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OLEGan [10]
3 years ago
14

(X+h)^3-3(x+h)-(x^3-3x) over h

Mathematics
1 answer:
adelina 88 [10]3 years ago
4 0
X^3 + h^3 - 3x-3h - x^3 +3x              h^3 - 3h              h^2 - 2h
-------------------------------------   =  ------------------   =
                h                                         h
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We are interested in the dimensions of a certain rectangle. this rectangle has length twice the side of the square and width thr
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Area of square = s^2
Area of Rectangle = lw
l = 2s

w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
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