Science pls help this is due today
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The length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to is 10.5ft.
The length of the arc of a circle is equal to the product of the circumference of the circle and the ratio of the angle made by the arc of the circle to 2π. It is given by the formula,
It is given that the radius of the circle is equal to 2 ft while the angle made by the arc at the centre of the circle is equal to . And we know the formula for the length of the arc, therefore, the length of the arc,
Hence, the length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to is 10.5ft.
Learn more about the Length of the Arc of a Circle:
We are given function for area.
where x = width, gives you the area of the dog pen in square feet.
We need to find the width that gives the maximum area.
And maximum area of the rectangular dog pen.
The given function is a quadratic function.
And a quadratic function represents a parabolic shape on the graph.
<em>The highest point of the parabola is the vertex of the parabola.</em>
<em>So, we need to find the vertex of the parabola for the given function.</em>
A = 27x-x^2.
Formula for x-coordinate of the vertex is = -b/2a.
Plugging values of a and b in formula, we get
-27/ 2(-1) = -27/-2 = 13.5
Therefore, 13.5 feet width would give maximum area.
Let us find the maximum area now.
Plugging x=13.5 in given function, we get
=364.5 - 182.25
= 182.25 square feet ≈ 182.3
<h3>Therefore, 13.5 feet width gives you the maximum area and 182.3 square feet is the maximum area.</h3>