EXAMPLE 3 (a) Set up the integral for the length of the arc of the hyperbola xy = 2 from the point (1, 2) to the point 3, 2 3 . (b) Use Simpson's Rule with n = 10 to estimate the arc length. SOLUTION (a) We have y = 2 x dy dx = and so the arc length is L = 3 1 + dy dx 2 dx 1 = 3 1 + 4 x4 dx 1 = 3 x4 + 4 x2 dx 1 . (b) Using Simpson's Rule with a = 1, b = 3, n = 10, Δx = 0.2, and f(x) = , we have L = 3 1 + 4 x4 dx 1 ≈ Δx 3 [f(1) + 4f(1.2) + 2f(1.4) + 4f(1.6) + ⋯ + 2f(2.6) + 4f(2.8) + f(3)] ≈ (rounded to four decimal places).

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation:

step-by-step explanation:

consider the parallelogram shown in the attached image.

in the parallelogram hijk, the length of hk is given as,

from the properties of parallelogram we know that the opposite sides of a parallelogram are parallel to each other and are equal in measure.

therefore, the length of the side ij must be equal to the length of the side hk and that is .

hence, the expression for the length of ij confirms that hijk is a parallelogram.