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Fittoniya [83]
2 years ago
5

A cable weighing 0.6 pounds per foot is attached to a small 80-pound robot, and then the robot is lowered into a 60-foot deep we

ll to retrieve a 7-pound wrench. The robot gets out of the well (carrying the wrench) by climbing up the cable with one end of the cable still attached to the robot. How much work does the robot do in climbing to the top of the well? Work = ________ foot-pounds
Mathematics
1 answer:
ollegr [7]2 years ago
5 0

Answer:6060 foot-pounds

Step-by-step explanation:

Given

Weight of cable(w')=0.6 pound per foot

depth of well=60 foot

weight of wrench=7 Pound

Now work done in raising monkey with wrench=w\cdot h

W_1=(80+7)\cdot 60=5220 foot-pounds

Now work done in raising rope

robot rises by climbing up the cable with one end of the cable still attached thus robot support half the weight of cable so work done

W_2==\int_{0}^{60}\frac{w'}{2}xdx

W_2=0.3\times 0.5\times  (x^2)_0^{60}

W_2=540 foot-pounds

W_{net}=5220+540=6060 foot-pounds

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2 years ago
Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sampl
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(a) The sample variance is 16.51

(a) The sample standard deviation is 4.06

Step-by-step explanation:

Given

\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}

Solving (a); The sample variance.

First, calculate the class midpoints.

This is the mean of the intervals.

i.e.

x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13

x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88

x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63

x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38

x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13

So, the table becomes:

\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}

Next, calculate the mean

\bar x = \frac{\sum fx}{\sum f}

\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}

\bar x = \frac{1845.73}{146}

\bar x = 12.64

Next, the sample variance is:

\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}

So, we have:

\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}

\sigma^2 = \frac{2393.6875}{145}

\sigma^2 = 16.51

The sample standard deviation is:

\sigma = \sqrt{\sigma^2}

\sigma = \sqrt{16.51}

\sigma = 4.06

6 0
2 years ago
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