1. Consider the following probiem: Find two numbers whose sum is 17 and whose pr
ID: 3115150 • Letter: 1
Question
1. Consider the following probiem: Find two numbers whose sum is 17 and whose product is as large as possible. (a) Experiment with the problem by making a table like the one following, showing the product of different pairs of numbers that add up to 17. On the basis or the evidence in your table, estimate the answer to the problem. (Round your answers to one decimal place. Enter your answers as a comma-separated list.) Second number y 16 15 Product p 16 30 42 First number x (b) Find a function that models the product in terms of x, the first of the two numbers Px) - (c) Use your model to soive the problem, Compare with your answer to part (a). (Enter your answers as a comma-separated sst.) Need Help? PoEHExplanation / Answer
Ans(a):
First number x
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from the above table we see that maximum product (72) occurs when numbers are (8,9) or (9,8)
so My estimate is middle of them that is maximum product occurs at (8+9)/2=8.5
then first number = x = 8.5
second number = y = 17-8.5= 8.5
product p = xy= 8.5*8.5=72.25
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Ans(b):
let x be the first number then other will be (17-x)
hence the product will be (x)(17-x)
then the function will be p(x)=(x)(17-x)
or p(x)=-x^2+17x
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Ans(c):
p(x)=-x^2+17x is a quadratic equation of type y=ax^2+bx+c and we know that max or min occurs at it's vertex
vertex is given by formula x=-b/(2a=-17/(2*(-1))=8.5
which is same x-value that we found in part a)
Hence answer is ,
first number = x = 8.5
second number = y = 17-8.5= 8.5
product p = xy= 8.5*8.5=72.25
Ans(a):
First number x
Second number y Product P 1 16 16 2 15 30 3 14 42 4 13 52 5 12 60 6 11 66 7 10 70 8 9 72 9 8 72 10 7 70 11 6 66 12 5 60 13 4 52 14 3 42 15 2 30 16 1 16 17 0 0Related Questions
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