What am I doing wrong?

A rancher wishes to build a fence to enclose a rectangular pen having area 24 square yards. Along one side the fence is to be ma

Gnoma [55]

Answer:

The value is $C \approx \$76$

Step-by-step explanation:

From the question we are told that

The area of the rectangular pen is $A = 24 \ yard^2$

The cost of material used to make one side is $z = \$ 6$

The cost of material used to make the other sides is $r = \$ 3$

Now , the fence to be build around the rectangular pen has four sides, the first opposite sides are equal, let assume each of the to be x yard and the other opposite sides are also equal as well let assume of the to be y yard

So the cost is mathematically represented as

$C = zx + r (x + 2y )$

=> $C = 6x + 3(x + 2y)$

=> $C = 9x + 6y$

Now the area of the fence is mathematically represented as

$A = x* y = 24$

=> $y = \frac{24}{x}$

=> $C = 9x + 6[\frac{24}{x} ]$

=> $C = 9x + [\frac{144}{x} ]$

Now differentiating

$C' = 9 + 144* (-2) x^{-2}$

$C' = 9 - 288x^{-2}$

At minimum $C' = 0$

So

$9 - 288x^{-2} = 0$

$x^{-2} = 0.03125$

$x = \sqrt{\frac{1}{0.03125} }$

$x = 5.66$

Now substituting for x in the equation above to obtain minimum cost

$C = 9(5.66) + [\frac{144}{5.66} ]$

$C \approx \$76$

8 0

3 years ago

Someone help me with this

Alex

Answer:

y=7.5x, y=9.25x, y=6x

Step-by-step explanation:

on the first table we have for 2 tikets $ 15 so the price for one ticket (also known as unit price) is 15/2= $ 7.5

the equation for the price of ticket must be

y= 7.5 x (where y is price you pay for x number of tikets)

on the second table you can pick that you have $37 for 4 tikets so unit price is 37/4= $9.25 per one ticket

y=9.25x

last table $12 for 2 tikets so for one ticket is 12/2=$6

y=6x

7 0

3 years ago

Read 2 more answers

If f(x) is the total cost, in dollars, of x cupcakes, which of the following statements best describes the meaning of f(5) = 12?

dezoksy [38]

Answer:

See below

Step-by-step explanation:

This a form of the proportional relationship:

f(x) = kx, where f(x) - total cost, k- cost of each item, x - number of items

We have:

f(5) = 12

It means:

Total cost of 5 cupcakes is $12

5 0

2 years ago

Mr. Yasin paid a total of 9.43 to buy three boxes of cereal. If he paid 3.99 for the 1st box and 2.97 for the 2nd box how much d

Vikentia [17]

Answer:

$2.47

Step-by-step explanation:

Pretend if Mr. Yasin didn't pay for the 3rd box, find out how much he had left after paying for the first 2 boxes.

9.43 - 3.99 - 2.97 = 2.47

8 0

2 years ago

Need help! much appreciated

Volgvan

Answer:

C-D = 6

A-B = 3.25

D = 118

Step-by-step explanation:

C-D = 6 because the line is the same as B-C

A-B = 3.25 because the line is the same as A-D

D = 118 because the angle of B is vertically opposite to D

7 0

3 years ago