billirisjordyn86
Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Among all pairs of numbers with a sum of 215, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Sagot :

Luv2Teach

Answer:

Step-by-step explanation:

This is calculus, but I don't get fractions in the end. To maximize or minimize any function, you need to find the derivative of it, set it equal to 0, then solve for the critical values.

Our given equation is

x + y = 215 and we want to maximize the product, xy. Therefore,

y = 215 - x so its product in terms of x is

x(215-x) which is

[tex]215x -x^2[/tex].  The derivative of this is

215 - 2x. Set it equal to 0 to maximize it.

215 - 2x = 0 so

-2x = -215 and

x = 107.5.

Sub this in to solve for y:

y + 107.5 = 215 and

y = 107.5

The product is 11556.25, not that you need it.

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.