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Prove: Methods for divisibility by 13.

  1. Method 2. ( R + 4L) 

If a 1.35 tonne car accelerate from 15.0km/h to 75km/h on a flat road in 4.00 seconds,


A. What is the distance travelled?


Prove:

The following methods are useful for divisibility by 11.

  1. 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.

  1. 4y^(4) −4y′′′ −23y′′ +12y′ +36y = 0 

Determine the unique solution of the initial value problem. 

  1. y′′ −2y′ +y=0,y(0)=7,y′(0)=4.


 Show that the functions 1, cos2 x, sin2 x are linearly dependent .


Determine all intervals on which the equation is normal. 

  1. (tanx)y′′′+y=0


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.

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