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My name is Ann [436]

3 years ago

11

How to write a rule for transformations

1 answer:

Luba_88 [7]3 years ago

4 0

What's the question?

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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

4 years ago

Y-3=-3y-43 how would i solve?

frez [133]

Answer: y−3=−3y−43

Step 1: Add 3y to both sides.

y−3+3y=−3y−43+3y

4y−3=−43

Step 2: Add 3 to both sides.

4y−3+3=−43+3

4y=−40

Step 3: Divide both sides by 4.

4y

4

=

−40

4

y=−10

Answer:

y=−10

Step-by-step explanation: brainliest:)

7 0

3 years ago

Eric made a scale drawing of the middle school. The scale he used was 1inch=5feet. If the gym is 30 inches by 20 inches in the d

BabaBlast [244]

Answer: 150 feet : 100 feet

Step-by-step explanation:

From the question, we are informed that the scale used by Eric was 1inch=5feet.

If the gym is 30 inches by 20 inches in the drawing, the acual length and width of the gym would be:

Length = 30 inches = 30 × 5 feet = 150 feet

Width = 20 inches = 20 × 5 feet = 100 feet

Therefore, the acual length and width of the gym would be 150 feet by 100 feet

6 0

3 years ago

Read 2 more answers

Which comparison is correct?<br> A. 7 -7<br> C. -9 > 4<br> D. -6 > -5

pashok25 [27]

Answer:

A is correct hope this helps

7 0

3 years ago

Read 2 more answers

Subtract. 5x^2-5x+1-(2x^2+9x-6)

Talja [164]

<h2>Hello!</h2>

The answer is:

$3x^{2} -14x+7$

<h2>Why?</h2>

To solve the problem we need to add/subtract like terms. We need to remember that like terms are the terms that share the same variable and the same exponent.

For example, we have:

$x^{2} +2x+3x=x^{2} +(2x+3x)=x^{2}+5x$

We have that we were able to add just the terms that were sharing the same variable and exponenr (x for this case).

So, we are given the expression:

$5x^2-5x+1-(2x^2+9x-6)=5x^{2}-2x^{2}-5x-9x+1-(-6)\\\\(5x^{2}-2x^{2})+(-5x-9x)+(1-(-6))=3x^{2}-14x+7$

Hence, the answer is:

$3x^{2} -14x+7$

Have a nice day!

4 0

3 years ago