Composition Definition and 374 Threads

I'm planning to plot phase diagrams of Temperature vs Composition. I found the formula ln(x) = \frac{\Delta H}{R} (\frac{1}{T_A} - \frac{1}{T}) from the Clapeyron equation. Its a ideal solution of 2 metals in L state and regular solution in S state. Eutectic temperature is at 850C and enthalpy...

Homework Statement A fuel has the following composition on a molar basis: 40.0% CH4, 24.0% C2H4, 16% C3H8, 10% CO2, 10% H2O. What is the composition of the fuel on a dry basis? What is the composition of the fuel on a mass basis? What is the average molecular weight of the fuel? [Relative...

the composition of ozone is O3 and the oxygen O2 present in atmosphere.considering the masses of O3 and O2 , the O3 is more heavier than O2 then also ozone is situated above the oxygen (O2) present in atmosphere. why is it so? advanced thanks.

Is it always true that the domain of f(g(x)) is the intersection of the domains of f(x) and g(x)? I've been having trouble with this and this answer would make me fully understand this concept. Thanks to everyone!

Homework Statement I have a problem with the next exercise: Given de function f(x,y)=\begin{Bmatrix} \displaystyle\frac{xy^2}{x^2+y^2} & \mbox{ if }& (x,y)\neq{(0,0)}\\0 & \mbox{if}& (x,y)=(0,0)\end{matrix} with \vec{g}(t)=\begin{Bmatrix} x=at \\y=bt \end{matrix},t\in{\mathbb{R}} a) Find...

Homework Statement A certain metal hydroxide, M(OH)2, contains 32.8% oxygen by mass. What is the identity of the metal M? Homework Equations O = 16.00 g x2 H = 1.008 g x2 The Attempt at a Solution I thought that 1g = 1% of the mass because there are 32g of O and it composed of...

Homework Statement 4.0 g of sulfur and 10.0 g of zinc are heated together, how much zinc will remain unreacted? Homework Equations The Attempt at a Solution If these two elements are heated together, wouldn't the total mass (g) be 14.0 by adding the amount of sulfur and zinc...

Homework Statement J represents a 3x2 matrix and H represents and 2x4 matrix. y = Hx and z = Jy, where y is a 2x1 matrix, z is a 3x1 matrix, and x is a 4x1 matrix. Form the composition J○H and simplify z = J○Hx. The Attempt at a Solution I don't know what my answer is going to look...

Homework Statement I have a question regarding how to compose 2 transformations, a rotation and a translation, of a linear algebra problem. Suppose we have a quadratic curve like the following one: (i) x^2 + y^4 - 6xy +2x -3y +6 = 0 We want to transform the above into its standard...

how to prove it please?

Can h(x)=(cos x)^x be written as a composition of two functions f and g where f(x)=x^n and g(x)=cosx ? where h=fog REASON FOR ASKING: I am wondering this in connect with a differentiation I was having trouble with (but can now solve thanks to this forum). I mistakenly thought that I could...

Hi. Is there a quick way of deriving the Galilean transformations from the Galilean composition formula for velocities? Cheers.

Homework Statement This is a problem from D'Inverno's "Introducing Einstein's Relativity". If vAB is the velocity of B with respect to A, vBC is the velocity of C with respect to B, and vAC is the velocity of C with respect to A (all velocities are in relativistic units, that is, c=1)...

Okay, so I see this pizza chart a lot on the web that points physical matter with mass making up 4.6% of all matter in the universe, followed by dark matter with 23% and dark energy with the rest. Where the heck did old fashion, normal energy go? is it not good enough to get it's own place...

Homework Statement Make [; f: A \rightarrow B ;], [; g: C \rightarrow D ;], [; h: E \rightarrow F ;] functions in which [; \text{Im} f \subseteq C;] and [; \text{Im} g \subseteq E;]. Show that [; f \circ ( g \circ h ) ;] and [; h \circ ( g \circ f ) ;] are valid if, and only if, [; f...

I was organizing pennies into categories based on what they were composed of; before 1982 (I believe) pennies were made out of 95% Cu, and after they were made primarily out of zinc. I thought that the ideal penny for a voltaic cell would use a Copper penny, and a Nickel. However, I found that...

