Recent content by NoOne0507

I came up with this question while studying for an upcoming exam. I had a design problem, my solution gave me a gain of about 5500 with a PI compensator. Does having that high of a gain screw with my system? It gives me the desired results in MATLAB, but are there any drawbacks to doing that?

I was recently trying to prove the variation of parameters formula for an nth degree equation, and I have come up with a question about the assumptions made during the derivation. During the derivation we assume that: u1'y1(k) + u2'y2(k) + . . . + un'yn(k) = 0 for k < n-1. It leads to the...

Homework Statement I have two problems with this: 1) I am not sure if I am using the right constant. 2) I have no idea if my values are realistic. The actual question: The rate of a reaction is 25.00 units per time at 20.00°C. The activation energy barrier for this reaction is 1.50 eV. a)...

That makes sense. It struck me as odd that that was the way to solve it, but it was asking for power, and I couldn't figure out any other way to get a unit of power. Thanks.

Well this is the full question: The voltage v is a constant 10 volts and the current i is described by the following function: i(t) = (5t^2+20+6)/(t^3+2t^2+t) Amps What is the total power delivered between t=1s and t=5s? I figured since P is a function of time it would work since ∫ dP = ∫...

I'm really only concerned with the setup so I'm just going to ask it in a general sense, rather than the specific problem. Homework Statement Suppose you have a constant voltage and the current is described by i(t). Find the total power delivered between time A and time B. Homework...

If V is a vectorspace and v is a vector in V. will the projection of v onto V be v?

Okay. Makes sense, thanks.

Straightforward question for anyone who knows how calculators work.

T(x,y,z)=60(y^2 + z^2 - x^2) T(0,0,0) = 0 T(1,0,0) = -60 T(-1,0,0) = -60 T(0,y,z) = 60(y^2+z^2), but since this is along a circle T(0,y,z) = 60 Which gives the minimum at (1,0,0) and (-1,0,0), and the max at (0,y,z) where y^2+z^2=1. Okay, so from (almost) the beginning: λ = -60, x≠0...

Well if x=0 then the constraint becomes y^2+z^2=1, with λ=60. So would the maxima occur anywhere in the yz unit circle? Which would yield (0, y, ±√(1-y^2)) as the maxima? And then the smallest λ would occur at x≠0, and y=z=0? Which would give Minima on x: [-1,0) U (0,1] y=0 z=0 Or am...

But couldn't x be any value? For x ≠ 0, λ=-60. And then when x = 0 we get 0=0 with no λ. If you do that for all the values you can get x=y=z=0, plug into the constraint and get the center of the circle, with no value for λ. How would that help find the max and the min?

Homework Statement A cannonball is heated with with temperature distribution T(x,y,z)=60(y2+z2-x2). The cannonball is a sphere of 1 ft with it's center at the origin a) Where are the max and min temperatures in the cannonball, and where do they occur?Homework Equations \nablaf=λ\nablag Where...

I was trying to prove the derivatives of the inverse trig functions, but I ran into a problem when I tried doing it with arcsecant and arccosecant. So the general process is this: y = arcsec(x) sec(y) = x dy/dx * sec(y)tan(y) = 1 dy/dx = 1/[sex(y)tan(y)] sec(y) = x And for tan(y) we...

Homework Statement The question is what has gone wrong in this proof, it is worth noting this a definite integral between pi/6 and pi/4: ∫ tan(x) dx = ∫ sin(x)/cos(x) dx Let u = 1/cos(x) and dv = sin(x) dx So du= sec(x)tan(x) and v = -cos(x) When we substitute back in we get: ∫ tan(x)...