CPhill

The graph  on the right here : https://prnt.sc/pghg5o  is the correct one

A global max or min usually refers to an absolute max or min of a function

A local max or min usually occurs on some specified finite  interval

Note that  these could be the same, in some cases

For instance.....for the function  y  = x^2, the absolute (or global )  min occurs at x  = 0

However.....if we specify the min on the interval from  x = -1 to x = 1......we are talking about a local min.....this is still at x  = 0.....so the absolute min and local min are the same in this case.....

Thanks, Nirvana!!!

OK, man  !!!

3(3) + 4(1)  =

9 + 4  =

13

We have that

a*(4)^2 + 5  = a*(6)^2 + 7     simplify

16a + 5  =  36a + 7      subtract  7, 16a from both side

-2  =  20a         divide both sides by 20

-2/20  = a  =  -1/10

- Write an expression for how much money you will earn if you work h hours. 

You will earn  10.10h  dollars

 Your friend works a different job but makes the same hourly wage as you, plus he receives tips. Write an expression for your friend’s total earnings for a week during which he works n hours and receives a total of $40 in tips. Then, evaluate the expression for n = 10 and explain what that number means. 

Your friend  will earn [ 10.10n + 40 ] dollars per week....where n is the number of hours he works   

If n = 10.....he works 10 hours....and he earns  10.10 * 10  + 40   =  $141 

 Write a single expression for the sum of your earnings for 3 weeks and your friend’s earnings for 2 weeks. You each work r hours per week and our friend receive $40 in tips per week. Simplify the expression. 

You will earn  3 * 10.10 r =  [30.30 r] dollars  for the three weeks

Your friend will earn 2*10.10 r + 40  = 20.20r + 40 for two weeks   

- Write an expression to show the difference between your and your friend’s earning for one week: you work h hours, your friend works n hours, and your friend earns t dollars in tips. (Hint: Be sure to consider the fact that you do not know who earns more money 

You  make 10.10 h  dollars per week

Your friend makes [10.10 n + t ] dollars per week

The difference is   l  10.10h - (10.10n + t)  l dollars.......we need the absolute value bars because we don't know which person earns more

Don't know if this helps....but....here's what I did, Jenny.....

I took the log  of each AU  and plotted these values

For a couple of examples

Mercury - .386 AU ⇒  log (.386)  ≈ -.413

Earth -  1 AU   ⇒ log (1)  =  0

Neptune - 39.5 AU  ⇒ log (39.5) ≈  1.59

Wolf 359 - 492000 ⇒ log (492000) ≈  5.69

Here is the pic :

Here's all you reaaly need to know here

If we divide the power on i   by  4  and we get a remainder of 1,  the result is  i

If we divide the power on i by 4  and get  a remainder of 2, the result is  -1

If we divide the power on i by 4  and get a remainder of 3, the result is  - i

If we divide the power on i  by 4  and get a whole number, the result is  1

So

i^4  = 4/4  =  1    = a whole number....so....the result is 1

i^5   =  5/4  = 1 + 1/4   = remainder of 1, so the result is i

i^6  = 6/4  = 1 + 2/4  = remainder of 2, so the result is -1

i^7 = 7/4  = 1 + 3/4 =  remainder of 3, so the result  = -i

i^8  = 8/4  = 2....whole number ....result is  1

i^9 = 9/4  = 2 + 1/4  = remainder = 1  so the result = i

i^10 = 10/4  = 2 + 2/4 =  remainder of 2  ....so the result is -1

b. The pattern is, for any integer n ≥ 1

i^(4n-3)  = i

i^(4n - 2)  = -1

i^(4n - 1)  = -i

i^(4n)  = 1

c.  i^2001  =  2001/4   =  500 + 1/4  ....remainder  = 1....so....the result  =   i

sqrt (x) < 7      square both sides

x < 49

But  x also has to be  ≥ 0

So.....the solutions are on this interval

0  ≤  x  < 49