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Determining the best place to sit at the movies based on a set of criteria.

A movie theater has a screen that is positioned 10 feet off the floor and is 25 feet high. The first row of seats is placed 9 feet from the screen and the rows are 3 feet apart. The floor of the seating area is inclined at an angle above the horizontal and the distance up the incline that you sit is x. The theater has 21 rows of seats. ---insert the first file image here--- Suppose you decide that the best place to sit is in the row where the angle subtended by the screen at your eyes is a maximum. Let's also suppose that your eyes are 4 feet above the floor. Show that: ---insert the second file image here--- Use a graph of theta as a function of x to estimate the value of x... click for more

Subject:

Math

Topic:

Calculus

Posting ID:

2358

OTA ID:

102499

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Finding the maximum area of a rectangle.

Find the maximum area of a rectangle in the first quadrant with one corner at the origin, two sides on the coordinate axes, and one corner on the graph of y=-lnx , y>0

Subject:

Math

Topic:

Calculus

Posting ID:

2455

OTA ID:

101298

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Area of a rectangle

A rectangular lot, 54 square yds. in area with a perimeter fence, is divided into 2 rectangular sections by a single connecting fence costing $2.00/yd. the perimeter fence costs $5.00/yd. Find the dimensions of the lot which minimizes the cost of fencing.

Subject:

Math

Topic:

Calculus

Posting ID:

2456

OTA ID:

101298

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Optimization of surface area with a known perimeter.

You have 80 inches of wire. You can break it into two pieces or leave it intact. You're going to bend the pieces into squares. What are the maximum and minimum possible total areas of these squares?

Subject:

Math

Topic:

Calculus

Posting ID:

2717

OTA ID:

103020

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Working with natural logs and ln x.

What is the square root of the ln of x?

Subject:

Math

Topic:

Calculus

Posting ID:

2718

OTA ID:

101298

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