Question

Gillian is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(-h + 10)(-h + 8). What is the maximum volume for the domain 0 10 years ago

Answer 1

Well what do you think the answer would be?

Answer 2

I'm not sure, honestly.

Answer 3

so you dont even know what to do with the function really? :'(

Answer 4

Where do I start from?

Answer 5

No :/ I'm really behind in my class, and I'm failing, and I'm just trying to get help and get caught up so that I can pass this semester.

Answer 6

well it is asking for the highest height possible from the given domain of 0<h<10. Do you understand what the damain is saying to you?

Answer 7

0 is less than h, which is less than 10? That's all I'm really getting from that..

Answer 8

There are two ways to solve this problem, one way is by graphing and the other is by plugging in the values from 0 to 10 individually(takes a while to do this)

Answer 9

A formula for the volume of this box is given.
For any box height h, you can calculate the box volume using this formula.

What would the volume be if h=6?

Answer 10

What does "domain 0<h<10" mean to you?

Answer 11

I alreagy asked that

Answer 12

maybe we can do something similar but with a really simple function just to get you jump started with the concept.

Answer 13

So, would you plug in 6 for 0<6<10, like that?

Answer 14

Yes, to answer my question, you'd just plug in h=6.

Answer 15

Prizzi and I have both asked you what "domain" means to you. Mind sharing that before we proceed further?

Answer 16

if you have a graphing calculator you would replace the 'h' with letter 'x' and input the function as

f(x)= x(-x+10)(-x+8)

Answer 17

Yeh :) sure, whatever you think will help!

Answer 18

then you would click =on the '2nd' key and click on 'graph' key.

Answer 19

I already answered that when Prizzi asked @math

Answer 20

@mathmale , sorry

Answer 21

Okay @Prizzi , I'm following so far

Answer 22

I will let them do their thing first and then jump in later to see if you're grasping enough information to move on and do things for yourself.

Answer 23

I don't have a graphing calculator though, so does anyone have a link to one that I can use?

Answer 24

Okay :) thank you @hwyl

Answer 25

https://app.geogebra.org/#cas

Answer 26

Thank you @hwyl :)

Answer 27

The concept of domain is the most important one in this problem. Ray has typed in, "0 is less than h, which is less than 10" What does this mean?

Case 1: h is measured only in integers: 8 feet, 2 feet, etc., without fractions;
Case 2: h is measured in mixed numbers, such as 3.999 feet.

Suppose, Ray, that you're going to concentrate on Case 1. What is the largest h that you would substitute into the formula for volume?

Answer 28

"0 is less than h, which is less than 10" tells us that we are NOT going to use any h value that is not a member of this set, (0, 10), or 0<h<10.

Answer 29

In other words, ""0 is less than h, which is less than 10" is the SET of h values for which the volume formula is valid / is defined. This, in a nutshell, is what you need to know about "domains"

Answer 30

"So, would you plug in 6 for 0<6<10, like that?" Not quite. 0<h<10 merely says that the value(s) of h that you use must be between 0 and 10. I arbitrarily chose h=6. Because that IS in the domain of your volume function, you CAN evaluate this function at h=6.

Were you able to do that?

Answer 31

What is the value of V(h) = h(-h + 10)(-h + 8) when h=6?

Answer 32

Okay, thank you :)

Answer 33

Sorry, I thought I sent that in, @mathmale and I just saw your last two responses.

Answer 34

v(6)= 6 (-6 + 10)(-6 + 8)

Answer 35

v(6) = -36 + 60 + -36 + 48.... is this correct at all? @hwyl

Answer 36

? @mathmale

Answer 37

U know calculas?

Answer 38

No lol not at all. I wouldn't even say I know Algebra, which is what I'm taking...

Answer 39

since this problem simply solve by caluculas by maxima and minima.

Answer 40

Okay

Answer 41

I do not know why we are stuck in the value of h = 6

Answer 42

I don't either .-. I'm lost. Mathmale gave me the number six to plug in.

Answer 43

i give u value of h=6 only
v(6)=6*(10-6)*(8-6)=6*4*2=?

Answer 44

I just took a guess at it guys. I've been trying to work on this one equation for 30 min and over and I have about 20 more lessons in Algebra to get done. Thank you guys for looking at my problem for me and helping the best you can :) you're awesome! @hwyl @Er.Mohd.AMIR You guys have a great day!!

Answer 45

Everytime we are given a domain problem, there should be an immediate anticipation of co-domain or range. Since you are doing just algebra or perhaps pre-calc, we will focus on domain and range.

As everyone have suggested, the DOMAIN is the specific value that you use or input into a function. Functions look just like the one that you have, V(h) = h(-h + 10)(-h + 8); it takes that f(x) form and in your case it is V(h). So whatever domain value we input, we put it in place of the x in f(x) or h in your V(h). The value or better termed as OUTPUT once we apply the domain is called the RANGE. For now, we can say that OUTPUT is your RANGE.

Since your problem involves a SET of domains from 0 to less than 10, we need to figure each of the domain's output. What you have been calculating is a domain with a value of 6.

Answer 46

Thank you :)

Answer 47

Earlier, you were asked if you want to do this graphically also, and it is really helpful to be able to show what the problem means graphically.

The term MAXIMUM is the high point in the function's graph. Just think that graphs have ups and downs just like hills, and the maximum is the value at the top or the highest peak of the hill; the minimum is the bottom or lowest point.

Answer 48

in this type Q u simply put values and find which one is more and which one is less what about if 0<h<1000 @hwyl

Answer 49

I've used GeoGebra to graph your volume function

Answer 50

And I would like for you to read the contents of this page rather than my having to write everything out (there's too much to type). http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-algebra/12-relative-extrema-minimums-maximums-01

Then, we will proceed once you've acquainted yourself with the idea.

Answer 51

AND http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx

Answer 52

ok, so basically the answer is h=3, If you had a graphing calculator and graphed the function, then went to the table for the graph you would see that x=3 would have the highest y value.

Answer 53

We need to establish how it came to be that the answer is h =3 whether that is by graph or by analysis.