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Norma-Jean [14]

3 years ago

5

What is 10 x 2.3-5 in standard notation?

1 answer:

timofeeve [1]3 years ago

4 0

Answer:I think it’s option d

Step-by-step explanation:

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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

Melissa Silva borrowed $6,300 from the bank. If she has already repaid

melamori03 [73]

The remaining balance would be $3,600.

$6,300/7 = 900 x 3 = $2,700
$6,300 - $2,700 = $3,600

8 0

2 years ago

the table shows the highest of four students arrange the students in order from shortest to tallest Kim 56.03 + x + 56.3 + 56.14

saul85 [17]

56.03 56.14 56.3 57.1

6 0

3 years ago

Sofia is comparing celluer plans. Company A charges a flat fee of 59.99 a month and .43 additional minutes. Company B charges 69

Vsevolod [243]

Answer: it will take 125 additional minutes for both costs to be equal.

Step-by-step explanation:

Let a represent the number of additional minutes that it will it take for the two to be the same.

Company A charges a flat fee of 59.99 a month and .43 additional minutes. This means that the total cost of a additional units would be

0.43x + 59.99

Company B charges 69.99 a month and .35 for additional minutes. This means that the total cost of a additional units would be

0.35x + 69.99

For the cost of the two plans to be the same, it means that

0.43x + 59.99 = 0.35x + 69.99

0.43x - 0.35x = 69.99 - 59.99

0.08x = 10

x = 125

5 0

3 years ago

Alenkinab [10]

well the absolute means positive so it would be a positive 1.6

6 0

2 years ago

Read 2 more answers