Download presentation

Presentation is loading. Please wait.

Published byLina Rackliffe Modified over 2 years ago

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: Q 1 mile 2 miles 3 miles x 3 - x Find x to minimize time

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 OutsideInside OutsideInside 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)

Similar presentations

OK

Section 8-1: Introduction to Irrational Algebraic Functions.

Section 8-1: Introduction to Irrational Algebraic Functions.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on product specification form Microsoft office ppt online maker Ppt on periscope View my ppt online ticket Ppt on latest technology in computer science Ppt on cartesian product sets Ppt on natural resources water Ppt on monetary economics Ppt on new zealand culture and family tradition Run ppt on html website