Suppose x and y are two possitive numbers. Write an expression for their average, and then for the reciprocal of their average

- toxicsugar22

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- anonymous

what is the average of n numbers?

- toxicsugar22

i dk am i dupposed to know or is it in the question

- anonymous

you are supposed to know.

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## More answers

- anonymous

suppose I had profits of 1000 dollars in one month and a profit of 500 dollars is the next month, what is my average profit for the two months?

- anonymous

in other words, what is my average profit per month?

- toxicsugar22

750

- anonymous

okay, good. how did you figure that out?

- anonymous

doing good sugar haha (:

- toxicsugar22

i added 1000 and 500 and divided by 2 to get the average

- anonymous

good.
so what if I told you that my profit for first month was 1000, second month was 500 and third month was 600. what is my average profit?

- toxicsugar22

700

- anonymous

very good. what did you do to get that answer?

- toxicsugar22

i added all three and divided it by three

- anonymous

good. so what if I told you my profit for the first month was x and my profit for second month was y, what is my average profit?

- toxicsugar22

would it be x+y divided by 2

- anonymous

exactly! very good!

- anonymous

so your expression is average = (x+y)/2

- anonymous

if you had 10 numbers, then your average would be
(a+b+c+d+e+f+g+h+i+j)/10

- anonymous

where a,b,c... are the 10 numbers

- toxicsugar22

ok and can u tell me how do i write the recipocal of the average

- anonymous

reciprocal of a number x is 1/x.
the reciprocal is a number, which when multiplied by x, gives you 1. 1 is called the multiplicative identity.
so, when you multiply x times 1/x, you get x/x = 1
similarly, what is the reciprocal of the number (x+y)/2 ?

- toxicsugar22

ok i got it its 2/(x+y)

- anonymous

okay very good!

- toxicsugar22

and one more quesion, for the same numbers x and y, write an expresiion for their average of their recipocals
how do i do that

- anonymous

what is the reciprocal of x?
what is the reciprocal of y?

- toxicsugar22

x/1 and y/1 is that right

- anonymous

so if you multiply x times x/1 you will get 1? are you sure?

- toxicsugar22

im srry 1/x and 1/y

- anonymous

okay good. so now you have two numbers 1/x and 1/y.
what is their average?

- toxicsugar22

2/xy

- anonymous

no. thats wrong. the average of two numbers a and b is (a+b)/2
so what is the average of two numbers 1/x and 1/y?

- toxicsugar22

(1/x+1/y)/2

- anonymous

okay. good. that is your answer.
you can simplify the expression further if you want, but that is the answer to your question.
1/x+1/y = (x+y)/xy
so (1/x+1/y)/2 = (x+y)/2xy

- toxicsugar22

ok thank you

- anonymous

or rather, 2(x+y)/xy

- anonymous

no, its the first one. sorry.

- toxicsugar22

ok thanks

- anonymous

(:

- toxicsugar22

hey can u help me with another question math mind can u try

- toxicsugar22

Andy drives 300 miles to Lake Tahoe at 70 miles per hour and returns home at 50 mph. What is his average speed for the round trip. (It is not 6o miles per hour.)
Write expressions for the time it takes for each leg of the trip if Andy drives a distance d, at speed r base 1 and returns at speed r base 2

- anonymous

post it up as a new question, it's better

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