Given DE is a mid segment of triangle ABC

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

Simplify 18/27??? Plz help

Rus_ich [418]

2/3 is the simplified form of 18/27

6 0

3 years ago

Read 2 more answers

There are eight members of a jazz club who are listed below. A concert director can choose some or all of them to be part of a l

bagirrra123 [75]

Answer:

40320 ways

Step-by-step explanation:

Given

Members = 8

Required

Number of ways they can be selected

Since, the order does not matter;

They can be selected in 8! ways

$8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1$

$8! = 40320\ ways$

<em>Hence, there are 40320 ways which the director can select them for the concert</em>

8 0

3 years ago

Carrie has 40 more nickels than Joan has dimes. They both have the same amount of money. How many coins does each girl have? Wha

LuckyWell [14K]

Answer:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be $x$ and $y$ the amounts of nickels and dimes that Carrie and Joan have, as $c$ the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

Carrie's amount of money:

$0.05\cdot x = c$ (Eq. 1)

Joan's amount of money:

$0.10\cdot y = c$ (Eq. 2)

Relation between amounts of coins:

$x = y+40$ (Eq. 3)

First we eliminate $c$ by equalizing (Eq. 1) and (Eq. 2):

$0.05\cdot x = 0.10\cdot y$

Then, we reduce the resulting formula by (Eq. 3):

$0.05\cdot (y+40) = 0.10\cdot y$

$y+40 = 2\cdot y$

$y = 40$

And rest of variable are now determined:

$x = 40+40$

$x = 80$

$c = 0.05\cdot (80)$

$c = 4$

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

5 0

3 years ago

Question b with explanation?

Step2247 [10]

Hello!

The answer is 40. All we have to do is find the number of 16 year olds who spent between 25-35 minutes in social media. That is 145. The number of 13 year olds who spent the same amount of time is only 105, therefore 40 more 16 year olds spent between 25 and 35 minutes on social media.

8 0

2 years ago