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

i wish i could you, i have no idea how to answer this

step-by-step explanation:

vwhat effect does the word head have on the meaning of this passage?

a. it demonstrates how intelligent he was.

b. it shows he was a favorite of the teachers.

c. it indicates he would be a good preacher.

d. it reveals how self-important he was.

how does the choice of the word head contribute to the passage’s tone?

a. it offers a sense of entitlement.

step-by-step explanation: