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goldenfox [79]
2 years ago
9

Please help me solve this with steps

Mathematics
1 answer:
OlgaM077 [116]2 years ago
6 0
Here is the answer for a:

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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 graphs below have the same shape. What is the equation of the blue<br>graph?​
Semenov [28]

Answer:

the answer is d

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

vertex- (5,0)

focus- (5,1/4)

axis of symmetry-  x=5

directrix- y=-1/4

ps. can u mark me brainliest if i get this aswer right plz????

thank u!!!!

5 0
2 years ago
What is 1/2 of 1% of 190 tons?
alex41 [277]
1% of 190  = 190 / 100 = 1.9 tons

1/2 of this = 0.95 tons Answer
5 0
3 years ago
I need help with this .....
insens350 [35]

Answer:

6.5 hours

Step-by-step explanation:

hope this helped u bye

4 0
3 years ago
Evaluate the expression:<br> 9 +7(5-2)<br> Using PEDMAS<br><br> yall i suck at math
ANEK [815]

Hello! :)

Let's use PEMDAS.

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

(5-2) = 3 Do parenthesis.

7 × 3 = 21 Multiply with what we got after doing the parenthesis.

9 + 21 = 30 Add with what we had left.

30

Hope this helps!

ELITEDIPER

5 0
3 years ago
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