CPhill

13.75*(82.03^-1)  =

13/75 / 82.03   = about 0.1676

sec s =3.0956

Using the inverse secant, we have.....

arcsec ( 3.0956)  = s   ≈  71.15°

l  1 - 2x  l   =   5x + 2

We need to solve these two equations

1 - 2x     = 5x + 2                      and      -( 1 - 2x)  = 5x + 2

                                                             -1 + 2x    = 5x + 2

add 2x to both sides                            subtract 2x from both sides

1  = 7x   + 2                                          -1    =  3x  + 2

                            subtract 2 from each side

-1  = 7x                                                 -3   = 3x

divide both sides by 7                         divide both sides by 3

-1/7  = x                 or                        -1   = x

Note  that the second solution is extraneous [it does not solve the original equation].....so.....

The only solution is  x = -1/7

Here's a graph of the solution : https://www.desmos.com/calculator/zxa5f3g7wa

2 x^2 - 5 x+ 2 y^2 - 3 y = 0

We need to complete the square on x and y

2( x^2 - (5/2)x + 25/16) + 2(y^2 - (3/2)y + 9/16)  =  50/16 + 18/16

2(x - 5/4)^2   + 2 (y - 3/4)^2   =   68/16      

2( x - 5/4)^2   + 2(y - 3/4)^2   =  17/4    divide both sides by 2

(x - 5/4)^2   + (y - 3/4)^2   =  17/8

So...the radius  = √(17/8)  = about 1.458

Let R be the average rate for the outbound trip.....and we know that Rate*Time = Distance......but......the distance out and back are the same.....so we have.....

R(5)  = (R + 1.1)4.9     simplify

5R  = 4.9R + 5.39     subtract 4.9R from each side

0.1R  = 5.39      divide both sides by 0.1

R = 53.9 km/hr   = the rate for the outbound trip

We'd have to know something else about the scores .......

For instance......there could be four scores which were 5, 9, 10 and 10  ..... and .this would average to 8.5....so 10 would be the high score

However.......there could have also been six scores that were 5, 7, 8, 9, 10 and 12.......and this would also average to 8.5.......but here, 12 is the high score

Or......we could have a situation where one 5 and seven 9's were recorded.....this also averages to 8.5......and here, 9 is the greatest score

Let N be the number......so

3/5  of N  = 48   means

(3/5)N  = 48       multiply both sides by 5/3

N = 48(5/3)

N = (48/3) *5

N = 16 * 5 

N = 80

I'm assuming you mean "PA" side by side.........

These can occupy any of 5 positions......and for each of these they can be arranged in 2 ways - PA or AP.....

And for all these arangements, the other four letters can be arranged in 4!  = 24 ways......so

5 * 2  *  24   =  

10 * 24  =

240   different arrangements, if "P" and "A" have to remain together

I'm assuming that you're saying that each digit costs 5 cents...if so, we have that.....

There are 401 numbers with 3 digits each [ 100 - 500]

There are 90 numbers with 2 digits each [ 10 - 99]

There are 9 digits with one number each [ 1 - 9]

So

5 * [ 401(3) + 90(2) + 9(1) ] =

5 * [ 1203 + 180 + 9]  =

5 * [1392]  =

6960 cents  =  $69.60

We have 7 choices for the first letter, 6 for the second, 5 for the third, etc.....so

7 * 6 * 5* .....*2 * 1    =  7!   = 5040 different ways