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scoundrel [369]
2 years ago
5

12.

Mathematics
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
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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
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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

------------------------------------------------------------------
Answer: Median = 37 mins (Answer D)
------------------------------------------------------------------

4 0
3 years ago
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