Answer:
see below
Step-by-step explanation:
All of the given data sets have x-values that are sequential with a difference of 1. That makes it easy to determine the sort of sequence the y-values make.
<u>first choice</u>: the y-values have a common difference of -2. This will be matched by a linear model.
<u>second choice</u>: the y-values have a common difference of +2. Again, this will be matched by a linear model.
<u>third choice</u>: the y-values have a common ratio of -2. This will be matched by an exponential model.
<u>fourth choice</u>: the y-value differences are 3, 5, 7, increasing by a constant amount (2). This is characteristic of a sequence that has a quadratic model.
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 30
Explanation:
So all of the angles in a triangle add up to 180 degrees and so if you split the triangle into separate triangles then you can add up the angles that are known and subtract from 180 to get the size of the missing angle e.g 90 + 56 = 146, 180 -146 = 34 for the other triangle 90 + 26 = 116, 180 - 116 = 64 and so 64 - 34 = 30
24/40 = T/30
40t= 24•(30)
T= 18
Hope this helps. :)
