MATHalino

Problem 01
A 5-m line AD intersect at 90° to line BC at D so that BD is 2 m and DC = 3 m. Point P is located somewhere on AD. The total length of the cables linking P to points A, B, and C is minimized. How far is P from A?
 

Problem 859
Determine the value of EIδ under P in Fig. P-859. What is the result if P is replaced by a clockwise couple M?
 

Problem
Chords AB and AC are drawn on a circle of radius 10 inches. Find the angle between the chords if the arc BAC is 28 inches long.
 

Problem 01
Determine the equation of the curve such that the sum of the distances of any point of the curve from two points whose coordinates are (–3, 0) and (3, 0) is always equal to 8.
 

Problem 02
A bullet is fired at an initial velocity of 150 m/s and an angle of 56° at the top of a 120 m tall building. Neglecting air resistance, determine the following:

1. The maximum height above the level ground that can be reached by the bullet.
2. The time for the bullet to hit the ground.
3. The velocity with which the bullet will hit the ground.

Moment distribution is based on the method of successive approximation developed by Hardy Cross (1885–1959) in his stay at the University of Illinois at Urbana-Champaign (UIUC). This method is applicable to all types of rigid frame analysis.
 

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.