CPhill

If we extended the top base of the figure by 8m and drew a perpendicular line to the base...the additional area would create a right "Pythagorean Triple" triangle with one of the legs  = 8m and a hypotenuse of 17m.....and the other leg = sqrt (17^2 - 8^2)  = sqrt (225) =  15m  = the length of the fence

Thus....disregarding the right triangle, we have a trapezoid with a height of 15m and two bases of 12m and 20m

So....the  area of a trapezoid  =

(height) / 2  *  (sum of the bases )   =

15 / 2  * ( 12 + 20)  =

7.5 *  32   =

240 m^2

So...we need three cans of weedkiller  =  3 * 19.75  =  59.25 pounds  (total cost) 

e^x   has the unique property that it is its own derivative...thus.....

f(x)  =  e^x

And

f¹⁰⁰ (x)  =  e^x

The first will produce vertical lines through a and -a on the x axis

The second will produce horizontal lines through b and -b on the y axis

Very nice, Melody !!!!

Let D be 1/2 of the  Diistance

And 40 min  2/3 hr

So   using Distance / Rate  = Time in Hours .......we have that

D/3  =  D/5   + 2/3    simplify

D/3  +  [3D + 10] / 15     cross-multiply

15D  = 3[ 3D + 10]

15D  =  9D + 30     subtract 9D from both sides

6D  = 30   divide both sides by 6

D  = 5 miles

So...the total distance is twice this  =  10 miles

Hey....I know who that "chick" is.....

"Mr. "Green Jeans" from "Captain Kangaroo".....before surgery, of course

OK...no prob....!!!

No....a rational function is one that has a polynomial in the numerator and the denominator....note that

(x + 3)  / (x^2 - 2)    would be an example....but...

 (x^2+2x+3)/3  is actually just

(1/3)x^2  + (2/3)x  +  1       and this is just a quadratic function.....

Those are pretty cool...especially the "Stuck In Space" one....!!!!

(x^5-1)/3, find f^-1(-31/96)

Write  

y = (x^5-1)/3       

3y  = x^5 - 1

3y + 1  =  x^5

(3y + 1)^(1/5)  = x        swap x and y

(3x + 1 )^(1/5)  = y  = f^-1 (x)

So

f -1 (-31/96)  =    ( 3 (-31/96)  + 1 )^(1/5)  = (3/96)^(1/5)  = .03125^(1/5)  = .5 =  1/2  !!!!!!