Answer:
Minus 9.09090909% decrease
Answer: The answer is 
Step-by-step explanation: Given that the penguin nursery is open two times in a day, where the number of hours open at the noon and afternoon are respectively given by

Therefore, the total number of hours 't' penguin nursery open every day is given by

Thus, the answer is

Answer:
Angle A is larger than angle C
Step-by-step explanation:
The reason for this is a visual concept. Since A is supplementary to angle B, then A is a greater measure than B, making B complimentary. B is complementary to Angle C making B the smallest angle, C the "medium angle" and A the largest angle. From this however, we can conclude angle A is larger than angle C.
Two ways of solving it:
The angle beside the 71 is equal to
180 - 71 = 109
so a triangle angles sums up to 180
so the reminaing is
x = 180 - 109 - 28 = 43
solution (2):
the exterior angle = sum of interior angles except the one near it.
28 + x = 71
x = 43
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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