Calculus Optimization Worksheet A Rain Gutter Is To Be Constructed

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Calculus optimization worksheet a rain gutter is to be constructed.

To calculate the area split the cross section of the gutter into two triangles and a rectangle. You da real mvps. Textbook solution for single variable calculus 8th edition james stewart chapter 3 7 problem 76e. Maximizing or minimizing some quantity so as to optimize some outcome calculus is the principal tool in finding the best solutions to these practical problems.

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle theta. How should theta be chosen so that the gutter will carry the maximum amount of water. How should θ be chosen so that the gutter will carry the maximum amount of water. 1 per month helps.

Verify if it is a maximum or minimum using the 2nd derivative test when easy otherwise use the 1st derivative test. The parts for each smartphone cost 50 and the labor and overhead for running the plant cost 6000 per day. Here are the steps in the optimization problem solving process. Differential calculus published in vacaville california usa a rain gutter is to be constructed from a metal sheet of width 30 cm.

1 a company has started selling a new type of smartphone at the price of 110 0 05 x where x is the number of smartphones manufactured per day. 1 draw a diagram depicting the problem scenario but show only the essentials. A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle θ. Optimization problems name calculus ab for each of the following define your variables write an equation representing the quantity to be maximized or minimized and solve the problem.

Thanks to all of you who support me on patreon. Determine what theta should be chosen so that the gutter will carry the most water when it is full. We need to begin by constructing a function which gives the area of the gutter in terms of theta. A rain gutter is to be constructed from a metal sheet of width 30cm by bending up one third of the sheet on each side by an angle theta from the horizontal theta zero represents the unbent sheet.