Differential Calculus

Find the dimensions of the largest circular cone that can be inscribed in a sphere of radius R.

Find the ratio of the altitude h to the base radius r of a right circular cylinder having the largest lateral surface area S, if the right circular cylinder is to be inscribed in a sphere of radius R.

please help
how to eliminate arbitrary constant where h is a parameter;
y=mx+h/m

Pasagot nga po ito pls..thanks

patulong namn po sa one sided limits

Help me for the solution of this problem:

What should be the maximum dimensions of a rectangular open box of a given volume V?

Geometrical Application

Find the eq. of the curve such that the x-intercept of the tangent line at any pt. (x, y) on it divided by the square of the ordinate is a constant.

A student club on a college charges monthly membership dues of P10, less 5 centavos for each member over 60. How many members would give the club, the most revenue from the monthly dues?

pls help me to solve this problems as well as the solution:

1. a large window consist of a rectangle with an equilateral triangle resting on its top. if the perimeter P of the window is fixed at 33 ft, find the dimension of the triangle that will maximize the area of the window.

2. A student club on a college charges monthly membership dues of P10, less 5 centavos for each member over 60. How many members would give the club, the most revenue from the monthly dues?