Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours dur
2 answers:
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Answer: Last option.
Step-by-step explanation:
Observe the base of the pyramid, which is a regular hexagon. You can see that there is a right triangle.
The area of the triangle can be calculated with this formula:
Where "b" is the base and "h" is the height.
You can say that the apothem is the height of the right triangle, then, you need to find the base applying the Pythagorean Theorem:
Then, the area of the triangle is:
Since the base of the pyramid is a regular hexagon, then you can multiply by 12 the area of the right triangle calculated above, in order to find the area of the hexagon. Then you get:
<u>Given</u>:
Let x represents the radius of the cylinder.
Given that the height of the cylinder is twice the radius of its base.
The height of the cylinder is 2x.
We need to determine the volume of the cylinder.
<u>Volume of the cylinder:</u>
The volume of the cylinder can be determined using the formula,
Substituting r = x and h = 2x, we get;
Simplifying, we get;
Thus, the expression that represents the volume of the cylinder is 2πx³ cubic units.
Hence, Option b is the correct answer.
Answer: 58 ft × 58 ft
Step-by-step explanation:
Let the length of the region = x feet
And, the width of the region = y feet
Since, the perimeter of the region = 234 feet ( Given )
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Again the area of the region, A = xy
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By differentiating the above equation with respect to x,
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For maxima or minima,
Again differentiating equation A'(x) with respect to x,
We get, A''(x) = -2
Hence, For x = 58.5 A''(x) = negative
⇒ For x = 58.5 feet the area A(x) is maximum,
⇒ The length of the region having maximum area = x = 58.5 feet
And, the width of the region having maximum area = y = 117-x= 117 - 58.5=58.5 feet,
⇒ The dimension of the region having the maximum area = 58.5 ft × 58.5 ft