To solve this problem, we need to use the Pigeonhole Principle, which states that if we have n items and k containers, with , then at least one container must have more than one item.
In this case, we have 100 people who each pick a number from 97 to 115, so we have 19 possible numbers .
To be sure that at least two people have the same number, we need to have more people than the number of possible numbers. Specifically, we need to have enough people to fill up all 19 possible numbers, plus one additional person to ensure that there are at least two people with the same number.
Therefore, we need at least people to be sure that two of them have the same number.
An object moving in the xy-plane is acted on by a conservative force described by the potential energy function
I need to find a unique description of Nul A, namely by listing the vectors that measure the null space
T must be a linear transformation, we assume. Can u find the T standard matrix.?
Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7).
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R.
b) Find the area of the triangle PQR.
Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate A - B?
Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 2A-3(B-C)?
What is the projection of onto ?
What is the dot product of and ?
Which of the following is not a vector quantity?
How to find all unit vectors normal to the plane which contains the points , and ?
What is a rank matrix?
How to find unit vector perpendicular to plane: 6x-2y+3z+8=0?
Can we say that a zero matrix is invertible?
How do I find the sum of three vectors?
How do I find the vertical component of a vector?