**Transcription for Educational Website:** --- **Problem Statement:** Suppose \( f(t) = 6(t - 4)^{-1/2} \). **(a) Find the derivative of \( f \).** \[ f'(t) = -3(t - 4)^{-3/2} \] *The derivative of the function \( f(t) \) is found using the power rule and chain rule of differentiation.* **(b) Find an equation for the tangent line to the graph of \( y = f(t) \) at the point \( (t, y) = (29, 6/5) \).** *Tangent line:* \[ y = -\frac{3}{125} x + \frac{237}{125} \] *This equation represents the tangent line at the specified point. The slope is calculated using the derivative \( f'(t) \), and the equation is found using the point-slope form.* --- **Additional Information:** In the provided answer section, the values for the derivative and tangent line are confirmed through a second attempt, indicated as "Attempt 2 of 2". *Note: There was an alert symbol (⚠) next to the equation of the tangent line, possibly indicating an error or a point of caution in a digital platform, which should be checked for accuracy.*

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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.