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Jishnu R.

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Trigonometry

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Question:

In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).

Jishnu R.

Answer:

Let 'a' be the length of the side opposite angle A, 'b' the length of the side adjacent to angle A and 'h' be the length of the hypotenuse. tan(A) = opposite side / adjacent side = a/b = 3/4 We can say that: a = 3k and b = 4k, where k is a coefficient of proportionality. Let us find h. Pythagora's theorem: h2 = (3k)2 + (4k)2 Solve for h: h = 5k sin(A) = a / h = 3k / 5k = 3/5 and cos(A) = 4k / 5k = 4/5

Basic Math

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Question:

Jim, Carla, and Tomy are members of the same family. Carla is 5 years older than Jim. Tomy is 6 years older than Carla. The sum of their three ages is 31 years. How old is each one them?

Jishnu R.

Answer:

Jim: 5 years, Carla: 10 years, Tomy: 16 years Let me explain. Let the ages of Jim, Carla, and Tomy be x,y and z respectively. we know that : Carla is 5 years older than Jim. that implies : y= x + 5 ----------- ( 1 ) Tomy is 6 years older than Carla which implies : z= y + 6 ------------ ( 2 ) and The sum of their three ages is 31 years that is, x + y + z = 31 -----------( 4 ) now apply the value of x in equation number ( 2 ) which makes ( 2 ) into z = x + 5 + 6 z= x + 11 ------- ( 5 ) now apply the value of z and equation ( 1 ) to ( 3 ) that is x + x + 5 + x + 11 = 31 3x + 16 = 31 3x = 15 x = 15/3 x = 5 applying x = 5 in (1 ) and ( 5 ) we have y = 10 z = 16 That is, Jim is 5 years old, Carla is 10 years old and Tomy is 16 years old.

C++ Programming

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Question:

What will 'i' and 'j' equal after the code below is executed? Explain your answer.

Jishnu R.

Answer:

After the above code executes, I will equal 6, but j will equal 5. Understanding the reason for this is fundamental to understanding how the unary increment (++) and decrement (--) operators work in C++. When these operators precede a variable, the value of the variable is modified first and then the modified value is used. For example, if we modified the above code snippet to instead say int j = ++i; I would be incremented to 6 and then j would be set to that modified value, so both would end up being equal to 6. However, when these operators follow a variable, the unmodified value of the variable is used and then it is incremented or decremented. That’s why, in the statement int j = i++; in the above code snippet, j is first set to the unmodified value of i (i.e., 5) and then i is incremented to 6.

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