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
Maths
There are two complex roots to the quadratic equation z^2 +(1−16i)z+(−80+10i)=0 . What is the value of the larger of the two norms of the two roots?
Math
Find the sum of all primes q<1000 such that for some prime p<q , both q divides p^3 -1 and p divides q^3 -1
physics
A string of 15 identical Christmas tree lights are connected in series to a 127 V source. The string dissipates 58 W.What is the equivalent resistance of the light string? Answer in units of Ω
physics
A string of 15 identical Christmas tree lights are connected in series to a 127 V source. The string dissipates 58 W.What is the equivalent resistance of the light string? Answer in units of Ω
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