SOLUTION: My question pertains to a rational function that appears on page 36 in W.W. Sawyer's short book(not a textbook) entitled What Is Calculus About? At one point on this page, Sawyer s

Algebra ->  Rational-functions -> SOLUTION: My question pertains to a rational function that appears on page 36 in W.W. Sawyer's short book(not a textbook) entitled What Is Calculus About? At one point on this page, Sawyer s      Log On


   

Question 170223: My question pertains to a rational function that appears on page 36 in W.W. Sawyer's short book(not a textbook) entitled What Is Calculus About? At one point on this page, Sawyer says that velocity equals (-1)x t^-2. So, the equation is v= (1)x t^-2. Sawyer notes that ^t-2 can be changed to 1/t^2. Then he says that v= -1/t^2.
But when I multiply -1/-1 times 1/t^2 I get -1/-t^2 instead of -1/t^2. I assume that I am doing something wrong. What am I doing wrong? Why does the correct transformation result in -1/t^2 rather than -1/-t^2?
Answer by maali40(13) About Me  (Show Source):
You can put this solution on YOUR website!
Seems your question is in regard to using implied multiplication in syntax or using a multiplication symbol (for example 3*4=12) (5b=5*b) (course we don't say 54=5*4 unless defined only have 0 to 9 in use and using implied multiplication then 67=6*7).The question here is are we not saying we are not using implied multiplication since say (-1)*t^..ETC,meaning then the exponent is -2 and have therefore -1/t^2 WHERE OF COURSE UNDERSTOOD t^-2 THE '-SIGN' NOT ALGEBRA OPERATOR BUT SYMBOL USED TO DENOTE RECIPROCAL (t^2)-1=1/t^2.If did have implied mulltiplication t^-x would be 1/t^1*x=(1/t^1)*x=x/t. Problem if using implied multiplication and wanted exponent to be -x=-1*x and said have t^(-x) ,there is a standard symbol named superscript which example of use is 5^(3) =5!/(5-3)! where note that is not algebra - operator but more like what most may think - is.So when see b=x/y and a^b understand did not want to say a^(x/y) also did not want to say (a^x)^(1/y)or (a^x)^(y^-1).Course if want an exponent b*c could do (a^b)^c.Did I correctlly assume your question was in regard to syntax so all would read the same? Hope helps you .Course remember I am not saying there is any worth in any of this except standard simple knowledge in country where who cares what you know?And I've heard for example POE died broke in jail.yours truly M. Ali ( just for fun won't check my typing anymore just post see if you find errors?)