Consider the initial value problem y = 3 – y, y (0) = 1. (a) Use Euler's method with five steps to estimate y (1). Work to full accuracy and then round the your final answer to three decimal places. y (1) = i (b) Find the exact solution to the differential equation and hence find y (1). Round your answer to three decimal places. y (1) = i (c) Without doing the calculation, roughly what would you expect the approximation for y (1) to be with ten steps? Round your answer to two decimal places. y (1) = i

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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.