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3 years ago

13

8x2y2 – + 4x4 – 7xy3

1 answer:

Elodia [21]3 years ago

3 0

<span>a
-7xy3 + 8x2y2 - + 4x4</span>

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llyssa and Mark conducted an experiment with two identical spinners that each contain 4 colors. They spun both spinners and reco

pychu [463]

Answer:

Step-by-step explanation:

Answer is a 2/25

7 0

3 years ago

Finding distance between each pair of points. how to know which is x1 y1 and x2 y2 when using (x2-x1)^2 + (y2-y1)^2? People are

denpristay [2]

<u>It doesn't matter what order the coordinates are in the distance formula as long as it stays in it's corresponding order.</u> In this case, (-7,5) could be (x1,y1) and (3,-5) could be (x2,y2) or vise versa, just as long as you don't mix up the coordinates (so no (-7,-5) or (3,5)). I'll demonstrate this below:

$\sqrt{(-7-3)^2+(5-(-5))^2}\\\sqrt{(-10)^2+(10)^2}\\\sqrt{100+100}\\\sqrt{200}\\\\\sqrt{(3-(-7))^2+(-5-5)^2}\\\sqrt{(10)^2+(-10)^2}\\\sqrt{100+100}\\\sqrt{200}$

<u>The distance between these points, no matter the order, is √200, or approximately 14.14 units.</u>

7 0

3 years ago

A farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. Find the maximum area he can close.

Margarita [4]

Answer:

Width of 37.5 feet and length of 50 feet will maximize the area.

Step-by-step explanation:

Let w represent width and l represent length of the pen.

We have been given that a farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. We are asked to find the dimensions that will maximize the area.

We can see from the attachment that the perimeter of the pens would be $4w+3l$ .

We can set our given information in an equation $4w+3l=300$ .

The area of the two pens would be $A=2l\cdot w$ .

From perimeter equation, we will get:

$w=\frac{300-3l}{4}$

Substituting this value in area equation, we will get:

$A=2l\cdot (\frac{300-3l}{4})$

Since we need to maximize area, so we need to find derivative of area function as:

$A=\frac{600l-6l^2}{4}$

Bring out the constant:

$A=\frac{1}{4}*\frac{d}{dl}(600l-6l^2)$

$A=\frac{1}{4}*(600-12l)$

$A=150-3l$

Now, we will set our derivative equal to 0 as:

$150-3l=0$

$150=3l$

$\frac{150}{3}=\frac{3l}{3}$

$50=l$

Now, we will substitute $l=50$ in equation $w=\frac{300-3l}{4}$ to solve for width as:

$w=\frac{300-3(50)}{4}$

$w=\frac{300-150}{4}$

$w=\frac{150}{4}$

$w=37.5$

Therefore, width of 37.5 feet and length of 50 feet will maximize the area.

8 0

3 years ago

Line has equation 3x + y = 15<br><br> Find the gradient of the line.

inessss [21]

Answer:

-3

Step-by-step explanation:

We can add -3x to put the equation into slope-intercept form.

y = -3x +15

The gradient of the line (slope) is the coefficient of x: -3.

The gradient is -3.

5 0

2 years ago

a rectangular prism has a volume of 810 cubic meters. it has a length of 10 meters and a width of 9 meters. What is the height o

Ainat [17]

Answer:

The height of the prism is 9 meters

Step-by-step explanation:

* Lets describe the rectangular prism

- The rectangular prism has six rectangular faces

- Two of them are bases and the other four are side faces

- The rectangular prism has three dimensions length, width , height

- The volume of any prism = Area of the base × its height

∵ The base of the rectangular prism is a rectangle

∵ Area any rectangle = length × width

∴ The volume of the rectangular prism V = length × width × height

* Lets solve the problem

∵ The volume of the prism is 810 meter³

∵ Its length is 10 meter

∵ Its width is 9 meters

∵ V = length × width × height

- Substitute the values of the volume , the length and the width in

the equation of V

∴ 810 = 10 × 9 × h

∴ 810 = 90 × h

- Divide both sides by 90

∴ 9 = h

∴ The height of the prism is 9 meters

6 0

3 years ago