Recent content by SEngstrom

Hmm simplest kind of math... Maybe first consider the special case when A and B are orthogonal (at right angles) so that A=ax, B=by, where x and y are orthogonal unit vectors. Then the original equations become a+b=2, a^2+b^2=2, since the length of the combined vector A+B is simply given by...

Express one variable in terms of the other (see which makes most sense). What are the conditions for having integer solutions?

If you let the axis of the ellipse be (a,b,c) and the cuboid have the size (2x,2y,z) - the point of contact is defined by (x/a)^2+(y/b)^2+(z/c)^2=1 Maximize x*y*z with this constraint. (x,y)=(0,36) would have zero volume so, no, that is not a maximum, local or otherwise.

Looks like the OP edited it and deleted it by mistake...

If you assume the cuboid's lateral dimensions to be (x,y), the point of contact at (x,y,z) with the ellipsoid will give you its height. Then given the various constraints you have - find (x,y) that maximizes the volume... There will be several points at the ends of these intervals that could be...

You don't need to find any minima - it's a matter of finding the interval that satisfies the bandwidth definition. For that you need to express things as real numbers, which is what the suggestion about spelling things out was about. Och, ja, jag är svensk :-)

Suggested starting point: define the bandwidth condition in terms of the given function, maybe in Mathematica code if that is the way you want to work this out. Spell it out - ambiguous (needs interpretation) as you present it.

The usual assumption about springs is that the force exerted by them is indeed linear (as in #2 above). All your solution needs is units. (Not all information given in the problem is necessary to solve it.)

All computer languages I can think of need boolean algebra to function, I wouldn't say it forms a basis. It is a way to write instructions to a computer - to perform a calculation; draw something; tell a device connected to it do something (output), possibly dependent on another device connected...

There is no difference except a little bit of connotation perhaps. The voltage between two points in a circuit is the same as the voltage drop between those points. To me, the latter expression has a verbal hint that the difference in voltage is driving a current (say, through a resistive...

I think that being careful when you do the work is a skill, and as such it is something you can practice consciously. Practice problems that require this kind of precision when it is not counting against your grade - and try to focus on the aspect you need to improve on. The other thing you can...

If it is a real-life example it may be worth bringing up the inadequate sampling employed to determine the fault rate for those pills...

Assume that the statement you have is true. Now add another term (do the sum to N instead of N-1). Add that term to the RHS and see if you can reshape that expression to the same form as it is now, only with N*(N+1)*(N+2)/3 instead. If you can, it must hold true for all N from there on. Then it...

First off - if 512 capsules were tested and only one was found OW that does not give a lot of confidence in the estimate of the OW rate... but that is not your problem I suspect. It seems the problem formulation is a little bit deceptive. The most reasonable way to view the "drawing of the...

To take the example of a steady circular orbit (e.g. Earth around the Sun) - the Earth is held in the orbit by acceleration that is directed towards the Sun but has a constant amplitude. The velocity vector changes but again its amplitude is constant. Since you only have to provide one...