Hello, I have been given the following problem and am hoping for some help... You have 1000 unlabeled gas cylinders, each are 0.25m3 and need to be able to identify the contents. They mostly contain oxygen and helium, but some contain xenon and uranium hexafluoride. You are given a scale...

Homework Statement Is the composition of two differentiable functions always differentiable? E.x. h(x) = sin(x) k(x) = 1/x for x not equal 0 Does this automatically mean h(k(x)) is differentiable? Thank you, M

Homework Statement Consider the following functions: Modified Dirichlet Function f(x) = 1/n if x=m/n of lowest forms, and f(x) = 0 if x is irrational find an integrable function g(x) such that the composition of g and f is NOT integrable The Attempt at a Solution Let g(x) = nx for all n in...

IS it possible? say if the specific heat is 800 and the composition is made up of 2 materials one which has specific heat of 850 and the other of 750

I will state here what I understand in this topic which I am a little confused: If I have 2 sinusoidal signals perfectly in phase, with distinct power levels, say -13dBm and -10dBm, the composition ("sum") of both signals is -8.23dBm. Or, for -10dBm and -10dBm signals, the sum is -7dBm...

Homework Statement Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is D_r \circ D_s? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.) Homework Equations Example 4.3.1...

Homework Statement I keep getting what I think is the "right answer", but it's not one of my choices :^( Here are the problems and answer choices. 1). 2). Homework Equations nothing really...or at least I don't think besides the fact that e^-x = 1/e^x The Attempt at a Solution 1). x + 14...

Hello, I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'(t)=floor(f(t)). I know that http://functions.wolfram.com/IntegerFunctions/Floor/22/04/" gives L(floor(t)) = (e^(-s))/(s(1-e^(-s))) instead -- are these equivalent?) and L(f(t)) =...

Hello, I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'=floor(f(t)). I know that L(floor(t)) = (e^(-s))/(s(1-e^(-s))) and that L(f(t)) = F(t) (of course), but I realized that I have no idea how to take the Laplace transform of a...

Homework Statement how to show using MVT that cos(cos x) is a contraction. Homework Equations | d/dx (cos(cos x)) | = | sin(cos x) sin(x) | < sin 1 < 1 The Attempt at a Solution Using that relation, the original problem is easily solved. My question is, how do we know: |...

I've been looking at different math books that have analysis problems to get more perspectives on how to approach various analysis problems. I was following along in the "Derivatives" section of the book "Mathematical Thinking" by D'Angelo and West, second edition, and arrived at a lemma with...

If our solar system originated from the same dust / gas cloud, why do we see such differences in abundance of elements from one body to another. I can come up with two possible answers: 1. Rotation of cloud centrifuged heavier elements towards edge (Almost certainly not true, because it would...

Homework Statement (-3x^2-15x-12)(√5) Homework Equations Quadratic formula? The Attempt at a Solution hmm, i know how to solve the first set of bracets, but what do i do with the radical? how do i multiply it to the polynomial?

Homework Statement The substance CoBr3 dot 4 NH3 dot 2 H2O ha a molar conductivity of 42 kS/m at infinite dilution. Indicate the composition of the coordination sphere. Homework Equations I don't know any relevant equations. The Attempt at a Solution Where can we read about how...

[b] I'm in desperate need of some help. I am so lost on this: 1. imagine a rocket ship R moving eastward with speed v with respect to the Earth and a rocket ship S moving westward with speed −v with respect to the earth, we wish to know the speed of R with respect to S. a. Go to a reference...

Homework Statement f and g are differentiable functions that have the following properties: i. f(x) < 0 for all values of x ii. g(5) = 2 If h(x)= f(x) / g(x) and h'(x) = f '(x) / g(x), then g(x) = _____? Homework Equations Quotient Rule with f(x) and g(x) The Attempt at a...

I need to write a loop that iterates several times to find the limit of this function f(x) = 5x(-x+1) lim f^n(0.75) n-> For[n = 0, n < 5, n++, x=0.75; f[x_] := 5x(-x+1) ]; ] what am i doing wrong?

Homework Statement Suppose T is a rotation by 30 degrees about the point 2, and S is a rotation by 45 degrees about the point 4. What is T composed with S? Can you describe this transformation geometrically? Homework Equations none The Attempt at a Solution I know T composed with S...

