one year ago
 22 replies
 3 Medals
Mathematics

RolyPoly:
Group Title
Consider integer solutions to the equation:
\[x_1+x_2+x_3+x_4+x_5=10\]
How many nonnegative integer solutions are there such that \(x_1 = x…
 updated one year ago
 12 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
<Recursion>
Consider f(0) = 0 and for n \(\ge\) 1, f(n) = f(⌊n/2⌋) + 1. Find a recursion formula for the function.
 updated one year ago
 37 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Compute
\[\log_2(\sum_{k=0}^{1024} C(1024,k) *k)\]
 updated one year ago
 1 reply
 1 Medal
Mathematics

RolyPoly:
Group Title
<Soft question>
How is calculus applied in Computer Science?
 updated one year ago
 No Medals Yet
Mathematics

RolyPoly:
Group Title
<Graph Theory>
Find the number of paths of length 5 in the complete bipartite graph \(K_{4,9}\).
 updated one year ago
 70 replies
 3 Medals
Mathematics

RolyPoly:
Group Title
Use Green's theorem to calculate the area under one arch of the cycloid:
x = t  sint
y = 1  cost
 updated one year ago
 No Medals Yet
Mathematics

RolyPoly:
Group Title
How to parametrize the equation y^2 = x^3?
 updated one year ago
 4 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
We have: \[\int_0^1 \int_{3y^2}^{4y^2}\int_{\sqrt{z3y^2}}^{\sqrt{z3y^2}} dxdzdy\]
Task: change the order of integral to dxdydz
 updated one year ago
 8 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
We have :
\[\int_0^1 \int_{\sqrt{44y^2}}^{\sqrt{44y^2}} \int_{x^2+3y^2}^{4y^2}dzdxdy\]
Task: change the order of integral to dxdzdy
 updated one year ago
 44 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Integrate f(x,y,z) = z over the region W bounded by z=1, x^2+16y^2 = 16 and z=x+5
 updated one year ago
 No Medals Yet
Mathematics

RolyPoly:
Group Title
\[f(x) =\begin{cases}0 & x = \text{rational}\\1 & x = \text{irrational}\end{cases}\]
Find \[\int_0^1f(x)dx\]
 updated one year ago
 40 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
How to prove that \(\sum_{k=0}^{\frac{n}{2}} C(n,2k) 3^{n2k} = 2^{n1}(2^n+1)\)?
 updated one year ago
 7 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Suppose in a party of 5 persons, every person brings a gift to the party for exchange. The gifts are distributed back to the persons randoml…
 updated one year ago
 No Medals Yet
Mathematics

RolyPoly:
Group Title
<Double integrals>
How to show that \(\int^1_0 \int_0^2 f(x,y) dy dx\) exists given \(\int_0^2 f(x,y) dy = 2\) ?
 updated one year ago
 6 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
<Double Integrals>
How to get \(\int_0^4 \int_0^{\sqrt{x}} ycos(x^2)dydx\) from \(\int_0^2 \int_{y^2}^4 ycos(x^2)dxdy\)?
 updated one year ago
 38 replies
 5 Medals
Mathematics

RolyPoly:
Group Title
How to find all the critical points of f(x,y) = sinx cosy?
 updated one year ago
 5 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
How to interpret the following question:
Graph the curve \(y^24x^3+4x^4 = 0\) and use the graph to determine where the extrema of f(x, y) =…
 updated one year ago
 6 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Under what conditions on the constant k will the function f(x, y, z) = \(kx^2 + kxz  2yz  y^2 +
\frac{k}{2} z^2\) have a nondegenerate l…
 updated one year ago
 3 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
In how many ways can seven identical candies distributed to 3 children {I, II, III} if each child can get any number of candies?
 updated one year ago
 30 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
Show that the curve traced parametrically by
\(x(t) = (cos(t  1), t^3  1,\frac{1}{t}  2)\) is tangent to the surface \(x^3 + y^3 + z^3  …
 updated one year ago
 21 replies
 2 Medals
Mathematics

RolyPoly:
Group Title
Show that (p↔q) ⇔ (¬p↔¬q) without using the truth table.
 updated one year ago
 9 replies
 1 Medal
Mathematics

RolyPoly:
Group Title
Can we treat p↔q and ¬(p⊕q) the same thing? They actually share the same truth value, but it just seems a little strange.
 updated one year ago
 10 replies
 No Medals Yet
Mathematics

RolyPoly:
Group Title
\[f(x) =\begin{cases}\frac{xy}{\sqrt{x^2+y^2}} & (x,y)\ne 0 \\0 & (x,y) = 0\end{cases}\]
a) Determine if f is differentiable at (0,0)
b) det…
 updated one year ago
 53 replies
 2 Medals
Mathematics

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