woah i need a little math help please.?

Question

Find the domain of the given function.

k(s) = the square root of -1 - s

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The perimeter of a rectangle is 60 inches. Express the area A(w) as a function of the width w.
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Find the domain of the given function.

K(v)= 2v^2-9 / v^2-v-90

Answer 1

k(s) = sqrt(-1-s)

This expression is only valid as a real number when s <= -1. So therefore the domain is all real numbers from -1 to -infinity
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let L=length, W=width, P=perimeter and A=area (of the rectangle). Therefore...
P=2L+2W
60=2L+2W
L = 30 - W

A=LW
A=(30-W)W (from the equation above)
A=-W^2 - 30W
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K(v) = 2v^2 - 9 / (v^2-v-90)
rewriting
K(v) = 2v^2 - 9 / [ (v-10)(v+9) ]

since the numerator cannot be zero, v cannot be 10 or -9

Therefore the domain is all real numbers except 10 and -9
ie.
inf >= v > 10 and 10 > v > -9 and -9 > v >= -inf

Answer 2

I'll give you the middle one:

60 = 2w + 2l so l = 30 - w

A(w) = w * l = w * (30 - w) = 30 w - w^2

Answer 3

perimeter:
2w+2l=perimeter
2w+2l=60
w*l=area

2(w+l)=60
w+l=30
l=30-w
w*(30-w)
30w-w^2