1 / 18

This is problem 49 page 219:

This is problem 49 page 219:

hao
Download Presentation

This is problem 49 page 219:

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. This is problem 49 page 219: A man is in a boat 2 miles from the nearest point on the coast. He is to go to a point Q, located 3 miles down the coast and 1 mile inland. If he can row at 2 miles per hour and walk at 4 miles per hour, toward what point on the coast should he row in order to reach point Q in the least amount of time.

  2. Need a picture: Find x to minimize time 2 miles 3 - x x 1 mile Q 3 miles

  3. Use the Pythagorean theorem twice to find the distance to row and walk To row: To walk:

  4. The time to row is: Notice I used unit analysis to find I had to divide by 2 and not multiply by 2 The time to walk is:

  5. The primary equation is the total time: We don’t need a “secondary equation”. Why? The primary equation only has one variable, there is no need to substitute for a second variable.

  6. To minimize, find the derivative = 0 This will be good chain rule practice Outside Inside Outside Inside Do you see another chain rule here?

  7. We need to solve this mess = 0 First, let’s clean it up a bit by multiplying constants Wow, let’s cheat and use MathPert to graph this and find the solution

  8. Click on this

  9. Now this

  10. Select “Type it in”

  11. note the use of ( ) everywhere and the use of negative exponents now click OK

  12. Make sure this is the equation we want and it is. Click OK again

  13. Here is our graph, we want where it equals 0, ie, the x-intercept click this about 4 times to get a better view

  14. This looks like the point

  15. Use the Point and Slope Tool click it and center the crosshairs on the intercept

  16. y = 0 and x = 1 this is where the derivative is equal to 0! We just use a ‘numerical” technique to solve the equation

  17. Just to make sure, evaluate at x = 1: You should get: The man should aim for a point 1 mile down the coast

  18. To review what I typed into MathPert: 1/2((x^2+4)^(-1/2)(x))-1/4((3-x)^2+1)(-1/2)(3-x)) “Count” the number of opening (( versus the number of closing )), they must match in any expression. I could also type, which is easier: x/2sqrt(x^2+4)-(3-x)/4sqrt((3-x)^2+1)

More Related