Drew Christianson
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 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 approved edit on Rate of increase in the area of a square Oct 1 revised Which loan type is cheapest? clarity & grammar Oct 1 suggested approved 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 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 and the left . 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 26 awarded Organizer Sep 26 revised What is the probability of getting 3 aces, a king and a queen latexify + tags Sep 26 suggested approved edit on What is the probability of getting 3 aces, a king and a queen Sep 25 comment Multiplying exponents by fractional exponents and whole numbers to the power of fractional exponents Why are you dividing the exponent by 2? Sep 24 revised Prove $n$ is composite when it divides $(n-1)!$ texifiy, clarify Sep 24 suggested approved edit on Prove $n$ is composite when it divides $(n-1)!$