8/9 + 2/3 + 1/6 = PLeASe HeLp A. 11/8 B. 11/15 C. 1 13/18 D. 1 2/9

A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

Basile [38]

Answer:

$W_{max}=480m\\ L_{max}=160m$

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

$x_{max}=-b/2a$
$f(x)_{max}=f(x_{max})$

Since our function is A(L)=640L-2L², we get

a=-2
b=640

plug in the value of a and b into the first formula:

$L_{max}=-(640)/2(-2)\implies 160$

$A(L)_{max}=640(160)-2(160)^2\implies 76800$

hence,the dimensions of the pen that will maximize the area are L=160m and W=76800/160=480m

and we're done!

3 0

2 years ago

The radius of a sphere is 12 units. Find the volume of the sphere. Write your answer in terms of pi.

stiv31 [10]

Answer:

V = 2304π units³

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = $\frac{4}{3}$ πr³ ( where r is the radius ) , then

V = $\frac{4}{3}$ π × 12³

= $\frac{4}{3}$ π × 1728

= 4π × 576

= 2304π units³

5 0

2 years ago

Given m|n, find the value of x. т (6x+4) (4X-14)

postnew [5]

Step-by-step explanation:

Here Is Your Answer........ please Make me as brainliest

5 0

2 years ago

Read 2 more answers

Which graph best represents the relationship between time and the number of teams registered?

alexdok [17]

<h2>Explanation:</h2><h2></h2>

The complete question is in the attached file. So we have to choose between two graphs. On of them is a linear model while the other is an exponential model. From the statements, we have a relationship between time and the number of teams registered. So we can establishes variables in the following form:

$x:\text{Time} \\ \\ y:\text{Number of teams registered}$

We also know that each week 6 teams register to participate, so:

$\bullet \ \text{For week 0:} \rightarrow \text{0 teams registered} \\ \\ \bullet \ \text{For week 1:} \rightarrow \text{6 teams registered} \\ \\ \bullet \ \text{For week 2:} \rightarrow \text{12 teams registered (Because 6+12)} \\ \\ \bullet \ \text{For week 3:} \rightarrow \text{18 teams registered (Because 12+6)}$

As you can see, as x increases one week, y increases at a constant ratio of 6. Therefore, this can be modeled by a linear function given by the form:

$y=6x$

In conclusion, the linear model (first graph below) is the one that bests represents the relationship between time and the number of teams registered.

7 0

3 years ago

What is -2(4n - 1) +15 I think that it is -8n - 13 but i am not sure plz help

ANEK [815]

Answer: Your right!

-8n-13

Step-by-step explanation:

-2(4n-1)+15=

-8n+2-15

Combine like terms- 2-5= -13

so -8n-13

8 0

3 years ago

8/9 + 2/3 + 1/6 = PLeASe HeLpA. 11/8B. 11/15C. 1 13/18D. 1 2/9