Friday
April 29, 2016

Posts by OIan

Total # Posts: 29

MATHS~~
How many positive integers less than or equal to 1000 are common multiples of the three numbers 27,225, and 135?
May 3, 2013

Here's a neat trick. If your average ceramic bowl has a mass of 200 g, what is the difference in Newtons between the weight of the bowls on the top of her head before and after she does the trick? Details and assumptions The acceleration of gravity is −9.8 m/s2.
May 3, 2013

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 use some ...
April 23, 2013

If you've ever watched sailing, you will sometimes see a sailor hanging off the side of the boat, for example in this shot from the movie "The Thomas Crown Affair." Eventually, of course, the sailboat tips over so far that a person cannot keep it balanced. ...
April 23, 2013

Ski boots are usually made with releasable bindings. This is done for safety – if you fall and your ski gets caught, the binding between the boot and the ski will release so the ski pops off rather than twisting your knee. Sometimes this leads to the embarrassing ...
April 23, 2013

MAths
What is the sum of all numbers that occur an odd number of times in rows 0 through 11 of Pascal's triangle? Details and assumptions The 0th row of the Pascal triangle is the vertex, which is 1. You only sum the number once, regardless of the number of times it appears in ...
April 23, 2013

Maths
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 the black cards is at ...
April 23, 2013

MAths
4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of p/q+r/s can be written as a/b, where a and b are positive, coprime integers. What is the value of a+b?
April 23, 2013

Maths
a and b are consecutive, positive integers such that a^2−b^2>22. What is the minimum possible value of a+b?
April 23, 2013

Maths!!!
4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of (p/q)+(r/s) can be written as a/b, where a and b are positive, coprime integers. What is the value of a+b?
April 23, 2013

MATHS!!!
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 and took 6 minutes ...
April 23, 2013

maths
Bibi wants to send invitations to some of her friends to come to her birthday party. She has contact information for 37 friends stored on her phone, but she only wants to invite 21 of those people to her party. She tries to send out a message to the 21 people, but her phone ...
April 23, 2013

Maths
For how many odd positive integers n<1000 does the number of positive divisors of n divide n?
April 22, 2013

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 initial ...
April 16, 2013

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 no electric field ...
April 16, 2013

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 15 cm. I fill the ...
April 16, 2013

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.
April 16, 2013

Maths
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.
April 16, 2013

Maths
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?
April 16, 2013

Maths
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?
April 16, 2013

Maths
Find the number of solutions to the equation 1/a+1/b+1/c+1/d=1 where a, b, c, d are positive integers and a≤b≤c≤d
April 16, 2013

Raj and Vikram are two travelers in ancient India, walking along the Silk road. On the first day of travel, Raj travels 5 yojanas, and on each successive day travels 3 yojanas more than the previous day. Vikram started at the same place and travels the same path, but started 5...
April 12, 2013

Maths
Let f(x)=2x^2+40x+25. Given that f(x) leaves the same remainder when divided by x−a as when divided by x+2a for a positive integer a, what is the value of a?
April 5, 2013

Maths
Suppose z=a+bi, where a and b are integers and i is the imaginary unit. We are given that |1+iz|=|1−iz| and |z−(13+15i)|<17. Find the largest possible value of a+b. i is the imaginary unit, where i^2=−1.
April 5, 2013

Maths
What is the sum of all real solutions to the equation x−6/4=−2/x?
April 5, 2013

MATHs
The three terms x+12, 3x+5 and 2x+25 are the first three terms of an arithmetic progression. What is the value of x?
April 5, 2013