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3 years ago

7

How much must Arthur earn in the next week?

1 answer:

raketka [301]3 years ago

5 0

Arthur must earn $53 in the next week

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A company determined that for each $1 increase in the price of their product, the

zaharov [31]

Answer:

To have maximum profit, the price must be increased by 5,

Step-by-step explanation:

Given that the price increase function is:

f(x) = -2x² + 20x + 150,

For maximum profit, then f(x) = 0.

Putting f(x) = 0, we have

-2x² + 20x + 150 = 0

Or

x² - 10x - 75 = 0

(x + 5)(x - 15) = 0

x = -5

Or

x = 15

Again, differentiating f(x) and equating to zero, we have

-4x + 20 = 0

4x = 20

x = 20/4

= 5

To have maximum profit, the price must be increased by 5,

5 0

3 years ago

Read 2 more answers

Jaylynn draw a hen on graph paper using scale of 1 unit on her graph paper represents 5cm.The hen has height of 11 units in the

lisabon 2012 [21]

Answer:

55

Step-by-step explanation:

There are 11 units used on the paper. If each unit is 5cm, that means you can do 11*5 and get 55 cm.

3 0

1 year ago

Read 2 more answers

Ernesto brought plastic tubes that are each 5.3 meters long. If Ernesto makes a line of 18 tubes by placing the end-to-end, how

VARVARA [1.3K]

5.3×18=95.4 meters. you multiply it because you are trying to find the full length.

3 0

2 years ago

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

Pls Help Will Mark Brainliest for quickest accurate answer and explanation!!

Furkat [3]

Answer:

The number of chicken and cows should be 19 and 11.

Step-by-step explanation:

The number of chicken and cows should be 19 and 11.

Given that,

The farm has 30 chickens and cows, and there are 82 chicken and cow legs all together.

Let x represent the number of chickens in the farm.

Let y represent the number of cows in the farm.

Based on the above information, the calculation is as follows:

x + y = 30

Since a chicken has 2 legs and a cow has 4 legs.

So,

2x + 4y = 82 - - - - - - - - - - - - 1

Now

Substituting x = 30 - y into equation 1, it becomes

2(30 - y) + 4y = 82

60 - 2y + 4y = 82

- 2y + 4y = 82 - 60

2y = 22

y = 11

Now

x = 30 - 11

= 19

8 0

2 years ago