Video Discussion: MSTE-00 Problem Set 1

Problems in the Quiz are actually randomly ordered in every load. Hence, the order here may not be the same order in your end. The good thing here is that you can directly follow the question that you need the solution most.

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Video Solution	Problem
	The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.
	By the conditions of a will, the sum of P25,000 is left to a girl to be held in a trust fund by her guardian until it amounts to P45,000. When will the girl receive the money if the fund is invested at 8% compounded quarterly?
	Find the distance between foci of the conic $8x^2 + 9y^2 = 288$.
	Find the approximate amount of material in an open rectangular box whose inside measurements are 1.60 m long, 1.00 m wide and 0.60 m deep, if the box is made of lumber which is 1.75 cm thick.
	Determine the equation of an open upward parabola with (2, 1) and (–4, 1) as ends of latus rectum.

	The pilot of an airplane left A and flew 200 miles in the direction S 20° 20' W. He then turned and flew 148 miles in the direction S 69° 40' E. If he now heads back to A, in what direction should he fly?
	Three forces 20 N, 30 N, and 40 N are in equilibrium. Find the angle between the 20 N and 40 N forces.
	The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. Find the area of the smallest circle.
	A circle with radius 6 has half its area removed by cutting off a border of uniform width. Find the width of the border.
	A rectangle ABCD which measures 18 by 24 units is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

A right cylindrical tank 2 m in diameter and 5 m long has its axis horizontal. It is filled with fuel to a depth of 1.5 m. Find the volume of fuel in the tank in liters
Solution by Geometry	Solution by Integration
	For triangle BOA, B is on the y-axis, O is the origin, and A is on the x-axis. Point C(5, 2) is on the line AB. Find the length of AB if the area of the triangle is 36 unit².
	A company purchased an equipment for a total of P960M including its freight and installation charges. What is its annual depreciation charge if salvage value is zero and the sinking fund deposit factor is 0.0430?
	A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
	Find the point in the parabola $y^2 = 4x$ at which the rate of change of the ordinate and abscissa are equal.