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x,y and z are positive integers such that x<y,x+y=201,z−x=200. What is the maximum value of x+y+z?

Let A,B and C be matrices such that A=(1 2 3 1 2 3) , B=(1 2 2 4 2 3) and C=AB. What is the sum of all the elements (entries) of matrix C?

The function f(x)=x^4−15(x^3)+81(x^2)−201x+182 has four complex roots, one of which is 3−2i. What is the sum of all real and imaginary coefficients of these roots? Details and assumptions i is the imaginary unit, where i2=−1.

The space shuttle had a top orbital speed of 8000 m/s and orbited in a circular orbit approximately 320 km above the earth's surface. How long was one orbit in seconds? Details and assumptions The radius of the earth is 6370 km.

I have a length of string and I want to know the maximum tension the string can support. I tie one end of the string to the ceiling and the other end to a glass of mass 100 g. The glass is cylindrical, with a cross-sectional radius of 4 cm and a height of...

A neutral solid conducting cylinder rotates about its axis with angular speed 1600 rad/s. In addition, there is an external magnetic field of induction B directed along the cylinder's axis. What must the magnitude of the magnetic field in Teslas so that n...

A source of ions at point O produces a slightly diverging beam with half-angle of divergence α0≪1. In order to collimate (re-focus) the beam, one can apply a uniform magnetic field along the z-axis (see the figure below). If all the ions have the same ini...

Calvin was making a trip to the University of Chicago. When he drove down, he took Lakeshore Drive, and averaged 35 miles per hour. On his way back, he took the I-94 highway, and averaged 50 miles per hour. Given that the return journey was 4 miles longer...

a and b are consecutive, positive integers such that a^2−b^2>22. What is the minimum possible value of a+b?

Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on th...

Consider a five-pointed star made of resistors as shown below. Each resistor has resistance R=6 Ω. Find the equivalent resistance in Ohms between the points A and B. Details and assumptions Note: Points ABCDE are labeled for easy reference if you need to...