Alattice point is a point whose coordinates are both integers. how many lattice points are on the boundary or inside the region bounded by the $x$-axis, the line $x=4$ and the curve $y=2\sqrt{x}$?

The chs baseball team was on the field and the batter popped the ball up. the equation b(t)=80t-16•16+3.5 represents the height of the ball above the ground in feet as a function of time in seconds. how long will the catcher have to get in position to catch the ball before it hits the ground? round to the nearest second

The midpoints of the sides of the large square are joined to form a smaller square. what is the area of the smaller square

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.