The Purplemath Forums

Would someone please outline the steps for this question, but without actually answering it? A vet designs a special diet for a cat. This diet requires that the cat be allowed no more than 1500 calories, but at least 400 g protein. The vet can special-order the animal's food, but would prefer instea...

Yes, that made plenty of sense. Thank you for your time.

A horse takes three steps to walk the same distance for which a pony takes four steps. Suppose that one step of the horse covers a half-metre. How many metres would the pony cover when taking twenty-four steps? I keep tying myself in knots, getting nowhere. Any ideas for an intelligent start on this...

Are there any sequences which are both arithmetic and geometric? I don't think so, but how would I prove this?

Use the set-up they show here: http://www.purplemath.com/modules/investmt.htm

-2 + 4y + 6 ------- ------- ----- LCD = (y+3) (y-3) (y-3) y^2 - 9 (y-3)^2 3-y -2 + 4y + 6 ---------- ---------- ------- (y+3)(y-3) (y-3)(y-3) -1(3-y) The denominator 3 - y is not equal to -1(3 - y); it is equal to -y + 3 = -y - (-3) = -(y - 3). Then you can put the negative on the 6.

With the equation 4(x-2)(x+6) , how would I determine the coordinates of the vertex ? One way is to multiply out the two factors (not the 4) and then use the formula they give here . A "cheat" way is to remember that the vertex is midway between the two x-intercepts. So use the two factor...

Do the graph of the quadratic. Anywhere it's below the axis is negative, so re-draw that part upside-down so it's above the axis. Solve x^2-1=0 to find where the original graph crosses the axis and where the new graph touches. Where x^2-1 was positive anyway, solve x^2-1<2. Where x^2-1 was negative ...

What did you get when you did the cross-multiplication and compared the results?

u = -28.593*ln(k) + 144.76 The object is to empirically define "c" and "j" in the following equation by back substitution: u = c*ln(j/k) ; only valid where k approaches j You can use log rules to take the multiplier out front of the logarithmic term inside as an exponent. Then y...