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

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

you would have to sell 24 bracelets.

step-by-step explanation:

84/3.5 = 24