Question

Among all pairs of numbers whose difference is 16, find a pair whose product is as small as possible.

Answer 1

x-y = 16 ---> y = x-16

P = x*y

P = x*(x-16)

P = x^2 - 16x

So your task is to minimize f(x) = x^2 - 16x

Answer 2

Thanks you so much!

Answer 3

tell me what you get when you minimize f(x)

Answer 4

wouldn{t it be negative 8

Answer 5

no

Answer 6

im confused then

Answer 7

find the vertex of y = x^2 - 16x

Answer 8

In my book it gives me the answers negative 8 and negative 64 i was just wondering how

Answer 9

solve it

Answer 10

do you know how to find the vertex?

Answer 11

Sorta yeah

Answer 12

the x coordinate of the vertex is

x = -b/(2a)

x = -(-16)/(2*1) ... Plug in a = 1 and b = -16

x = 16/2

x = 8

So the x coordinate of the vertex is 8. This means that one of the number is 8.

The other number is y = x-16 ---> y = 8-16 ---> y = -8

So the two numbers are 8 and -8. Notice they are 16 units apart (so they are separated by a distance of 16 units) and they multiply to -64

Answer 13

oh, okay i understand it now!

Answer 14

Can you help me on another one

Answer 15

that's great, your book gave the answers in an odd format though (oh well)

Answer 16

yeah sure

Answer 17

You have 600 feet of fencing to enclose a rectangular plot. if you do not fence the side alone the river(600 - 2x), find the length and width of the plot that will maximize the area?whats the largest area that can be enclosed?

Answer 18

And answers on the book are , length-300ft, width-150ft and maximum area 45000qt ft (if it helps out)

Answer 19

Let x = length and y = width

Draw a picture to get