13.11. Show that if y is the boundary of the triangle with vertices at z = 0, z = 3i, and z= -4 oriented in the counterclockwise direction, then -7)dz ≤ 48. s
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- Suppose P,Q,R,S are four collinear points such that: a. Q is between P and R. b. R is between Q and S. c. PQ = QS Prove that PR = QS.Suppose that a > 0 is a positive integer, and n > a. How many lattice paths are there from (0, 0) to (n, n) that do not go above the line y = x + a? hint: Catalan NumberSuppose ABC is a triangle in the hyperbolic plane and D is a point on the segment BC. The segment AD divides ΔABC into two new triangles. How are the defects of ΔABD and ΔACD related to the defect of ΔABC?
- In , triangle ABC, lines CD is perpendicular to AB, and in traingle XYZ, lines ZW is perpendicular to XY. If AB = XY and CD = ZW, then: a. Traingle ABC is congruent to triangle XYZ b. Triangle ABC and XYZ have the same perimeter c. Triangle ABC is simillar to XYZ d. Triangle ABC and XYZ have the same area.Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0) = 1 and s’(2) = 1.Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0) traversed in this order.
- Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (15,7), (−9,−3), and (−9,7), respectively. The epicenter of an earthquake is determined to be 13 units from X, 13units from Y, and 13 units from Z. Where on the coordinate plane is the epicenter located?Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (4,4), (−12,−4), and (−6,9), respectively. The epicenter of an earthquake is determined to be 5 units from X, 13 units from Y, and 10 units from Z. Where on the coordinate plane is the epicenter located?