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3 years ago

15

A chain 18 feet long whose weight is 84 pounds is hanging over the edge of a tall building and does not touch the ground. How mu

ch work is required to lift the entire chain to the top of the building

1 answer:

coldgirl [10]3 years ago

8 0

Answer:

756 feet pound

Step-by-step explanation:

Length of the chain, L = 18 feet

weight of chain, W = 84 pound

If we lift the centre of gravity of the chain, it will entirely lift up. The centre of gravity of the uniform chain is at its mid point. So, the work done

W = weight x half of length

W = 84 x 9

W = 756 feet pound

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Answer:

15 human years is 1 year for a medum sized dog

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after that each human year would be 5 years for a dog estimated

Step-by-step explanation:

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What is the interquartile rang of the following data set? 9,30,2,48,42,18,81,5,55,73,11

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2 years ago

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

irga5000 [103]

Answer:

The rocket hits the ground at a time of 11.59 seconds.

Step-by-step explanation:

The height of the rocket, after x seconds, is given by the following equation:

$y = -16x^2 + 177x + 98$

It hits the ground when $y = 0$ , so we have to find x for which $y = 0$ , which is a quadratic equation.

Finding the roots of a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$y = -16x^2 + 177x + 98$

$-16x^2 + 177x + 98 = 0$

So

$a = -16, b = 177, c = 98$

$\bigtriangleup = 177^{2} - 4(-16)(98) = 37601$

$x_{1} = \frac{-177 + \sqrt{37601}}{2*(-16)} = -0.53$

$x_{2} = \frac{-177 - \sqrt{37601}}{2*(-16)} = 11.59$

Since time is a positive measure, the rocket hits the ground at a time of 11.59 seconds.

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3 years ago

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

<u>x = 2</u>
<u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

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2 years ago

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timama [110]

Answer:

Step-by-step explanation:

6). Equation of the line has been given as,

4x + 9y = -9

By converting this equation into y-intercept form,

9y = -4x - 9

$y=-\frac{4}{9}x-\frac{9}{9}$

$y=-\frac{4}{9}x-1$

By comparing this equation with y = mx + b

Here, m = Slope of the line

b = y-intercept

Slope of the equation (m) = $-\frac{4}{9}$

y-intercept (b) = -1

8). Equation of the line is,

5x + 3y = 12

3y = -5x + 12

$y=-\frac{5}{3}x+\frac{12}{3}$

$y=-\frac{5}{3}x+4$

Slope of the line = $-\frac{5}{3}$

y-intercept = 4

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2 years ago