Saturday
December 7, 2013

# Posts by Tony

Total # Posts: 759

maths
53

Logarithms
if loga(b)=1/48 what is the value of logb(a^2) ?

calculus
If x=t^3 and y=3t^5, where t is any real number, what is the derivative of y with respect to x at x=125 ?

Algebra
If the sum of 3 non-zero distinct real numbers a, b and c is 2 , and the two sets {a,b,c} and {1/a ,1/b ,1/c} are the same, what is the value of a^2 +b^2 +c^2 ?

Trigonometry
Given that tan84=T , how many solutions are there to tanx=T in the domain [0,1000] ?

Trigonometry
Let O be the origin and P be a point in the fourth quadrant on the x-y plane. Let 270<z<360 be the angle formed by OP with the positive x-axis. Similarly Q is a point in the fourth quadrant on the x-y plane where |OQ|=|OP| and the angle formed by OQ and the x-axis is 7z ...

Algebra
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b

P&P
Peter is walking from the library to school at a rate of 40 meters per minute. At the same time, Paul is walking from school to the library. After they meet each other, Peter still needs 6 minutes to get to school, while Paul is 200 meters away from the library. What is the di...

Ratios
If the ratio of x+y to x−y is 279/262 , then the ratio of y to x can be written as a/b where a and b are coprime positive integers. Find a+b

Numbers
What is the smallest possible natural number x>5 , that leaves a remainder of 5 whenever it is divided by 14 , 8 or 77

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