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Use mathematical induction to prove that 2n > n2 , for n > 5 .Find, showing all working, a recursive definition of the sequence with general term
tn = 6 (n + 1)!/3n, n >= 1
partial order relation and also draw its Hasse diagram
r: You get a 95 in MMW
Write these proposistions symbols using p, q, and r, and logical connectives.
1.You get a 95 in MMW, but you do not do every exercise in the class.
2. You get a 95 on the final examination, you do every exercise in the class and you get 95 in MMW
D.State the converse, inverse and contrapositive of the following propositions.
1. If you will review your lessons, them you will pass MMW.
Converse:
Inverse:
Contrapositive:
2.The beat will sink if it is overloaded
Converse:
Inverse:
Contrapositive:
Prove that for any integer n
n, if n
n is an odd integer, then 6n
2
+5n+1
6n2+5n+1 is an even integer.
A bank password consists of two letters of the English alphabet followed by two digits. How many different passwords are there?
At a school education fair, 50 students were interviewed about their interested programmes of study and all of them have shown interest in at least one of the three programmes in the survey. From the results of the interviews, there were 26 students who were interested in studying IT programmes, 18 were interested in Business programmes, 20 were interested in Hospitality programmes and 5 students were interested in all three programmes. How many of the students were interested in exactly
(i) two programmes only?
(ii) one programme only?
The heart beat rate has to be well regulated to provide enough oxygenated blood
throughout the body and so depends on feedback with the body’s oxygen demand. A simple discrete model of heart beat regulation is given by:
xt+1 = kxt(1 - xt)
Here xt represents the normalised heart beat rate at time t recorded once per minute. That is, the normalisation involves dividing the actual hear rate in beats per minute by 80 beats per minute.
The parameter k is a positive real number (hopefully) greater than 0.
(a) Assuming k = 1 what are the steady state solutions (also known as fixed points) for xt? That is, when xt+1 = xt
(b) Assuming k = 2 what are the fixed points?
(c) Write a MATLAB program using array operations to generate a table (with headings) of the normalised heart beat rate per minute starting at time t = 0 with the value of x0 entered by the user. Run your program with the maximum time set to 30 minutes. Show table and MATLAB code for x0 = 0.1 and k = 2
Find, showing all working, a recursive definition of the sequence with general term
tn = 6 (n + 1)!/3n, n >= 1
There are 3 black balls, 4 blue balls and 5 red balls in a box. In how many ways can we choose 3 balls at the same time with different colors?
#339914 on Dec 2023