Recent content by johnhuntsman

Homework Statement Find the critical points of f. f(x,y)=2+\sqrt{3(x-1)^2+4(y+1)^2}Homework Equations For fx(x,y) I get: f_x(x,y)=0+\frac{1*6(x-1)}{2\sqrt{3(x-1)^2+4(y+1)^2}}=\frac{3(x-1)}{\sqrt{3(x-1)^2+4(y+1)^2}} For fy(x,y) I get...

Alright then. I gotcha. Thanks, I do appreciate it.

I can see that it converges to π / 4, and I can prove it be substituting some things and simplifying it that way. But I don't understand why they can just at the very beginning of the problem rewrite it in that way from the get go.

I used Wolfram Alpha to evaluate: lim tan[(2nπ)/(1 + 8n)] n->infinity it says that it can use the continuity of tan(n) at n = π / 4 to rewrite the aforementioned function as: tan[lim ((2nπ)/(1 + 8n))] n->infinity What is it talking about? I was taught to use certain properties of trig...

My teacher did say not to take change in original fluid level into account, but I gotcha. Thanks, I appreciate it.

Nevermind I suppose it'd be the other way around. Fluid would be sucked in (as air would be) because the pressure in the mouth is less. So that leaves me at a complete loss as far as what the answer is concerned. Would it be patm - ρgh? ρgh being the change in pressure necessary to bring up...

Shouldn't it be atmospheric pressure? I would imagine there'd be more. I suppose p = patm + ρgh should've been the answer then?

There was a question on a quiz I just took and I want to make sure I got it right. Something like: "A beaker filled with to 2/3 its height with a fluid of density ρ = 1500kg / m3. You place a straw in the fluid such that the fluid in the straw is at a height equal to that of the fluid prior to...

Ah. My bad. I was assuming for some reason that it wasn't fired straight up. And yeah, I just wish it said split or something rather than "explodes". Anyway, I appreciate the help : D

"After a shell explodes at the top of its trajectory, the center of gravity of the fragments has an acceleration, in the absence of air resistance, equal to g and downward." Why isn't there an x-component? I get why there would be a downward component with a = g, but shouldn't there at...

The manager of a fast food restaurant determines that the average time that her customers wait for their food is 2.5 minutes. The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. She doesn't want to give away free hamburgers to...

Alright thanks. I appreciate it.

So what you're saying is that w is to 40ft what 9 - x is to 6ft? Or rather, "what width of small triangle is to width of large triangle, height of small triangle is to height of large triangle."

How'd you get that? [Edit] Or perhaps more importantly, does that get you to 4.88E4 lbs.? [Edit]

A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 3 ft and the deep end, 9 ft. If the pool is full of water, estimate the force on one of the sides. They mean one of the trapezoidal sides, not the rectangular ones. Anyway, I've...