4. Suppose f A → B is a bijection. Prove that f-1: BA is a bijection.

Prove by mathematical induction that for any positive integer n, the sum of the cubes of the first n natural numbers is given by: n Σκ k=1 (n(n + 1))²

Calibri BIUAAAA ויו Text in Italian is not being checked. Do you want to add it as a proofing language? Task 12 Fig 1 75 75 75 Fig 2 Fig 3j Add Figures 1 to 3 each shows a top view and a front view of models. Make use of the lineated paper for isometric projection and take each block on the paper as being 10mm x 10mm. Use the indicated sizes and draw an isometric view of each of the three models Samsung Galaxy A04e

Use the Cauchy Riemann equations (polar form version). Also, describe what happens at the branch cut.

b. i. Show that the following matrix is orthogonal. A = ドードー ii Find the inverse of matrix A. Show all working in an organized/orderly manner. 2 3 -619 A = 42 3 1 5 B-1127) a. Given D = , decode the following message: 32, 24, 42, 28, 24, 40, 50, 60, 132, 96, 12, 24

QUESTION 4 Peter says that the following expressions can be simplified into one trigonometric ratio without the use of a calculator. Prove that Peter is correct by simplifying the following expressions into one trigonometric ratio: 4.1 sin 43° + sin 17º (5)

Question 3 a. Using Laplace theorem, find the determinant of the following matrix. 3 5 2 4 1 3 7 6 A= 2 48 3 569 7

Choose all of the statements that are true: 16 is even -16 is even 401 is even √2 is even π is even 2π is even If n is an integer, then n(n + 1) is always even.

Is the number "-4" even, odd, or neither? Use the definition of even/odd to explain why your answer makes sense.