1. A right triangle has legs of length h and r and a hypotenuse of length 4. It is revolved about the leg of length h to sweep out a circular cone. What values of h and r maximize volume of the cone?

2. A rectangular page in a textbook (with width x and length y) has an area of 98^2, top and bottom margins set at 1 in, and left and right margins set at 1/2 in. The printable area of the page is the rectangle that lies within the margins. What are the dimensions of the page that maximize the printable area?

3. What point on the graph of f(x)= 5/2 - x^2 is closest to the origin? (Hint: you can minimize the square of the distance)

4. A line segment of length 10 joins the points (0,p) and (q,0) to form a triangle in the first quadrant. Find the values of p and q that maximize the area of the triangle.

5. A metal cistern in the shape of a right circular cylinder with volume V= 50 m^3 needs to be painted each year to prevent corrosion. The paint is only applied to surfaces exposed to the elements ( the outside cylinder wall and the circular top.) Find the dimensions r and h of the cylinder that minimize the area of the painted surfaces.

Operate along its production possibilities frontier : In deciding where to operate along its production possibilities frontier, a society is answering the question of |

The mean value theorem occurs at the midpoint : Prove: if f(x) = a2x^2 + a1x +a0 (a2 is not = 0), then the number c whose existence is guaranteed by the Mean Value Theorem occurs at the midpoint of the interval [a,b]. |

What traits does the leader possess : What traits (that is, what attributes and characteristics), does the leader possess that you think make this leader effective. How would you describe this leaders' personality |

Explain how to plug in the numbers in a calculator : (3/2) * (0.75 (√2(2+1)) -1)/0.25) *1 = 3.95can you explain with in details how to get to 3.95 answer, explain how to plug in the numbers in a calculator |

A right triangle has legs of length h and r and a hypotenuse : 1. A right triangle has legs of length h and r and a hypotenuse of length 4. It is revolved about the leg of length h to sweep out a circular cone. What values of h and r maximize volume of the cone?2. A rectangular page in a textbook (with width x a.. |

Discuss marketing concepts-the 4 ps of marketing : You should consider and discuss marketing concepts such as the 4 P's of marketing (product, price, place, and promotion), target market, research and development, trend forecasting, etc\ |

What two things were not allowed in spanish colonies : What two things were not allowed in spanish colonies. |

Define three criteria for evaluating effective group work : Define the three criteria for evaluating effective team/group work (as stated in the textbook) and analyze whether the "team" in the video is effective or not. |

Compare activities of soviet film industry : Compare the activities of the Soviet film industry during the War Communism period (1918-1920) and during the years of the New Economic Policy (1921-1924) |

## Validity of arguments using euler circlestruth tables arevalidity of arguments using euler circles.truth tables are related to euler circles. arguments in the form of euler |

## Cnsider quadrilateral abcd with a -34 b 26 c 2-1 and dquestion consider quadrilateral abcd with a -34 b 26 c 2-1 and d -3-3. find the area and perimeter of abcd. please |

## Express the manufacturers monthly profit as a functiona manufacturer can produce cassette tape records at a cost of $40 a piece,its estimates that if the tape records are sold for p dollar a piece.consumer will buy 120-p of them a month , express the manufacturers monthly profit as a function of pric.. |

## Is there linear relation between square footage and askingone of the biggest factors in determining the value of a home is the square footage. the accompanying data represent |

## What is angualr velocityif the mass of 41 kg and height 1.28 m. radius of rotation is 0.78 m and Angular velocity is 0.27 rad/s. If r2 is 0.39 m. So what is angualr velocity? |

## What is the speed of the currentA boat can travel 54 mph in still water. if it travels 236 miles with the current in the same length of time it travels 196 miles against the current what is the speed of the current? |

## Find the tax the owner will have to payBusiness and finance. In Bucks County, the property tax rate is $25.32 per $1000 of assessed value. If a house and property have a value of $128,000, find the tax the owner will have to pay. |

## Depict a quadratic equation in the variable xWrite a quadratic equation in the variable x having the given number as solutions.Type the equation in standard form, ax^2 + b x + c =0 Solution: 6, only solution the equation is ? =0 |

## Plan for the distribution of salary increasesDevelop a plan for the distribution of salary increases. Suppose you are employed in a local industry, and your supervisor has assigned you to distribute annual raises that must average 4% per department among 6 team members. |

## What type of growth pattern is representedWhat type of growth pattern is represented here: 5x10^3, 1x10^4, 2x10^4, 4x10^4, 8x10^4? |

## What are the mean and standard deviation of the scoresSuppose that Ford's performance scores really are Normally distributed. This year, managers with scores less than 31 received C's and those with scores above 595 received A's. What are the mean and standard deviation of the scores? |

## Create a system of linear equations from your own lifeCreate your system of linear equations then write a brief paper describing the system. Is this a consistent system or inconsistent system? |

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