Author Topic: Domains, Domains, Domains ! (Read 681 times) Tweet Share

monkeywantsabanana · « **on:** April 20, 2011, 05:08:35 pm »

Hey guys

Can you guys help me with this question - finding the domain when there's two variables :-S

I'm not really sure how I'm suppose to set it out

I've done all the parts except the domain and the graph:

7
a)
i) $A= (10+x)y-x^2$
ii) $P= 2(10+x+y)$

b)
i) $y=40-x$
ii) $(1025/2) meters^2$
iii)THE DOMAIN??

I'm not sure how i should do this because there's x and y

Any help is appreciated !

xZero · « **Reply #1 on:** April 20, 2011, 05:16:32 pm »

well since x and y are lengths, they can't be negative, so x > 0 and y > 0. From part i), ~~y = 40 - x, since we know that y > 0, then x < 40. Hence the domain is 0 < x < 40~~

Edit: Looking at the diagram, y > x, hence the domain is (0,20)

monkeywantsabanana · « **Reply #2 on:** April 20, 2011, 05:23:08 pm »

Yea i thought so too...
but the book says otherwise.

they reckon it's 0≤x≤20

Our teacher said something about this before in another question 0 I wrote it down but i don't understand what she did !

xZero · « **Reply #3 on:** April 20, 2011, 05:25:41 pm »

ohh haha i see, why don't you imagine x = 39 and see what happens to the diagram

monkeywantsabanana · « **Reply #4 on:** April 20, 2011, 05:32:36 pm »

The graph's positive intercept is 24. I don't see why it can't be 23. Why 20?

Milkshake · « **Reply #5 on:** April 20, 2011, 05:36:55 pm »

Going to take a stab at it.
I think its the domain is [0,20], because if you look at the diagram, y>x
If x = 21
Then y = 40-21 = 19, which means y is smaller than x?

xZero · « **Reply #6 on:** April 20, 2011, 05:38:31 pm »

Quote from: Milkshake on April 20, 2011, 05:36:55 pm

Going to take a stab at it.
I think its the domain is [0,20], because if you look at the diagram, y>x
If x = 21
Then y = 40-21 = 19, which means y is smaller than x?

yeh y>x or else the diagram won't work, if x>y, then the shape of the region will be different. However i reckon the domain is (0,20) since it can't be 0 and 20 is not included. If x is 0, then the region will only be bounded by 2 sides, and if x is 20, then it will become a rectangle, which is a different shape.

Edit: this question sucks tbh :S

luffy · « **Reply #7 on:** April 20, 2011, 06:15:33 pm »

Below is my working out to the questions - I did it quite quickly, so sorry for any errors that I may have made:

7)a)i):
$A = y(10 + x) - x^2$

ii):
$P = y + 10 + x + x + (y - x) + 10 + x$

$P = 2x + 2y + 20$

b) i):
If P = 100,
$100 = 2x + 2y + 20$

Rearranging the equation gives:
$y = 40 - x$

sub $y=40-x$ into the Area equation:

$A = (10 + x)(40-x) - x^2$

$A = 400 + 30x - x^2 - x^2$

$A = -2x^2 + 30x + 400$

ii)
$A = -2(x^2 - 15x - 200)$

$A = -2[(x - \frac{15}{2})^2 - \frac{225}{4} - 200]$

$A = -2[(x - \frac{15}{2})^2 - \frac{1025}{4}$

$A = -2(x - \frac{15}{2})^2 + \frac{1025}{2}$

Therefore, Max Area is $\frac{1025}{2} \textup{ }m^2$

iii)
We immediately know that $x>0$ because it is a length.
$y = 40 - x$

Also, due to the diagram,
$y > x$

$\therefore 40 - x > x$

$40 > 2x$

$x < 20$

$\therefore x \in (0,20)$

Whether or not 20 is included is debatable. I think for the purposes of this question, it shouldn't be included due to the diagram.

monkeywantsabanana · « **Reply #8 on:** April 20, 2011, 06:51:49 pm »

I think that's meant to say :

$A = -2[(x - \frac{15}{2})^2 - \frac{225}{4} - \frac{800}{4}]$

$A = -2[(x - \frac{15}{2})^2 - \frac{1025}{4}]$

$A = -2(x - \frac{15}{2})^2 - \frac{1025}{2}$

But THANK YOU SO MUCH FOR THE DOMAIN PART

I understand now.

Thanks !

luffy · « **Reply #9 on:** April 20, 2011, 06:55:41 pm »

Quote from: monkeywantsabanana on April 20, 2011, 06:51:49 pm

I think that's meant to say :

$A = -2[(x - \frac{15}{2})^2 - \frac{225}{4} - \frac{800}{4}]$

$A = -2[(x - \frac{15}{2})^2 - \frac{1025}{4}]$

$A = -2(x - \frac{15}{2})^2 - \frac{1025}{2}$

But THANK YOU SO MUCH FOR THE DOMAIN PART

I understand now.

Thanks !

Ah. Sorry - I fixed my original post.

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Author Topic: Domains, Domains, Domains ! (Read 681 times) Tweet Share

monkeywantsabanana

Domains, Domains, Domains !

xZero

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xZero

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