3 years ago

Jim is running on a trail that is 5/4 of a mile long. So far he has run 2/3 of the trail. How many miles has he run so far?

1 answer:

7 0

You have to subtract 5/4 by 2/3 but in order to do that you must find a common denominator or least common multiple so the least common denominator of 4 and 3 is 12 so you have to multiply 4 by 3 and three by 4 to make both denominators 12 but you have to do the same thing on the top as you did the bottom so: 5/4*3= 15/12 and 2/3*4=8/12 Then 15/12-8/12 is 7/12 so Jim has to run 7/12 more

You might be interested in

14. Consider the function f(x, y) = yx^4 * e^x². Find fxyxyx (x, y).

Alex787 [66]

The second partial derivatives of $f$ exist everywhere in its domain. By Schwarz's theorem, the mixed second-order partials derivatives are equal:

$f_{xy} = f_{yx}$

Then

$f(x,y) = y x^4 e^{x^2} \\\\ \implies f_y = x^4 e^{x^2} \\\\ \implies f_{yx} = f_{xy} = g(x) \\\\ \implies f_{xyx} = g'(x) \\\\ \implies f_{xyxy} = 0 \\\\ \implies f_{xyxyx} = \boxed{0}$

We don't actually need to compute $g$ and $g'$ to know that they are both free of $y$ . So when we differentiate for a second time with respect to $y$ , the whole thing cancels out.