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Komok [63]
3 years ago
13

Determine how long it will take an object to rotate through 20.0 revolutions at an angular velocity of 2.8 radians per second. U

se π=3.14. Round the answer to the nearest tenth.
Mathematics
1 answer:
Andreyy893 years ago
5 0
The conversion factor between radians and revolution as measures of angle is 2π rad is equal to 1 revolution. Converting the given angular velocity to rev/s,
                (2.8 rad) x (1 rev / 6.28 rad) = 70/157 revolution per second
Dividing the given angle, 20 rev by the velocity,
                                 (20 rev) / (70/157 rev/s) = 44 6/7 s
Thus, the answer is approximately 44.9 seconds. 
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Old Faithful in Yellowstone National Park has a predictable eruption time. The park
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How often does Old Faithful blow?

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A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t
frosja888 [35]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y  

  • since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

\mathbf{L = 3x - 2( \dfrac{1000000}{x})}

\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}

\mathbf{ x^2= \dfrac{2000000}{3} }

\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }

\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}

Now, if we replace the value with equation (1), then y will be:

\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\  \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}

\mathbf{x =500\sqrt{6}}

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

\mathbf{L = 3( \dfrac{1000  \sqrt{6}}{3}) + 2(500 \sqrt{6})}

\mathbf{L =1000  \sqrt{6} + 1000 \sqrt{6}}

\mathbf{L =2000  \sqrt{6} }

\mathbf{L \simeq 4899 \ ft}

Learn more about the area of a rectangle here:

brainly.com/question/25292087

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