Hi,
Let W be the sum of all the people's weights, let P be the total number of pizza slices available.
If:
I have P slices of pizza (P<=W)
I have n people I want to split the pizza with
I want to use people's weight to determine how many slices they get (more weight -> more slices)
I don't...
I'm trying to build a home aquaponics system, and a key component of the design I got off the internet is a bell siphon. So I'm trying to understand the physics of this siphon effect so I can optimize the weight and dimensions of the siphon to fit the size of my system.
From what I read on the...
I have an electric motor that I am using to turn an auger to dispense pet food. I want to measure the average torque required to turn this auger at a given rpm.
I know Powerin = Voltage into motor * Current into motor
and Powerout = Torque exerted by shaft * RPM of auger
and Powerout...
I was inspired by this article
http://science.howstuffworks.com/environmental/green-science/house-music-energy-crisis1.htm
to wonder if one could put piezoelectric crystals in the sole of a shoe and perhaps harness the energy to charge their iPod?
Can someone let me know if this is feasible...
Homework Statement
Calculate the attractive force between a pair of Cu2+ and O2- ions in the ceramic CuO that has an interatomic separation of 200pm.
Homework Equations
E_A= -\frac{(z_1\cdot e)(z_2\cdot e)}{4\pi\cdot\epsilon_o\cdot r}
Where z_1 and z_2 are the valences of the two ion...
Homework Statement
Zinc has a density of 7.17 Mg/m^3. Calculate (a) the number of Zn atoms per cm^3, (b) the mass of a single Zn atom and (c) the atomic volume of Zn.
Homework Equations
atomic mass of zinc = 65.39 g/mol
The Attempt at a Solution
For part (a) I use the fact that...
Homework Statement
Find the energy of a He+ electron going form the n=4 state to the n=2 state.
Homework Equations
E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}
Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level.
^ I think those are...
Homework Statement
Using the Bohr model of the atom, compute the energy in eV of the one electron in Li2+.
Homework Equations
E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2}
Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level.
^ I think...
Homework Statement
A particle oscillates with amplitude A in a one-dimensional potential that is symmetric about x=0. Meaning U(x)=U(-x)
First find velocity at displacement x in terms of U(A), U(x), and m.
Then show that the period is given by ##4\sqrt{\frac{m}{2U(A)}}\int_0^A...
The definition given is...
"Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group ##G/K## is the group whose elements are the fibers (sets of elements projecting to single elements of H) with group operation defined above: namely if ##X## is the fiber above...
Homework Statement
If ##I## is a proper Ideal in a commutative ring ##R##, then ##R## has a subring isomorphic to ##\frac{R}{I}##.
Book says false...
Homework Equations
##I## being a proper ideal in ##R## means ##I## is a proper subset of ##R## where
(i) if ##a,b\in{R}## then ##a+b\in{R}##...
Homework Statement
Let ##R## be a PID and let ##\pi\in{R}## be an irreducible element. If ##B\in{R}## and ##\pi\not{|}B##, prove ##\pi## and ##B## are relatively prime.
Homework Equations
##\pi## being irreducible means for any ##a,b\in{R}## such that ##ab=\pi##, one of #a# and #b# must be...
Homework Statement
True or False?
Let R and S be two isomorphic commutative rings (S=/={0}). Then any ring homomorphism from R to S is an isomorphism.
Homework Equations
R being a commutative ring means it's an abelian group under addition, and has the following additional properties...
Homework Statement
If R=\mathbb{Q}[\sqrt{2}], then Frac(R)=\mathbb{R}
Homework Equations
\mathbb{Q}[\sqrt{2}]=\{a+b\sqrt{2} | a,b\in{\mathbb{Q}}\}
Frac(R) is the fraction field of R is basically \{\frac{a+b\sqrt{2}}{c+d\sqrt{2}} | a,b,c,d\in{\mathbb{Q}}\}.
The Attempt at a Solution
Back...
I can't decide if I want to pursue a PhD in math or not.
I like the idea because it would let me keep studying math (interesting), and the challenge would help show me what I am capable of (intellectual potential).
But I can't help but wonder if I would be happier if I changed my major to...
Homework Statement
Show there exists a function f: \mathbb{R} \rightarrow \mathbb{R} s.t. f^2=f but f\neq{0,1}.
Homework Equations
Here f^2=f means for arbitrary a\in{\mathbb{R}}, f(a)^2=f(a)
The Attempt at a Solution
I came up with the function f(a)= \begin{cases}
0, & \text{if }a\text{>...
Homework Statement
Prove that every real number x in [0,1] has a decimal expansion.
Homework Equations
Let x\in{[0,1]}, then the decimal expansion for x is an infinite sequence (k_{i})^{\infty}_{i=1} such that for all i, k_i is an integer between 0 and 9 and such that...
Homework Statement
Are all subgroups of a cyclic group cyclic themselves?
Homework Equations
G being cyclic means there exists an element g in G such that <g>=G, meaning we can obtain the whole group G by raising g to powers.
The Attempt at a Solution
Let's look at an arbitrary...
Homework Statement
Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root.
Homework Equations
G being a group means it is a set with operation * satisfying...
Homework Statement
True or False? Every infinite group has an element of infinite order.
Homework Equations
A group is a set G along with an operation * such that
if a,b,c \in G then
(a*b)*c=a*(b*c)
there exists an e in G such that a*e=a
for every a in G there exists an a' such...
I was wondering what are the main types of "applied math" I could choose to study in grad school and how I can know which one I would enjoy most?
Math Classes I loved were:
linear algebra, number theory, intro to real analysis, discrete math, intro to abstract alg
Classes I disliked...
Homework Statement
\frac{d^2 y}{dx^2}\cdot\frac{dy}{dx}=x(x+1), \hspace{10pt} y(0)=1, \hspace{5pt} y'(0)=2
Homework Equations
None I can think of...
The Attempt at a Solution
The only thing I even thought to try was turn it into the form:
\frac{d^2 y}{dx^2}{dy}=x(x+1){dx}...