A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 330 yd of fencing is available, find the largest total area that can be enclosed.

The longer side of the rectangle   x  = 165 yd

The other side   y  =  55 yd

Step-by-step explanation:

Total area to be enclosed  ( A(t) )

A(t)  =  x* y    

As the river is one of the longer side of the corrals, we have total length to fence

Perimeter of the area minus length of one side, plus the fence between corrals. That means

Length of fence =  330 yd  = 3*y + x

y = ( 330 - x ) / 3

Then area as a function of x become

A(x)  = x* ( 330 - x ) /3    ⇒   A(x)  = (330*x -x² ) / 3

Taking derivatives on both sides of the equation

A´(x)  = 3 * ( 330 - 2x )/ 9

A´(x)  = 0     ⇒     3 * ( 330 - 2x )/ 9  = 0

330 - 2x  = 0

x  =  330 / 2

x = 165 yd

And  y =  (  330 - x ) / 3

y  =  ( 330 - 165 ) / 3

y  =  165 / 3

y  =  55 yd

Total area enclosed

A(max) =  165*55

A(max) = 9075 yd²

go and ask your mom to you

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional