ElectricPavlov

On August 3   distance will be    5km + .1 + .1 + .1 = 5.3km

   yes it is an arithmetic sequence because it increases at a constant rate ......each term differs from the previous term by a constant amount.

distance for nth term =   (5 + .1n)   km

If he starts at 5km on Aug 1st and THEN increases 0.1 km daily

    distance for nth day =  5 + .1(n-1)     on the n=16th day      distance = 5.15 km

Initially, they are both the same    after 1 year he will get a $1000 raise with each method.    After the first year, the 5% one begins to be better and better due to compounding.

At 10 years the 5% option will be paying him    20000(1.05)^10 = 32577.89 / yr

   the 1000 increase per year will only be paying  30,000      (20000 + 1000*10)

x+y = 120

x-y  = 40         Add the two equations together

2x = 160

x = 80            since   x+y=120       y= 40 

b  y = 4-x        sub into the first equation

    4-x = -x^2+2x+4       subtract 4 and add x to both sides

      0  = -x^2 + 3x           simplify

       0 = -x(x-3)              so x = 0 or 3           x+y = 4     results in y = 4   or 1        (0,4)  or (3,1)

c Graphically:

(a+b)/(a*b) = 7/9      (Given)     expand

a/(a*b)   +   b/(a*b)  = 7/9          simplify

1/b + 1/a = 7/9                           Ta-Da !

Calculate the sum of  NINE terms (sub in n=9).....  Then Calculate the sum of TEN terms (sub in n=10)...

   the 10th term is the difference  

36 possible rolls...only 3 add up to 10      4 6   5 5   6 4     3/36 = 1/12

Set h >=6   and solve for t

6>= -4.9 t^2 + 14 t - 0.4

0 >= -4.9 t^2 + 14 t - 6.4     Use Quadratic Formula or graphing to find   t = .5714  and   2.286  sec

So between    (.5714, 2.286)    the cannonball is = to or higher than 6 m

You have posted a lot of very similar questions....you SHOULD be understanding how to get the answer......YOU try it and see what you get,,,,then, if you need more help , re-post on this thread.....   OK?   You CAN do it!  Try it.....

   After distributive property.....collect 'like' terms...... then.....

Yes.....for this Q there is no division in the last step as shown.