Find the circumference given the area = 113.1 ft². Use 3.14 for π as necessary.
2 answers:
The circumference of the circle is 37.68 ft
Step-by-step explanation:
Given,
The area of the circle is 113.1 sq ft
To find the circumference of the circle we need to find the radius of the circle first
Formula
The area of circle with radius r is = π sq unit
The circumference of circle with radius r is = 2πr unit
Let us take the radius of the circle is r ft
According to the problem,
π
or,
or,
or, r =
or, r = 6
Now,
The circumference of the circle is 2×3.14×6 ft = 37.68 ft
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Answer:
a) maximum; the parabola opens downward
b) positive; it must lie above the x-axis
c) x = 1.5
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.
The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.
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<h3>a, b.</h3>If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.
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<h3>c.</h3>The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:
x = (-2 +5)/2 = 3/2
The x-coordinate of the vertex is x = 1.5.
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<em>Additional comment</em>
The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.
Since the side of a triangle cannot have a negative length, we discard the solution x = -9.
Answer: x = 6