ITS Sys Admin Pat is dealing with a computer virus outbreak. Pat esti- mates that every second at least 1 uninfected computer becomes infected for every 5 computers already infected on campus. To be exact there will be (C/5 newly infected computers in the next second if there are currently C infected computers. Pat is able to disinfect at most 10 computers per second. If Pat knows that there are at least 60 infected computers now, prove by induction that in n seconds there will be at least 12 6 10 + 50 infected computers. 5

Solution :

Let the base case, n = 0

Given at at least computers are infected

So,

Therefore, n = 0 is not true

Let suppose, it is true for n = k

Then,

We have to show that it is also true for

That is at the end of (k+1) second,

Now, the number of the infected computer that is added between and  second =

Now the number of the infected computer decreased between and  second is = 10.

Hence at the end of the second.

Number of the computers

Hence Proved

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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