Recent content by zhuyilun

Homework Statement if f has a continuous partial derivatives on R^3 and c is any circle ,then the integral of gradient f dot dr over c is zero integral of f(x,y) ds over -c= - integral of f(x,y) ds over c Homework Equations The Attempt at a Solution if the condition is not...

Homework Statement A uniform rod of mass 2.90×10^−2 kg and length 0.410m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.160 kg, are mounted so that they can slide along the rod. They are initially held by...

hi, i think i kinda get it. but i don't get where the extra u( infront of f(u)) come from

i think i didnt type the question correctly, its supposed to be a double integral of f(x+y) over the region R and that value is equal to a single integral of u*f(u) du from u=0 to u=1

Homework Statement let f be continuous on [0,1] and let R be triangular region with vertices (0,0),(1,0) and (0,1) show that\int\intf(x+y) dA= \intu*f(u)du from 0 to 1 Homework Equations The Attempt at a Solution i don't know how to start this question. can anyone give me a hint...

i get this part now~! thanks, but what is the relationship between 8-shot burst and 1000 rounds per second

Homework Statement A soldier on a firing range fires an 8-shot burst from an assault weapon at a full automatic rate of 1000 rounds per minute. Each bullet has a mass of 7.49 g and a speed of 299 m/s relative to the ground as it leaves the barrel of the weapon. Homework Equations...

could you please explain it a little bit more?

Homework Statement if (2,1) is a critical point of f and fxx(2,1)fyy(2,1) < (fxy(2,1))^2 then f has a saddle point at (2,1) Homework Equations The Attempt at a Solution i think its right but it turns out to be wrong can someone tell me why?

Homework Statement bounded by x^2+y^2=r^2 and y^2 +z^2=r^2 i guess r is just a random constant Homework Equations The Attempt at a Solution i don't even have a clue of how to start this question

initially a has 0.5*(2)^2*3.5=7 j energy. i tried, but this is not the correct answer

Homework Statement Blocks a (mass 3.50 kg ) and b(mass 10.00 kg ) move on a frictionless, horizontal surface. Initially, block b is at rest and block a is moving toward it at 2.00 m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and...

i get it now, thank you so much

i) but doesn't fx and fy have to be continuous at (a,b)? iv) can you explain a little bit more about it, i still don't get it thank you

i am sorry, but what do you mean by " three coordinate planes". and can you explain a little bit more about how to find sides of the pyramid