In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
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
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?
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.
What will 'i' and 'j' equal after the code below is executed? Explain your 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.