Homework Statement
See the document attached as it contains a diagram
Homework Equations
cos(theta) = adjacent/hypotenuse, sin(theta) = opposite/hypotenuse, tan(theta) = opposite/adjacent
The Attempt at a Solution
See document attached
Stephen, yes integration along AD is what I am asking about. SteamKing, I did notice that there was no change in y coordinate. However, why would the curve integral be 0 (as the answers say)? It makes no sense as some force is used to move the particle from A to D so it cannot be 0?
Im doing some revision of vector calculus and came across the following problem
Q: Calculate the work done by the force field F = 3xyi - 2j in moving from A: (1,0,0) to D: (2,0,0) and then from D: (2,0,0) to B: (2,sqrt(3),0)
I got stuck and decided to look at the answers. In the answers (part...
Im trying to find the integral of ( sec(t)^2 ) / ( (tan(t)^3) + (tan(t)^2) ). I've managed to get the
integral into the form
1 / (u^3 + u^2) where u = tan(t), however I am having difficulty proceeeding from there.
Could someone take a look at the working out I have attached and let me...
For this function
y=\sqrt{2ln(x)+1}
if I use the chain rule properly, should I be getting this answer?
\frac{dy}{dx}=\frac{2}{x} \times \frac{1}{2} \times \frac{1}{\sqrt{2ln(x)+1}}
My aim of doing this is to verify that
\frac{dy}{dx}=\frac{1}{xy}
To the original poster, I would say invest some time looking into the job market
and any astrophysics or science societies before deciding to change degrees.
I was interested in wireless communications during my undergrad degree, but job prospects
were quite low, so I am now studying to...
For the following problem
\frac{dw}{d\theta}=\theta w^{2}sin(\theta^{2}), w(0)=1
I am not able to obtain the solution
w=\frac{2}{1+cos(\theta^{2})}
Can anyone point out my mistake?
I have attached my working out in a picture format below (may need to enlarge it)
thanks
Is the following statement valid?
sinh{x^2}=\frac{e^{x^2}-e^{x^2}}{2}
Reason I ask cause I know that sinh{x}=\frac{e^{x}-e^{x}}{2}, so i assume the same rules can apply
For a normal distribution with E[x]=0 and Var(X)=1, how do we determine the Z-value of a particular percentage ?
i.e. if the percentage is 5%, how do we know that Z(5%)= 1.645 ?
is there a calculation involved or do we get it from observing the x-axis of the normal distribution ?
Homework Statement
Given the following defined transformation
T(a + bt+ct^{2}) = (a+c) - (c+b)t + (a+b+c)t^{2}
find the matrix with respect to the standard basis
From my understanding, the standard basis for a 3 element vector would
be
(0,0,1)^{T} (0,1,0)^{T}...