Homework Statement Form the composition f o g o h and give the domain. f(x) = x - 1, g(x) = 4x, h(x) = x2 Homework Equations The Attempt at a Solution f(g(h(x))) = 4x2-1 The domain of x is any real number.

Homework Statement Does there exist a continuous function f: R -> R such that f'(f(x)) = x ? Homework Equations The Attempt at a Solution I was trying to find an example, but wasn't able to, and if I had to take a guess whether such a function exists or not, I'd say no. Here...

I am trying to find the chemical composition for basic, college chemistry lab quality thermite. I saw that it was a white/grey powder substance. Trying to figure out what the exact chemical composition might be. :)

% (by mass) composition Homework Statement Dopamine, C8 H11 O2 N is a neutroransmitter. Determine the percent (by mass) composition of each of the elements in dopamite.Homework Equations The Attempt at a Solution 8C atoms= 12 (12.0) = 44.0amu 11H atoms = 11 (1.0) = 11.0 amu 2O atoms = 2...

1. Show that the set {f:R-{0,1}\rightarrow [b]R-{0,1}}, of functions under composition, is isomorphic to S _{3} f_{1} = x f_{2} = 1 - x f_{3} = \frac {1}{x} f_{4} = 1 - \frac {1}{x} f_{5} = \frac {1}{1 - x} f_{6} = \frac {x}{x - 1} Homework Equations The Attempt at a Solution...

I have a homework problem as follows: Let f(x) = 2x, (-inf < x < inf). Can you think of functions g and h which satisfy the two equations g \circ f = 2gh and h \circ f = h^2 - g^2? I know that g \circ f = g(f(x)), which then = g(2x) for the first question. I can't figure out how to work...

Homework Statement Let A,B be sets and let f:A \rightarrow B and g,h:B \rightarrow A be functions. (1) Suppose h o f is an injective map from A to itself. Show that f is injective. (2) Suppose now that f o g = 1_{B} and hof = 1_{A}. Show that f is bijective and g=h. P.S. given that f...

My daughter, Evo Child, is a university student and an English tutor, (her university pays her to tutor other students). She's been tutoring since High School (honors English). She asked me if I thought anyone at PF would be interested in having help with their English. She will be glad to...

A = (0, infinity), B = C = D = R where R is all real numbers f: A->B, g: B->C, h: C->D f(x) = lnx, g(y) = 3y, h(z) = e^z h o g o f ? -------------------------------------------- For the following to be defined doesn't 1) range(f) ⊆ domain(g) 2) range(g o f) ⊆ domain(h) So g o f should be...

For the following to be defined doesn't 1) range(f) ⊆ domain(g) 2) range(g) ⊆ domain(h) Is that correct? So R ⊆ R for 1, and R ⊆ R for the other so it is ok? --- Second question: but how can you have the function h with the range of all real numbers when the exponential function only has a...

This website gives a break down of the ten most abundant elements from spectrum analysis of the sun http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961112a.html" Presumably this result is only valid for the surface/near surface of the sun. If there were any heavier elements present...

Homework Statement You are given a sample of cinnamon oil with some kerosene oil dissolved in it.Propose a method to determine atleast approximately the percentage of kerosene oil present in this sample,by volume. N.B. 1) you are provided with facilities for various types of distillation 2)...

Homework Statement An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO2 and 73.30 mL of H2O vapor at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl...

Homework Statement A = {0, 1, 2, 3} f and g are functions mapping A to A where f = {(0,1),(1,2),(2,0),(3,3)} and g = {(0,2),(1,3),(2,0),(3,1)} find (f o g)(1) Homework Equations The Attempt at a Solution The answer is 3 but i can not get it.. the (1) on the right side...

Homework Statement I am running an experiment in which I have a compound of SiO2 Na2 K2O PbO I am trying to figure out the percent composition of oxygen given that the percent composition of the compound is: 46% SiO2 5% Na2 4% K2O and 45% PbO Homework Equations 46% SiO2 5% Na2 4% K2O and...

I have been able to find lots of information about experiments that have been done to determine how different compositions of matter respond in a gravitaional field. However, I have not been able to find any information about experiments done to determine any difference in strength of the...