Would it make sense to think about the bounds of integration as the level sets of the function? As in, I need to integrate from the c=5 level set to the c=0 level set (since the c=0 level set gives the maximum value for the function)?
And then to use that as the bounds for the double integral?
But I thought that since it is a two variable function that it would have to be a double integral. (Also we haven't covered triple integrals in class yet so I don't think he'd assign a problem like that on the homework)
Homework Statement
(exact wording from my homework set) Set up an iterated integral for the volume of the region which is above the plane z=5 and below the graph of f(x,y)=21-(x^2+y^2)^2. Pay attention to what the region of integration should be!
Homework Equations
Not sure.
The...
Homework Statement
The total intensity I(T) radiated from a blackbody (at all wavelengths λ) is equal to the integral over all wavelengths, 0 < λ < ∞, of the Planck distribution (4.28). (a) By changing variables to x = hc/λkBT, show that ¡(T) has the form I(T) = σT4 where a is a constant...
Wait so could the answer be related to the ratio of the densities? The weight over weight portion of the equation, when I compute it, will just end up being a constant with the information I am given, so could that mean that the density of the air in the envelope has to be greater than the...
Homework Statement
Hot air balloons use a burner (typically around 2 MW of power output) to heat the air in
the envelope (the balloon part of the hot air balloon). Consider a typical envelope with a
volume of V = 2800 m3. The weight of the balloon (envelope, basket and passengers, but not...
As a follow up to let everyone know: I didn't receive the position and the interview mainly focused on OSHA and other safety standards that I was unfamiliar with and couldn't have truly prepared for unless I had known that it was going to be incorporated as a larger chunk of importance of the...
Thanks :) I understand that you wouldn't know what exactly will be asked but it helps to have ideas. Probably should have posted a small exerpt of the duties summery to give a better idea too.
This is a list from the job description of duties I will be required to perform.
1. Set up and...
Ok so I have my AA in General Studies, Science Emphasis and I applied for and have scheduled an interview for a job entitled Science Lab Tech out at my local community college where I graduated.
I know the interview will be with a commity and I have been told that I won't be able to fake any...
I am attempting to get back into the academic world of physics. I have my associates degree and cannot continue taking classes with financial aid through my local community college. It won't be until the fall semester until I can attend a university so for now I would like to learn on my own...
I just found a sheet with a few calc problems at my tutoring job and its been months since I did any calc so I decided to brush up a bit and test how much i remembered. Obviously not much all things considered but you've refreshed my memory. Thanks :)
Homework Statement
Intergrate:
\int\frac{3 dx}{\left(2-x\right)^{2}}
By substituion.
Homework Equations
n/a
The Attempt at a Solution
Ok so first I take the integer out to get:
3\cdot\int\frac{dx}{\left(2-x\right)^{2}}
Now I let u = 2 - x and du = dx to get...
Boy@n: I understand and agree with your points. I think you are right. I think that human collective evolutionary awareness must be developed to a more advanced level in order to alleviate suffering at the hands of other humans. Humanity as a species must become more enlightened.
However, I...
What I am trying to get at is that all nations have one very powerful trait in common: homo sapien. We are all human. What difference does it make if one person hails from longitude 51 deg 34' 11" latitude 35 deg 25' 13" or if another person comes from Pahrump, Nevada? What difference does it...
Why do humans categorically analyze situations with other humans with the mentality of “us against them?”
I ask this question because to me much of humanities strife and suffering has been at the hands of other humans. For example the recent case of the Floridian ministers plans to...
Oh bloody hell. :mad: G**d*** m*****f****** piece of s*** integral... grrrr.
Thank you for your help jav. I truly appreciate it. Now I must bang my head against a brick wall somemore :smile:
I have no idea what I am doing wrong. I keep getting one when I should be getting two. It is part of a numerical integration problem. I've got the numerical integration part down which is ironic. The part I am having problems with is finding the actual value of the integral. I need this to find...
Homework Statement
y=sec^{-1}\frac{1}{t}, 0<t<1
Homework Equations
\frac{d}{dx}sec^{-1} x= \frac{1}{\left|x\right|\cdot\sqrt{x^{2}-1}}
The Attempt at a Solution
Basically to simplify things I used u substitution so I let u=1/t then du/dt=-1/t2 and I got:
y=sec^{-1}u\rightarrow...
Homework Statement
\int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}}
Homework Equations
Let u=lnx
du=\frac{1}{x}dx
x=2 \rightarrow u=ln2
x=4 \rightarrow u=ln4
The Attempt at a Solution
so with the u substitution we have:
\int^{ln4}_{ln2} \frac{1}{u^{2}}du
which goes to...
