Two positive numbers have a sum of 60. what is the maximum product of one number times the square of the second number?
a) 3481
b) 3600
c) 27,000
d) 32,000
e) 36,000
So Idk if this is right, but I have ....
x+y=60
p=xy^2
p=x(60x)^2
P'=2x(60x)+(60x^2)
x=.5021 x= 119.498
idk if this is right so far, or if i forgot something. how do I find the max product?
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

why did you square the more complicated factor, why not square the x
p = x^2(60x)
= 60x^2  x^3
dp/dx = 120x  3x^2
= 0 for a max of p
3x(40  x) = 0
x = 0 or x = 40
obviously x=0 will produce the minimum product
if x = 40
then 6040 = 20
so the two numbers are 40 and 20 (with 40 as the number that was squared in the product)
Your way should have worked too, but I notice that you jumped from
.... (60x)^2 to
.....(60x^2) , that is an error.
my product is (40^2)(20) = 32 000
btw, your two numbers don't even add up to 60 👍
 👎
 ℹ️
 🚩
answered by Reiny
Answer this Question
Related Questions

math
find each sum or difference 1. 1/2 + 1/3 1. 1/6 2. 1/3 3. 2/3 4. 1/6 I got 2/3 because I added the 2 numerators and got 2 then I kept the LCM as the denominator so I got 2/3. 2. 3 1/5 + 6 1/2 1. 3 2/7 2. 3 7/10 3. 9 2/7 4. 9 7/10 I got number 3
 asked by { Alice} please helppp
 8,707 views

ALGEBRA
which of the following are reasonable answer for the product of two negatives and a positive a. 20** b. 10 c. 20 d. 10 Which statement about the product is true 5.5⋅√5 a. The product is rational b. The product is irrational**** c. The product is
 asked by BUBBLES
 4,743 views

math
The Sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number.What is the value of the greater number minus the lesser number? The list of numbers 41,35,30,x,y,15 has a median of 25 . The mode of the list of
 asked by Anonymous
 5,204 views

math
The sum of two positive numbers is 90. Find a function that models their product P in terms of x, one of the numbers.
 asked by monic
 2,638 views

Algebra
My answer *** What is the product of (–6.8)2? a. –13.6 b. 46.24*** c. –46.24 d. 13.6 2. Simplify the expression  Square root 196 . a. 98 b. –14*** c. 14 d. 392 3. Simplify the expression square root 100/49 . a. 10/7 b. 17*** c. 5/7 d. 20/7 4. Find
 asked by c
 14,109 views

Geometry
Find one counterexample to show that each conjecture is false. The product of two positive numbers is greater than either number.
 asked by Catelin
 9,763 views

Algebra
Please check all of my answers and tell me if they are right. 1. What is the simplified form of the following expression? 7m^2 + 6.5n – 4n + 2.5m^2 – n (1 point) A. 9.5m^2 + 1.5n*** B. 4.5m^2 + 1.5n C. 1.5m^2 – 4.2n D. 9.5m^2 – 1.5n 2. Simplify the
 asked by HELP
 5,737 views

math
Can someone help me with prime and composite numbers? Prime numbers are counting numbers that can be divided evenly bt only two numbers:1 and themselves. A prime number can also be described as a counting number with exactly two factors, 1 and itself. So,
 asked by haylo
 6,721 views

algebra
One number is 4 times and then positive number. The sum of the two numbers is 620. Find the two numbers.
 asked by kate
 1,827 views

Multiple Choice HELP!
What is a counterexample for the conjecture? Conjecture: The product of two positive numbers is greater than the sum of the two numbers. A. 3 and 5 B. 2 and 2 C. A counterexample exists, but it is not shown above. D. There is no counterexample. The
 asked by ALEXA
 4,255 views

mathematics
if the sum of three consecutive positive number is 315. What is the numbers?
 asked by ram
 2,083 views

Physics
How is the attractive electrostatic force between a proton and an electron indicated in Coulomb's law? the sum of the charges indicates a positive force the product of the charges indicates a positive force the product of the charges indicates a negative
 asked by Katy
 1,411 views

Algebra 2
What is the maximum product of two numbers whose sum is 22? What numbers yield this product?
 asked by Peter
 6,635 views

ms.sue math
Which sum will be irrational? a. 3 + 2 b. √19 + 7/2 ****** c. 18/3 + 11/10000 d. –6 + (–3.251) Which product will be rational? A.17.12 * 33 ***** B. √ of 3 * √ of 9 C.4*pie D. √ of 20 * 15 A whole number is added to a number with two digits
 asked by Anonymous
 5,488 views

math
Find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum.
 asked by anon
 7,315 views

Advanced Math
1.Tasha believes that she can rewrite the difference 12036 as a product of the GCF of the two numbers and another difference.Is she correct?Explain your answer. 2.Explain how to find the GCF of three numbers 3.Xiao's teacher asked him to rewrite the sum
 asked by Hailey 6th grade
 4,634 views

math
the sum of two numbers exceeds their product by one. their differences is equal to their product less five . find the two numbers
 asked by seraphine
 4,883 views

calculus
find the two numbers whose sum is 10, if the product of one by the cube of other is a maximum.
 asked by jen
 2,924 views

algebra
The product of two consecutive positive even numbers is 840. What are the numbers? (Enter solutions from smallest to largest.)
 asked by darren
 1,275 views

calculus
find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
 asked by tony
 2,893 views
Still need help?
You can ask a new question or browse existing questions.