A bucket that weighs 5 pounds and a rope of negligible weight are used to draw water from a well that is 80 feet deep. The bucket is filled with 45 pounds of water and is pulled up at a rate of 2.5 feet per second, but water leaks out of a hole in the bucket at a rate of 0.2 pounds per second. Find the work done pulling the bucket to the top of the well. Your answer must include the correct units.

## What are the dimensions of the study plotA rectangular study plot is to be enclosed by 625 m of fencing. What are the dimensions of the study plot that will have the largest area? |

## Calculate its eigenvalueLet u = [2,1,1]^T, v = [1,3,2]^T (i.e. they are column vectors). Caclulate v^Tu and uv^T. Show that u is an eigenvector of the matrix uv^T and calculate its eigenvalue. |

## At what rate is the radius changing after ten minutesA spherical ballon is being inflated at the rate of 5 cubic inches a minute. At what rate is the radius changing after ten minutes? |

## Find the area of region using definite integralsCompactness and find the Area of region using definite integrals |

## Integrating a differential equationIntegrating a differential equation given the initial values and exponentiate both sides of the equation for to solve for P(t) |

## Implications-contrapositives and conversesUse truth tables to prove that an implication is always equivalent to its contrapositive. Site an example where this is so. Use truth tables to prove that an implication may not be equivalent to its converse. Site an example where this is so. |

## Find the absolute relative approximate error at the endUse the Newton-Raphson method of finding roots of equations to find the minimum number of computers that need to be sold to make a profit. Conduct three iterations to estimate the root of the above equations. |

## State eulers circuit theoremState Euler's Circuit Theorem. Explain why this theorem should be true and explain Cantor's Diagonalization Argument. Give examples and explain what this argument was used for. |

## Find the expectation is a person buys two ticketsA lottery has one 2000.00 prize, two 1000.00 prizes and ten 500.00 prizes. Two thousand tickets are sold at 5.00 each. Find the expectation is a person buys two tickets? |

## Explain information about poisson distributionInformation about "Poisson Distribution". During cross country pipeline construction, day production rates of more than 120 girth welds are not unusual. On pipe laying barges operating around the clock, |

## What are the dimensions of the corral of maximum areaa rancher wishes to enclose a rectangular corral with 320 feet of fencing. the fencing only required 3 sides because of an existing wall. what are the dimensions of the corral of maximum area? |

## Find a linear formula for the costThe monthly charge for a waste collection serive is $32 for 100 kg of waste and $48 for 180 kg of waste. Find a linear formula for the cost, C, of waste collection as a function of the number of kilograms of waste, w. |

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