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).

If x + 10 = 70, what is x? a. 40 b. 50 c. 60 d. 70 e. 80

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?

Ms. green tells you that a right triangle has a hypotenuse if 13 and a leg of 5. she ask you to find the other leg of the triangle. what is you're answer?