July 2014

Problem
A circle of radius r rolls along a horizontal line without skidding.

1. Find the equation traced by a point on the circumference of the circle.
2. Determine the length of one arc of the curve.
3. Calculate the area bounded by one arc of the curve and the horizontal line.

Problem 821
Find the moment of inertia about the indicated x-axis for the shaded area shown in Fig. P-821.
 

Problem 1
Show that the largest triangle of given perimeter is equilateral.
 

Let F be a function of several variables, say x, y, and z. In symbols,

The partial derivative of F with respect to x is denoted by

and can be found by differentiating f(x, y, z) in terms of x and treating the variables y and z as constants.
 

Problem 6
Eliminate the c₁ and c₂ from x = c₁ cos ωt + c₂ sin ωt. ω being a parameter not to be eliminated.
 

Problem 5
Eliminate A and B from x = A sin (ωt + B). ω being a parameter not to be eliminated.