Calculate the difference quotient and average velocity, Basic Statistics

 

A girl named Alice fell asleep during a discussion about the difference quotient.

She did not think it could possibly have anything to do with real life. While dreaming she saw a white rabbit. The white rabbit told her she shouldn't fall asleep during math class. The rabbit told her that even the most abstract topics sometimes produced solutions to challenging real world problems. He also told her of the power of the number zero, and the great things could be accomplished if she understood inffinitesimals. But beware said the rabbit, when doing these computations you must be very careful. The rabbit showed her the following calculation:

Lets begin by saying that x = 1 and y = 1.

Ok, said Alice. Then what? The rabbit showed her the following equation.

x2 - y2 = x2 - xy:

He asked Alice if the equation represented a true statement. Alice frowned. She didn't like math. She studied the equation hard. She didn't know what the rabbit was asking. Then the rabbit helped her out. This is a problem from

MAT0024 he told her. You studied this problem two semesters ago. You liked math back then, he told Alice, you even got an A in that class. Just plug in

x = 1 and y = 1 and see if it is true. She wrote the following:

x2 - y2 = x2 - xy:

Alice plugged in x = 1 and y = 1 and obtained

12 - 12 = 12 - 1 = 1

and that results in

0 = 0:

Yes!, it is a true statement Alice proclaimed. Ok, good said the rabbit. If x = 1 and y = 1, then the equation is a true statement. But do you really, really believe it is a true statement Alice? Yes, of course she replied. Ok good, but now I want you to factor the equation and then plug in x = 1 and y = 1. Alice was good at factoring. On the left side of the equation she used the di_erence of squares formula and on the right side of the equation she factored out an x. Just like the rabbit told her, she factored, then cancelled like terms, then plugged in the x = 1 and y = 1. this is what she got.

x2 - y2 = x2 - xy:

Factoring the left hand side using the difference of squares and factoring x from right hand side, we get

(x + y)(x - y) = x(x - y):

Dividing both sides by x - y we get

(x + y) = x:

Since x = 1 and y = 1, we get

2 = 1:

Hey! said Alice, how did I end up with 2 = 1 when I was using a true statement? Was my factoring wrong, she asked. Nope, said the rabbit. The rabbit then hopped away. Wondering what type of math magic awaited her in a world where 2 = 1, Alice followed the rabbit down the hole.

While sliding down the rabbit hole, Alice's speed was given by the function

f(x) = 4x2;

where x is in seconds and f(x) represents feet. It took Alice 20 seconds to slide all the way into wonderland. If a human's instantaneous velocity is more than 80 feet per second upon entry into wonderland, he/she will be killed. Did Alice survive the trip into wonderland? Make the following calculations:

1. Calculate Alice's average velocity over the intervals [19:5; 20]; [19:9; 20]; [19:99; 20], and then estimate Alice's instantaneous rate of change at x = 20.

2. Calculate the difference quotient for f(x) and let h = 0; x = 20 (make sure you simplify the difference quotient before plugging in these values).

What does this say about Alice's instantaneous rate of change at x = 20?

Posted Date: 3/18/2013 5:24:51 AM | Location : United States







Related Discussions:- Calculate the difference quotient and average velocity, Assignment Help, Ask Question on Calculate the difference quotient and average velocity, Get Answer, Expert's Help, Calculate the difference quotient and average velocity Discussions

Write discussion on Calculate the difference quotient and average velocity
Your posts are moderated
Related Questions
what is the relationship of cost accounting to financial and management accounting?

A sample of 40 golfers showed that their average on a particular course was 94 with a standard deviation of 6. a. Find the 95% confidence interval of the mean score for all golf

Check numbers for No Neighboring States with Video Gaming, 2% inflation, 4 Average Bets Numbers for 2018 Average Return -0.082 Net Income -$2,052,859 End of Year Cash $5,0

A study was conducted at a major north-eastern American medical centre regarding blood cholesterol levels and heart-attack incidents. A total of 28 heart-attack patients had their

AFRS - Talk about AGENCY FINANCIAL REPORTING SYSTEM.

Define the Management or Managerial Accounting System. Ans.  As the name suggest management or managerial accounting system refers to the Management of the firm or company,

Consider the two events A and B with P(A) = 0.4 and P(B) = 0.3. (a) If A and B are independent then compute the probability that Both A and B happen

why indux number considerd as an economic barrometer

From the following cost, production and sales data of Decors Motor Ltd., prepare comparative income statement for three years under (i) absorption costing method, and (ii) marginal

solution of problems based on coefficient of covariance