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4 years ago

12

I need help solving this equation -3=9/(5-2k)/5

1 answer:

Amanda [17]4 years ago

3 0

Solve for k by simplifying both sides of the equation, then isolating the variable.

k= 14/5

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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

Solve for x: 3(x + 1) = −2(x − 1) + 6.

Firlakuza [10]

The answer would be x=1

8 0

3 years ago

Read 2 more answers

Please help! :)

sweet-ann [11.9K]

Answer:

Second option is correct

$Arc\ length = \frac{3}{4} \pi\ in$

Step-by-step explanation:

Given:

Central angle = 15°

Radius of the circle = 9 in

Arc length = ?

Given formula is

$\frac{Arc\ length}{Circumfrance} = \frac{n}{360}$

Where n is the central angle of the sector.

Write the given formula for Arc length of the sector.

$Arc\ length = Circumfrance\times \frac{n}{360}$

We know that the the circumference of the circle is $2\pi r$ , where r is the radius of the circle,

$Arc\ length = 2\pi r\times \frac{n}{360}$

Now we substitute central angle value and radius value in above equation.

$Arc\ length = 2\pi 9\times \frac{15}{360}$

$Arc\ length = 18\times \pi \frac{15}{360}$

$Arc\ length = \frac{18\times 15}{360} \pi$ ----------( $\frac{18}{360}=\frac{1}{20}$ )

$Arc\ length = \frac{15}{20} \pi$

Divide the numerator and denominator by 5.

$Arc\ length = \frac{3}{4} \pi\ in$

Therefore the arc length of the sector is $\frac{3}{4} \pi\ in$

4 0

3 years ago

15=3(2x+4)-3 prove x=1

kherson [118]

Answer:

X=1

Step-by-step explanation:

6x+12-3=15

6x+9=15

6x+9-9=15-9

6x=6

X=1

4 0

4 years ago

Read 2 more answers

Who out there likes dragon ball? Die hard fans are allowed to be my friend.

kupik [55]

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4 0

4 years ago