(a+3a²+2a³)-(-a³+a²)

A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are use

Rashid [163]

Answer:

$A = L W= 9*\frac{9}{2}=\frac{81}{2} m^2$

Step-by-step explanation:

For this case we assume that the total perimeter is 18 ft, we have a wall and the two sides perpendicular to the wall measure x units each one so then the side above measure P-2x= 18-2x.

And we are interested about the maximum area.

For this case since we have a recatangular area we know that the area is given by:

$A= LW$

Where L is the length and W the width, if we replace from the values on the figure we got:

$A(x)= x *(18-2x) = 18x -2x^2$

And as we can see we have a quadratic function for the area, in order to maximize this function we can use derivates.

If we find the first derivate respect to x we got:

$\frac{dA}{dx} = 18-4x=0$

We set this equal to 0 in order to find the critical points and for this case we got:

$18-4x=0$

And if we solve for x we got:

$x=\frac{18}{4}=\frac{9}{2} m$

We can calculate the second derivate for A(x) and we got:

$\frac{d^2 A}{dx^2}= -4$

And since the second derivate is negative then the value for x would represent a maximum.

Then since we have the value for x we can solve for the other side like this:

$L= 18-2x = 18-2 \frac{9}{2}= 18-9 =9m$

And then since we have the two values we can find the maximum area like this:

$A = L W= 9*\frac{9}{2}=\frac{81}{2} m^2$

8 0

3 years ago

Stefan sells Jim a bicycle for $138 and a helmet for $16.The total cost for Jim is 140% of what Stefan spent originally to buy t

alukav5142 [94]

Answer:

$110, $44

Step-by-step explanation:

Let x = the total cost to Stefan

Jim buys for:

bicycle: $138

helmet: $16

total: $138 + $16 = $154

Jim's price of $154 is 140% of Stefan's cost, x.

154 = 140% × x

1.4x = 154

x = 110

Stefan spent $110.

Stefan's profit:

$154 - $110 = $44

Answer: $110, $44

5 0

3 years ago

This question is like impossible idk

7nadin3 [17]

If the problem was written x + 4x. We would know to add like the coefficients together and get 5x same thing with the radicals.

$\sqrt{3} + 4 \sqrt{3} = 5 \sqrt{3}$

3 0

4 years ago

(3x - 4x - 2 + 3x - 6 = 180<br> 7x – 8 =

skelet666 [1.2K]

If we collect like terms of the first equation, we can simplify to

2x - 8 = 180

If we add 8 to both sides, we get

2x = 188

And that means x = 94

If we substitute this into the second equation, we get

7(94) - 8 = ?

7 x 94 is equal to 658

658 - 8 = 650

8 0

2 years ago

The figure shows the letter Z and four of its transformed images—A, B, C, and D:

tiny-mole [99]

Given:

The figure shows the letter Z and four of its transformed images—A, B, C, and D.

To find:

Which of the following rules will transform the pre-image of Z in quadrant 2 into its image in quadrant 1?

Solution:

From the figure it is clear that the pre-image of Z in quadrant 2 and its image in quadrant 1 (image A) are the mirror image of each other along the y-axis.

It means the pre-image of Z in quadrant 2 reflected across the y-axis to get the image in quadrant 1.

If a figure reflected across the y-axis, then rule of transformation is

$(x,y)\to (-x,y)$

So, the rule $(x,y)\to (-x,y)$ transform the pre-image of Z in quadrant 2 into its image in quadrant 1.

Therefore, the correct option is c.

3 0

3 years ago