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scoundrel [369]

2 years ago

5

12.

1 answer:

UkoKoshka [18]2 years ago

8 0

Answer:

C. y = 3/4x – 12

Step-by-step explanation:

y = 3/4x + b

-18 = 3/4(-8) + b

-18 = -6 + b

-12 = b

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

3 years ago

the mass of a mineral is 9.6g the mineral is placed in a graduated cylinder containing 8.o mL of water. the water level rises to

Ray Of Light [21]

The volume of the mineral = increase in volume of the water whuich is 16 - 8 = 8mls.

Therefore the mineral's density = 9.6 / 8

= 1.2 g/ ml answer

6 0

2 years ago

Read 2 more answers

The lines represented by the equations 5y + 2x = –25 and y= -5/2x – 1 are?

Schach [20]

Answer the same

the same line

Step-by-step explanation:

3 0

3 years ago

Ivan's has 3/4 pound of hamburger meat. She makes 3 hamburgers patties.each patty weighs the same amount.hiw much dies each hamb

gulaghasi [49]

25 percent
because use quarters as and example

7 0

3 years ago

Read 2 more answers

What is the median of the lengths of Kate's workout

Alik [6]

Arranging them in ascending order :
21 , 21 , 30 , 44, 49, 52

Median = (30 + 44) ÷ 2
Median = 37 mins

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Answer: Median = 37 mins (Answer D)
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4 0

3 years ago