30 POINTS NO CAP PUT REALL STUFF
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Answer:
Ginny made a mistake in step 1 when she identified b = 31. It should be b=-31
Step-by-step explanation:
Ginny factored as shown:
ac = –180 and
b = 31
36(–5) = –180 and 36 + (–5) = 31
+ 36x – 5x – 30
6x(x + 6) – 5(x + 6)
(x + 6)(6x – 5)
b is the coefficient of x and from the trinomial , b=-31.
Therefore Ginny made a mistake in step 1 when she identified b = 31. It should be b = –31.
The correct steps are: :
ac = –180 and
b = -31
36(–5) = –180 and -36+5 = -31
The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
- Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.
- Maximum volume of the box is approximately 1048.6 in.³
The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let <em>x </em>represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, <em>V</em>, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;
Which gives;
6•x² - 106•x + 315 = 0
Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
- Width ≈ 18 - 2×4.55 in. = 8.89 in.
- Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.
- Height = x ≈ 4.55 in.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
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