Homework Statement
Prove or disprove: Every translation is a product of two non-involutory rotations.
Homework EquationsThe Attempt at a Solution :[/B]
I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...
Yes, I know how to prove the third condition. ai=b-1/n as a goes to infinity. But what about the second condition? how should I prove that Ac is an event? Ac=[b, infinity)
Homework Statement
Suppose that the sample space is the set of all real numbers and that every interval of the form (-infinity, b] for any real number b is an event. Show that for any real number b (-infinity, b) must also be an event.
The Attempt at a Solution
use the 3 conditions required...
is the horizontal asymptote correct? is there any other horizontal asymptote that I am missing? I got a graph like this, but I'm not sure if it is correct
when x=-1 arctan is undefined but as x approaches x=-1 (x-1)/(x+1) approaches negative infinity and positive infinity from left and right. Let (x-1)/(x+1) = t, then arctan(t) approaches pi/2 and -pi/2 as t approaches the two infinity is this correct? then there is no vertical asymptote?
I think the limit of arctan((x-1)/(x+1)) as x approaches -1 from the right is pi/2 and as x approaches -1 from the left is -pi/2, which means there is no vertical asymptote here but a jump discontinuity here right?
I am so far able to find the domain, intercepts, concavity and increase/decrease. But I am stuck at finding the asymptotes for the graph.
I think there is no vertical asymptote or is there one at x=-1?
I think the horizontal asymptote is y=pi/4
Homework Statement
A sample containing 3.65 mol of a monatomic ideal gas is heated from 289K to 458K, and the entropy remains constant. If the initial volume of the sample was 0.0980m^2, by what factor did the pressure increase or decrease during this process?
Homework EquationsThe Attempt at...
Homework Statement
Two moles of an ideal gas undergo a reversible isothermal expansion from 3.37×10−2m3 to 4.29×10−2m3 at a temperature of 29.6 ∘C.
What is the change in entropy ΔS of the gas?
Homework Equations
pV=nRT
The Attempt at a Solution
W=∫V2V1pdV,
I don't know how to use this...