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3 years ago

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1 answer:

Licemer1 [7]3 years ago

4 0

$\huge \color{red}{ ꧁\mathrm{Answer}}꧂$

The answer is 2112

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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 $(0, 253.125 m^2]$ .

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4 years ago

Spongebob rectangular body has an area of (x 2 −15x 54) feet. what is his width and height in feet?

marusya05 [52]

I hope this helps you

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4 years ago

Help me I don't know nothing about inequality!!!

I am Lyosha [343]

A.x>9

hope this helps

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3 years ago

Please help!!! Which system of inequality’s is shown below???!!! Use picture below to help you! ;)

irina1246 [14]

Answer:

b

Step-by-step explanation:

...

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3 years ago

What is the equation in slope-intercept form of the line

kari74 [83]

Answer:

-5/2x+3

Step-by-step explanation:

you reciprocate the slope since you are trying to find a line perpendicular.

From this m=2/5 to -5/2

then use the formula y-y1 =m(x-x1)

then you put in the points

y - - 2= -5/2(x- 2)

y+2= -5/2x +5

-2 -2

y= -5/2+ 3

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3 years ago