8. (seconds) 0. 3 6 9 12 p(t) (feet) 3 5.5 7 13 17 The position of a particle, A, moving along the x-axis is modeled by a twice-differentiable function P, where time t is measured in seconds and p (t) is measured in feet. Selected values of p (t) are shown in the table above. (a) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to 12 approximate the value of p (t)dt Show the computations that lead to your answer. (b) Use the data in the table to approximate p' (10) using the average rate of change of p (t) over the interval 9 < t < 12. Show the computations that lead to your answer. Indicate units of measure.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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