Pe (3) Show that the composite of two translations is again a translation (4) Show that the inverse of a translation is again a translation. (5) Suppose that f is an isometry which has no fixed point...
Please answer all questions Q2 2015 a) show that the function f(x) = pi/2-x-sin(x) has at least one root x* in the interval [0,pi/2] b)in a fixed-point formulation of the root-finding problem, the equation f(x) = 0 is rewritten in the equivalent form x = g(x). thus the root x* satisfies the equation x* = g(x*), and then the numerical iteration scheme takes the form x(n+1) = g(x(n)) prove that the iterations converge to the root, provided that the starting...
Show that the function flx)- x+8x+5 has exactly one zero in the interval [-1, 01. Which theorem can be used to determine whether a function f(x) has any zeros a given interval? O A. Extreme value theorem O B. Intermediate value theorem OC. Rolle's Theorem O D. Mean value theorem apply this theorem, evaluate the function fix)x +8x+5 teach endpoint of the interval [-1, 01 f-1)(Simplify your answer.) f(0) (Simplify your answer.) According to the intermediate value theorem, f(x) x...
show all steps please (1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 +sin0 0 dt2 where g 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0)~0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length...
) 8. Suppose a triangle is constructed where two sides have fixed length a and b, but the third side has variable length x You can imagine there is a pivot point where the sides of fixed length a and b meet, forming an angle of θ. By changing the angle θ, the opposite side will either stretch or contract (a) Let K(x)- Vs(s - a)(s -b)(s - x), where s is the semiperimeter of the triangle. Accord ing to...
(5 points) A spring is suspended vertically from a fixed support. The spring has spring constant k 40 N m-1.An object of mass m- kg is attached to the bottom of the spring. The subject is subject to damping with damping constant β N m-1 s. Let y(t) be the displacement in metres at the end of the spring below its equilibrium position, at time t seconds. (a) Give a value of B which would result in underdamping. B4 Give...
A spring is suspended vertically from a fixed support. the spring has spring constant k = 8nm^-1 (5 points) A spring is suspended vertically from a fixed support. The spring has spring constant k 8N m-1. An object of mass m kg is attached to the bottom of the spring. The subject is subject to damping with damping constant β N m-1 s. Let y(t) be the displacement in metres at the end of the spring below its equilibrium position,...
(5 points A spring is suspended vertically from a fixed support. The sp ng has spring constant k 35 N m 1 An object of mass m 큼 kg is attached to the bottom of the spring The subject is subiect to damping with damping constant β N m 1 s Let t be the displacement in metres at the end of the s nng below its equilibrium position, at time t seconds. (a) Give a value of which would...
(5 points) A spring is suspended vertically from a fixed support. The spring has spring constant k=28 N m−1k=28 N m−1. An object of mass m=14 kgm=14 kg is attached to the bottom of the spring. The subject is subject to damping with damping constant β N m−1 sβ N m−1 s. Let y(t)y(t) be the displacement in metres at the end of the spring below its equilibrium position, at time tt seconds. (a) Give a value of ββ which...
Q3 Preliminary material The homework assignment is found on the next page. Our goal in this homework is to develop an algorithm for solving equations of the form f (x) (1) = X where f is a function S S, for some S C R". This kind of problem is sometimes called fixed point problem, and a solution x of problem (1) is called a fixed point of f. The algorithm we will consider is the following: a Step 0....