4.5 Optimization and modeling.notebook
October 26, 2016
DO NOW Week 2
Topic 1: Unit Circle
Without aid, find the following measurements in radians:
Block 1
Topic 2: Writing Equations
2. cos(7pi/6)
1. cubic roots 3 and 2 (multiplicity 2), and y­
int (0, 5)
3. arctan(­1)
2. (1, 3), (2, 27)
1. sin(5pi/6)
4. arccos(­1/2)
exponential
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4.5 Optimization and modeling.notebook
October 26, 2016
Section 4.5: Optimization and Modeling
Example:
1. What are the dimensions of an aluminum can that holds 40 cubic inches of juice and that uses the least material (i.e. aluminum)? Assume that the can is cylindrical, and is capped on both ends.
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4.5 Optimization and modeling.notebook
October 26, 2016
Practical Tips for Modeling Optimization Problems:
1. Make sure that you know what quantity or function is to be optimized.
2. If possible, make several sketches showing how the elements that vary are related. Label your sketches clearly by assigning variable to quantities which change.
3. Try to obtain a formula for the function to be optimized in terms of the variables that you identified in the previous step. If necessary, eliminate from this formula all but one variable. Identify the domain over which this variable varies.
4. Find the critical points and evaluate the function at these points and the endpoints (if relevant) to find the global maxima and minima.
Section 4.5: Optimization and Modeling
Assignment (part 1) worksheet 3
4.5 Optimization and modeling.notebook
October 26, 2016
DO NOW Week 2
Topic 1: Unit Circle
Without aid, find the following measurements in radians:
Block 2
Topic 2: Writing Equations
1. polynomial roots 3 and 2, and y­int (0, 5)
1. sin(2pi/3)
2. cos(pi/6)
2. (1, 2), (2, 8)
3. arcsin(1/2)
4. arccos(­√(2)/2)
exponential
Section 4.5: Optimization and Modeling
Example:
2. Alaina wants to get to the bus stop as quickly as possible. The bus stop is across a grassy park, 2000 feet west and 600 feet north of her starting position. Alaina can walk west along the edge of the park on the sidewalk at a speed of 6 ft/sec. She can also travel through the grass in the park, but only at a rate of 4 ft/sec. What path will get her to the bus stop the fastest?
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4.5 Optimization and modeling.notebook
October 26, 2016
3. One hallway which is 4 feet wide meets another hallway which is 8 feet wide at a right angle. What is the length of the longest ladder which can be carried horizontally around the corner?
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4.5 Optimization and modeling.notebook
October 26, 2016
Section 4.5: Optimization and Modeling
Assignment 4.5 (part 2)
worksheet
DO NOW QUIZ
Topic 1: Unit Circle
Without aid, find the following measurements in radians:
1. sin(pi/6)
Topic 2: Writing Equations
1. Cubic through
2. cos(2pi/3)
(2, 0), (5, 0), (­1, 0), (0, 3)
3. arctan(1)
2. (0, 3), (1, 27)
4. arccos(­1)
exponential
3. linear (8, ­6) , (4, 2)
4. Quadratic (3, 0), (­1, 0) , (0, 4)
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4.5 Optimization and modeling.notebook
October 26, 2016
Section 4.5: Optimization and Modeling
Assignment 4.5 (part 3)
pages 203 #'s 13, 17, 19, 21
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