MATHalino

Problem 861
For the beam shown in Fig. P-861, determine the value of EIδ at 2 m and 4 m from the left support.
 

Problem 860
Determine the value of EIδ at the end of the overhang and midway between the supports for the beam shown in Fig. P-860.
 

In Polar Coordinate System, the references are a fixed point and a fixed line. The fixed point is called the pole and the fixed line is called the polar axis. The location of a point is expressed according to its distance from the pole and its angle from the polar axis. The distance is denoted by r and the angle by θ.

Problem
The line y = 2x + 8 intersects the parabola y = x² at points A and B. Point C is on the parabolic arc AOB where O is the origin. Locate C to maximize the area of the triangle ABC.
 

Problem
A goat is tied outside a silo of radius 10 m by a rope just long enough for the goat to reach the opposite side of the silo. Find the area available for grazing by the goat. Note that the goat may not enter the silo.
 

Problem
What is the perimeter of the curve r = 4(1 + sin θ)?
 

The answer is 32 units. For detailed solution, follow the link by clicking on the figure.
 

The length of arc in polar plane is given by the formula:

The formula above is derived in two ways.
 

The length of arc in rectangular coordinates is given by the following formulas:

See the derivations here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-xy-plane-...
 

Problem
An airplane flew from Davao City whose latitude is 14° N and longitude of 121.5° E on a course of S 30° W and maintaining uniform altitude. At what longitude will the plane cross the equator?
A. 110° 30' East
B. 122° 26' East
C. 113° 33' East
D. 116° 11' East
 

Problem
Gas is escaping from a spherical balloon at the rate of 2 cm³/min. Find the rate at which the surface area is decreasing, in cm²/min, when the radius is 8 cm..