Search & Filtering
Prove: 12|N iff 4| N ^ 3 | N.
Prove:
The following methods are useful for divisibility by 11.
- Get the difference of the sum of the digits in the odd places and the sum
of the digits in the even places. If the result is divisible by 11, then 11|N.
Prove that if 𝑎|𝑏 and 𝑏≠0, then |𝑎| ≤ |𝑏|.
Find the general solution.
- 4y^(4) −4y′′′ −23y′′ +12y′ +36y = 0
Determine the unique solution of the initial value problem.
- y′′ −2y′ +y=0,y(0)=7,y′(0)=4.
Show that the functions 1, cos2 x, sin2 x are linearly dependent .
Random samples of size n-2 are drawn from a finite population consisting of the following numbers 5,6,7,8, and 9.
a. How many possible outcomes are there? b. List all the possible samples and the corresponding mean for each.
sample.
c. Construct the sampling distribution of the sample means.
To compute economic profits, which costs are used?
1. A solenoid consists of 200 turns of wire and has a length of 0.15m. What is the magnetic field inside
the solenoid if the current through it is a.) 0.24A, b.) 0.50A and c.) 1.2A
2. A circular wire loop with an area, A = 0.1m2 , is placed in magnetic field of magnitude B = 0.25 T.
Calculate the magnetic flux through the loop when a.) the plane of the loop is perpendicular to the field,
and b.) the normal plane of the loop makes an angle of 300 with respect to the field.
At a certain speed, the root-mean-square-speed of the molecules of hydrogen in a sample
of gas is 1055 ms-1
. Compute the root-mean square speed of molecules of oxygen at the
same temperature.
