Let w(s, t) = f(u(s, t), v(s, where f, u, and v are differentiable, and the following applies. u(3, 7) = 5 v(3, 7) = −5 us(3, 7) = −1 vs(3, 7) = −7 ut(3, 7) = 4 vt(3, 7) = −4 fu(5, −5) = −9 fv(5, −5) = −3 find ws(3, 7) and wt(3, 7). ws(3, 7) = wt(3, 7) =

Look at this pattern ; 1,4,9, number 10000 belongs in this pattern . what’s the place of this number?

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.