Write and then solve the differential equation for the statement: "the rate of change of y with respect to x is inversely proportional to the square root of y."

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.

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.

Suppose you are choosing a 6-digit personal access code. this code is made up of 4 digits chosen from 1 to 9, followed by 2 letters chosen from a to z. any of these digits or letters can be repeated. find the total number of personal access codes that can be formed. 492,804 341,172 39,917,124 4,435,236