Pranav B.

Civil Engineer

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Trigonometry

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Question:

The area of a right triangle is 50. One of its angles is 45o. Find the lengths of the sides and hypotenuse of the triangle.?

Pranav B.

Answer:

The triangle is right and the size one of its angles is 45 degrees; the third angle has a size 45 degrees and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse. Area = (1/2)x2 = 50 , solve for x: x = 10 We now use Pythagora to find H: x2 + x2 = H2 Solve for H: H = 10 sqrt(2)

Civil Engineering

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Question:

The survey carried out to delineate natural features, such as hills, rivers, forests and man- made features, such as towns, villages, buildings, roads, transmission lines and canals is classified as?

Pranav B.

Answer:

Topographic survey is carried out to delineate natural features.

Statistics

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Question:

You have 50 red marbles, 50 blue marbles and 2 jars. One of the jars is chosen at random and then one marble will be chosen from that jar at random. How would you maximize the chance of drawing a red marble? What is the probability of doing so? All 100 marbles should be placed in the jars.

Pranav B.

Answer:

What if you put a single red marble in one jar and the rest of the marbles in the other jar? This way, you are guaranteed at least a 50% chance of getting a red marble (since one marble picked at random, doesn’t leave any room for choice). Now that you have 49 red marbles left in the other jar, you have a nearly even chance of picking a red marble (49 out of 99). So let’s calculate the total probability. P( red marble ) = P( Jar 1 ) * P( red marble in Jar 1 ) + P( Jar 2 ) * P( red marble in Jar 2 ) P( red marble ) = 0.5 * 1 + 0.5 * 49/99 P( red marble ) = 0.7474 Thus, we end up with ~75% chance of picking a red marble.

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