Ok I understand the whole dividing the two equations part but I am stuck trying to solve for the general equation. This is what I have:
\frac{v_{1}-\acute{v_{1}}}{v_{1}^{2}-\acute{v_{1}^{2}}}=\frac{v_{2}-\acute{v_{2}}}{v_{2}^{2}-\acute{v_{2}^{2}}}
I am not sure where to go from here. I...
Homework Statement
I am basically being asked to use the law of conservation of momentum and kinetic energy to derive two equations for the final velocity of the two masses involved in the system. (i.e. \acute{v_{1}} and \acute{v_{2}})
Homework Equations
Conservation of Momentum...
Nevermind, got the answer :D
Homework Statement
I need to prove using mathematical induction that:
\sum^{n}_{i=1} i^{3}= 1^{3}+2^{3}+3^{3}+...+n^{3}=\left[\frac{(n+1)\cdot n}{2}\right]^{2}
Homework Equations
\sum^{n}_{i=1} i^{3}= 1^{3}+2^{3}+3^{3}+...+n^{3}=\left[\frac{(n+1)\cdot...
I think it will open up many doors for me. Honestly, I don't know how I am going to get in, if it will be through U of A ROTC or if I will go through their Officer Trainning School. But reguardless, if I do end up going in I will most likely go career for the AFRL. I am thinking that if I go to...
I am thinking about going into the Air Force ROTC program at University of Arizona if I can get accepted. Hints, tips, ideas, opinions, words of praise?
I would throw politicians and their political parties in a black hole. I am sick of people being party line without looking at the ideals that these people promote. [/rant]
Wait, the force isn't constant. The friction force is constant. The net force is not. This is because the friction force is lowering the magnitude of the net force as the motion proceeds within the system. I am not sure how to express this mathematically, possibly
F_{net}=F_{final}-F_{initial}...
Honestly, you got me. Are you taking the 30 degree angle into equation? They gave it for a reason although right now I can't for the life of me figure it out.
Draw a free body diagram and all of the relevant forces.
Friction is constantly opposing the motion and slowing down your system. You have to take that into effect.
I might try a=F(net)\m for your kinematics equations. Remember for F(net) to include friction force.
Homework Statement
The mass of block a or Ma is equal to 3.00 kg and the mass of block b or Mb is equal to 1.50 kg. The two blocks are connected by a string and are sitting on an incline of 38\circ with block b being the higher on the incline than block a. The string between them is taut. I...
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. :)
Homework Statement
I need to find the derivative of:
y=\left(4x+3\right)^{4}\cdot\left(x+1\right)^{-3}
Homework Equations
Chain Rule
Quotient or Product Rule
The Attempt at a Solution
So I tried to use quotient rule because...
Awesome. So going by what you said Dick, I figured out that I messed up by putting that h in the numerator (slopy fraction solving :) ) I worked it out and got the right answer. Thanks for your help Dick.
Homework Statement
This is the larger problem to the small portion that I already posted in the Precalc Hw help forum. I still can't figure out how to get to the answer.
The problem is this:
I am trying to find the derivative of f(x)=x+\frac{9}{x}.
Homework Equations
I know via power...
Ahhhhh, I see said the blind man to the deaf dog with no ears. Thank you!
Btw how did you figure out that that's what I was trying to do? That was pretty amazing. :D
Homework Statement
I am supposed to find the first and second order derivative of
p=\left(\frac{q^{2}+3}{12q}\right)\left(\frac{q^{4}-1}{q^{3}}\right)
Homework Equations
Derivation Sum and Difference as well as Product and Quotient Rules
The Attempt at a Solution
I tried to cross...
Homework Statement
I am trying to figure out of \frac{9}{x+h} can be split into some thing like
\frac{9}{x} + ?
Homework Equations
None
The Attempt at a Solution
I am not sure what to do. I am trying to do this as part of a larger limits problem.
Homework Statement
I have to find the tangent to the curve the given point \left(-2,-8\right) for the equation y=x^{3}.
Homework Equations
f(x)=\lim_{h\rightarrow0} \frac{f(x+h)-f(x)}{h}
The Attempt at a Solution
I started the normal way of substitution:
\lim_{h\rightarrow0}...
Homework Statement
All the problem is asking me to do is find the limit. I have to do it algebraicly too which sucks. I can't figure out how to do it.
\lim_{x\rightarrow0} \frac{\frac{1}{x+2}-\frac{1}{2}}{x}
Homework Equations
I am not sure really.
The Attempt at a Solution
One...
Ok, with my second time around taking calculus 1 I am finally beginning to understand the whole concept of the Precise definition of a limit. However, I hate them. Never before in my life have I had the feeling or a need to drink, smoke, drive at 100mph and kill someone all at the same time...