Find two positive numbers whose sum is 170 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) First Second Product, P Number, x Number 40 170 - 40 40(170 – 40) = 5,200 50 170 – 50 50(170 – 50) = 6,000 60 170 – 60 60(170 – 60) = 6600 70 170 – 70 70(170 – 70) = 7000 80 170 - 80 80(170 – 80) = 7200 90 170 – 90 90(170 – 90) = 7200 (b) Write the product P as a function of x. x(170 – x) P(x) = (c) Use calculus to find the critical number of the function in part (b). Then find the two numbers. (Enter your answers as a comma-sep. x= 85

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.4: Partial Fractions
Problem 1SE: Can any quotient of polynomials be decomposed into at least two partial fractions? If so, explain...
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Find two positive numbers whose sum is 170 and whose product is a maximum.
(a)
Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
First
Second
Product, P
Number, x
Number
40
170 – 40
40(170 – 40) = 5,200
-
50
170 – 50
50(170 – 50) = 6,000
60
170 – 60
60(170 – 60) = 6600
-
|
70
170 – 70
70(170 – 70) = 7000
%3D
80
170
80
80(170 – 80) = 7200
90
170 – 90
90(170 -
90) = 7200
%3D
(b)
Write the product P as a function of x.
P(x) =
x(170 – x)
(c)
Use calculus to find the critical number of the function in part (b). Then find the two numbers. (Enter your answers as a comma-separated list.)
x = 85
Transcribed Image Text:Find two positive numbers whose sum is 170 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) First Second Product, P Number, x Number 40 170 – 40 40(170 – 40) = 5,200 - 50 170 – 50 50(170 – 50) = 6,000 60 170 – 60 60(170 – 60) = 6600 - | 70 170 – 70 70(170 – 70) = 7000 %3D 80 170 80 80(170 – 80) = 7200 90 170 – 90 90(170 - 90) = 7200 %3D (b) Write the product P as a function of x. P(x) = x(170 – x) (c) Use calculus to find the critical number of the function in part (b). Then find the two numbers. (Enter your answers as a comma-separated list.) x = 85
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