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:
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Answer:
under the 48 is -24
on the right side of 6 is -5
on the right side of 48 is -40
Answer:
91
Step-by-step explanation:
117/9 is 13 which means she earns 13 for each hour and for 7 hours it will be 13 multiply by 7 and that gives 91
So the question is asking: (x-4)(x-2)
because there is a bracket in between the two expressions it means we have to multiply them together: (x-4) x (x-2)
you can break down the question into smaller parts:
x multiply x
x multiply -2
-4 multiply x
-4 multiply -2
here are the answers:
x^2 (means x squared)
-2x
-4x
8 (because when you multiply two negative numbers it makes a positive)
now you put it into an expression (this is expanding):
x^2 - 2x - 4x + 8
to simplify it you collect like terms:
x^2 - 6x + 8
The above is the answer :)
Answer:
2 and - 
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3y = 6x + 9 ( divide all terms by 3 )
y = 2x + 3 ← in slope- intercept form
with slope m = 2
(i)
Parallel lines have equal slopes, thus
the slope of line t is 2
(ii)
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= - , thus
the slope of line r is -
