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bio website andrew-christianson.github.io
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visits member for 3 years
seen Sep 2 at 22:11

Oct
2
comment Rate of increase in the area of a square
@jordan is 2a, and the rate of change of a w.r.t. t is $\frac{da}{dt}$ so, the rate of change of the right hand side w.r.t. t is $2a\frac{da}{dt}$. This does follow from the chain rule, but I thought an English explanation might prove more useful to do.
Oct
2
comment Rate of increase in the area of a square
@jordan what do you mean "to use the chain rule". The equation $\frac{dP}{dt}=2a\frac{da}{dt}$ follows from this line of reasoning: The problem is phrased entirely in rates of change (both givens and the desired answer). So we need to move the equation for the area of a static sphere ($P = a^2$) into one with rates of change. Specifically, we're concerned with change relative to time (t). So, what's the rate of change of P relative to t? Merely $\frac{dP}{dt}$ by definition of the derivative. Whats the rate of change of $a^2$ relative to t? Well, the rate of change of $a^2$ w.r.t. to a
Oct
2
comment Rate of increase in the area of a square
@jordan there really are only three essential symbols in pedja's answer: $P$ , $a$ , and $t$. $P$ is the area of the square, $a$ is the side length, and $t$ is just your time variable. $dP$, for example, is just shorthand to say, "the change in P" However, that's pretty meaningless without knowing what P is changing relative to. So, we write $\frac{dP}{dt}$, meaning the change in P relative to the change in t. $\frac{da}{dt}$ follows a similar pattern Pedja's first step, then, is implicit differentiation of the area formula $P = a^2$. From there, everything is replaced by givens.
Oct
2
revised Rate of increase in the area of a square
spelling correction, clarity
Oct
2
suggested suggested edit on Rate of increase in the area of a square
Oct
1
revised Which loan type is cheapest?
clarity & grammar
Oct
1
suggested suggested edit on Which loan type is cheapest?
Oct
1
answered Equation of a rectangle
Sep
29
comment Calculating edge coordinates of arrowhead. (pretty basic trigonometry)
You're welcome, glad to help.
Sep
27
answered Calculating edge coordinates of arrowhead. (pretty basic trigonometry)
Sep
27
comment Combinatorics - Building strings with symbols from two alphabets
No worries. Just jumped out as a book problem.
Sep
27
awarded  Commentator
Sep
27
revised Economics formula
removing overzealous HW tag
Sep
27
suggested suggested edit on Economics formula
Sep
27
comment Economics formula
@anon I think you're right, I'll untag it as such. Got a bit over zealous. Chris if this is a homework problem, please retag it as such. Additionally, i think "1n" must mean natural log, they play into the calculation on elasticity. Chris should be the one to clarify, though.
Sep
27
comment Calculating edge coordinates of arrowhead. (pretty basic trigonometry)
I think @pic has the right idea. Alternatively, you could repharse the same problem as vector addition. Namely, have A to B be a vector, and create a vector each for the left and right edges of the arrow head. Given b, the angle of the body of the arrow from horizontal, the right would be <S*cos(b+pi+a) , S*sin(b+pi+a)> and the left <S*cos(b+pi-a) , S*sin(b+pi-a)>. C, then is V_AB + V_left and D is V_AB + V_right.
Sep
27
comment Combinatorics - Building strings with symbols from two alphabets
Welcome to math.SE! If this is a homework question, please tag it as such. Additionally, the community may be more willing to help if you provide some context for the question and show your work up to the point you get stuck - it's easier to teach you how to do the problem than give you the answer.
Sep
27
comment Economics formula
Oh, and this is math.SE not econ.SE, so you may want to define elastic/inelastic in the question.
Sep
27
comment Economics formula
A few things. First, welcome to math.SE! I tagged this as homework as that's how the question reads. HW questions are fine, but if it's not, feel free to retag. Second, the community here is more than willing to help you learn, but not to just give you the answers. If you provide some more context and offer an explication of your work this far, people we be much more willing to help. Thirdly, I left you '1n' in paraens in your equation because I'm not sure what you're referring to. Any additional information w.r.t to that part of equation will be helpful.
Sep
27
revised Economics formula
Typeset, tag