Step-by-step explanation:
Given
perpendicular (p) = a
hypotenuse (h) = 3√2
sin 45 ° = p/h
1 /√2 = a / 3√2
Cross multiply
3√2 = a √2
a = 3√2 / √2
Therefore a = 3.
Area=legnth times width
area=5 and 5/8
legnth=1 and 1/2
convert all to imporopoer fractions
5 and 5/8=5+5/8=40/8+5/8=45/8
1 and 1/2=1+1/2=2/2+1/2=3/2
area=45/8
legnth=3/2
area=legnth times width
45/8=3/2 times width
multiply both sides by 2/3 to clear fraction (3/2 times 2/3=6/6=1 and 1 times width=width so)
90/24=width
simplify
15/4=width
15/4=12/4+3/4=3+3/4=3 and 3/4
width=3 and 3/4 yards
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
<h3>How can the dimensions and volume of the box be calculated?</h3>
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.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
Learn more about differentiation and integration here:
brainly.com/question/13058734
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The answer is the last on 12
Answer:
third quadrant
Step-by-step explanation:
quadrant III