Question

Help, picture attached. Show working thanks

I only need help with 1.d) which is finding the domain of A(x)

Answer 1

what's your area function?

Answer 2

your area should be a quadratic (upside down parabola)
since area is positive, set your area function = 0.
you'll get the two x-values that make your area zero. the x's between these two values is your domain of A(x).

Answer 3

yep but how do u solve it?
0=10y + xy -x^2

Answer 4

What do you mean, how do you solve it? You said you need the domain?

Answer 5

yeh how do u solve 0=10y + xy - x^2?? @dpaInc said i need to solve it first to figure out that domain.

Answer 6

If you're asking how to solve for y, you add x^2 to both sides so you get
x^2=10y+xy
Pull a y out front of the right side and you get
x^2=y(10+x)
And therefore
y=x^2/(10+x)

Answer 7

your area is in terms of two variables. get it in terms of 1 by using the perimeter constraint.

Answer 8

Is this for a Calculus class?

Answer 9

so i can use the equation from part c?

Answer 10

nope, i haven't learnt Calculus yet.

Answer 11

domain of y=x^2/(10+x)
\[{x \in \mathbb{R}~:x+10 \neq 0}\]

Answer 12

yes @JayDS

Answer 13

um i solved it but i get the wrong x values?

Answer 14

\[0=2x ^{2}+16x+260\]

\[-260 = -2x ^{2} + 16x\]

\[-260 -2x(x-8)\]

\[-2x = -26\] or x-8=-260
x = 130 or x = -252

Answer 15

-2x = -260*

Answer 16

your area function should be
A(x) = -2x^2 + 16x + 260

Answer 17

yep can u solve it? when i solved it i seemed to have got the wrong answers as shown in my working above.

Answer 18

setting A(x)=0, i get irrational roots...

Answer 19

hmm i'm not too sure but the answers say the domain is (0, 13) and i'm not sure how they got that

Answer 20

hang on.. my perimeter equation was wrong...

Answer 21

the P equation is y = -x + 26

Answer 22

perimeter*

Answer 23

hmmm i keep getting the same thing...
my perimeter is the same

Answer 24

wait..
look at you perimeter equation...
x can only be as big as y.

Answer 25

it doesn't make sense if x is bigger than y (according to the figure).

Answer 26

so the most x can get is 13... the least is 0.

Answer 27

um i don't quite get it

Answer 28

the Perimeter equation is y= - x + 26 but how can you tell that x at most is 13? u can't.