# Video Discussion: MSTE-00 Final Preboard

## Civil Engineering Refresher - Final Preboard: Point of Tangency of Line and Circle

A circle has its center at (3, -27). It is tangent to the line $3x + 4y - 26 = 0$. Locate the point of tangency.

Solution Problem
Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get (a) at least 1 six when 6 dice are rolled, (b) at least two sixes when 12 dice are rolled, or (c) at least 3 sixes when 18 dice are rolled. What is the answer?
From point A on level ground, the angles of elevation of the top D and bottom B of a flagpole situated on the top of a hill are measured as 47°54' and 39°45', respectively. Find the height of the hill if the height of the flagpole is 115.5 ft.
What time between 2 and 3 o 'clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o 'clock mark?
Work in progress... Video solution is not yet available for now. For the mean time, you may follow this link for the solution: https://mathalino.com/node/3465 From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 2/3, of a step toward the cliff 1/3. What is his chance of escaping the cliff?
A person buys a piece of property for P100,000 down payment and ten deferred semi-annual payments of P8,000 each starting three years from now. What is the present worth of the investment if the rate of interest is 12 percent compounded semi-annually?
Find the angle, in degrees, between $2x - y + z = 10$ and $x + y + 2z = 11$.
The two sides of a triangle are 25 cm and 26 cm, while the altitude to the third side is 24 cm. Find the area of the triangle in cm2
After M students took the test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers to 70%?
How many integers between 18 and 70 inclusive are divisible by either 7 or 9 but not both?
If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?
Work in progress... A lead pencil whose ends are regular hexagons was cut from a cylindrical piece of wood with the least waste. If the original piece was 8 in. long and ½ in. in diameter, find the volume of the pencil.

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