ElectricPavlov

I THINK you meant how many possible values of 'n' are there?

Since  the two roots are positive....

this means the solution looks like this:

(x-a)(x-b)        where  a and  b   are the roots   

a and b must ADD to m   and must multiply to n   AND m<20      or   <=19   and POSITIVE integers AND PRIME

primes below   19

3  5   7   11  13   17   19     Two of these added together  must be <= to 19

3 +  3,7,11,13

5 + 5,7,11,13

7+ 7,11

I think that is all the combos   ====>   TEN   possible values of 'n'   (only 6 values of 'm')

OK,,   SUBSTITUTION method

The FIRST equation tells you what  y =     Substitue this value of y in to the 2nd equation....

-3x - 3 (-5x-17) =3    and solve for 'x'......

                then use this value of 'x' that you find and substitute back into EITHER of the equations to find the 'y' value

-3x + 15x +51 = 3

12x + 51 = 3

12x = -48

x = - 4            y =  -5(-4)-17

                          y = 3

I do not have a praphing calculator...but I can answer the first one....

Look at the data points

with x = 0    all of the equations will result  in y=1    EXCEPT for the 3rd one...toss the 3rd choice

with  x = 3   only the second equation yields  y = -2   so it is the winner...

  Just to be sure , check at x=4   for the second equation,   y = 1   Check!

Glad you're here DBZ !   Keep Kalculatin'  !

f^-1 is the inverse of f(x)

(2x+3)/(x-4)   = y       solve for 'x'

first do the division on the left to get

2+ 11/(x-4) = y          subtract 2 from each side

11/(x-4) = y-2          re-arrange

11/(y-2) = x-4          add 4 to both sides

11/(y-2) + 4 = x       change y to x and x to y

11/(x-2) +4 = y        simplify

(11 + 4x -8 )/(x-2) = y

(4x+3) / (x-2) = f^-1

I am editing this because Lagtho correctly pointed out I used a cone instead of a cylinder  !!

cone volume - sphere volume = water volume

CYLINDER volume - sphere volume = water volume

pi r^2 h  - 4/3 pi r^3 = water vol     (this assumes the water can squeeze past the sphere to fill the tip of the cone)

pi 30^2  100   - 4/3 pi 12^3 = water vol

= 275365  cm^3

Nice job DBZ !

No you don't......you are dealing with radii     one radius is  8 the inner is 5

Ooops....dbz      volume  is 4/3 pi r^3

Volume of the 8cm sphere - volume of 5 cm sphere = glass volume

volume of a sphere = 4/3 pi r^3     Get your calculations on !

= 4/3 pi (8^3 - 5^3)   = 516 pi = 1620.2 cm^3