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sladkih [1.3K]
2 years ago
14

PLEASE HELP!!!

Mathematics
1 answer:
lana [24]2 years ago
4 0

EXPLANATION: By definition two lines are said to be parallel when the distance between two lines is same when measured from any point on one line.

However the criteria for intersection is that the distance between two lines should change and eventually should change to zero at intersection point.


Step-by-step explanation:

.

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An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the
Nitella [24]

Answer:

W=2452.5 J

Step-by-step explanation:

The work is define as the integral of the force times distance. So we have:

W=\int^{a}_{b}Fxdx

Now, we can write the force in terms of density.

F=m*g=\rho Vg

V is the volume (V=2*1*1=2 m³)

So the work will be:

W=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0}19620xdx=19620(\frac{x^{2}}{2})|^{0.5}_{0}

The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.

W=19620(\frac{x^{2}}{2})|^{0.5}_{0}=19620(\frac{0.5^{2}}{2})

W=2452.5 J

I hope it helps you!

8 0
3 years ago
An open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the
natka813 [3]

Please find the attachment.

Let x represent the side length of the squares.

We have been given that an open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. We are asked to find the volume of the box.

The side of box will be 8-x-x=8-2x and 10-x-x=10-2x.

The height of the box will be x.

The volume of box will be area of base times height.

\text{Volume of box}=(8-2x)(10-2x)\cdot x

Now we will use FOIL to simplify our expression.

\text{Volume of box}=(80-16x-20x+4x^2)\cdot x

\text{Volume of box}=(80-36x+4x^2)\cdot x

Now we will distribute x.

\text{Volume of box}=80x-36x^2+4x^3

V(x)=80x-36x^2+4x^3

Therefore, the volume of the box would be V(x)=80x-36x^2+4x^3.

6 0
2 years ago
PLEASE HELP ILL GIVE U BRAINLEST PLUS 50 POINTS IF U GET IT RIGHT
timama [110]

Answer:

{x}^{2}  + 17x + 3

Step-by-step explanation:

on the picture

if it's helpful ❤❤❤❤

THANK YOU

7 0
3 years ago
Problem Page The price of a notebook was $3.90 yesterday. Today, the price fell to $3.40 . Find the percentage decrease. Round y
OleMash [197]
Always find the difference in prices first. 
<span>3.45 - 3.20 = $.25 difference </span>

<span>Always divide the difference by the original price. Change this number into a per cent. </span>
<span>.25/3.45 = .07246 = 7.2% decrease </span>
6 0
3 years ago
Read 2 more answers
The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is cl
gladu [14]

Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

  • from perihelion to the sun in terms of ellipse is a-c;
  • from aphelion to the sun in terms of ellipse is a+c.

Then

\left\{\begin{array}{l}a-c=741,000,000\\a+c=817,000,000\end{array}\right.

Add these two equations:

2a=1,558,000,000 \\ \\a=779,000,000

and subtract first equation from the second:

2c=76,000,000 \\ \\c=38,000,000.

Note that b=\sqrt{a^2-c^2}, thus

b=\sqrt{779,000,000^2-38,000,000^2}=\sqrt{605,397,000,000,000,000}.

The equation for the planet's orbit is

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\Rightarrow \dfrac{x^2}{606,841,000,000,000,000}+\dfrac{y^2}{605,397,000,000,000,000}=1.

7 0
3 years ago
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