(Total 16 marks) 9. The vertices of the triangle PQR are defined by the position vectors...
pls answer 4,5,6 and 7 An) a) Find the magnitude of both vectors. b) Find dot product and cross product of both vectors c) Find the projection of w onto v 2) Let а:31 + 5, + 7k and b--6r +-10, + mk where m e R. a) Find the value for m such that vectors are orthogonal b) Find the value of m such that the cross product of the vectors is zero 3) a) Find the distance from...
Question 3 Consider the triangle constructed from the points () = (0,0), Q = (2,0) and P = (L cos 0, L sin (). (a) Write a function for the area of the triangle in terms of 0 and L, namely A(0, L). 3 (b) Show that if the triangle has a perimeter of 6 then L = 2 - cose (c) Sketch the domain of A on a OL-axes to ensure that the following conditions hold • L represent...
Please do 2,4, and 10 d s and y when n the Argand dilagram, the origin is the numbers representing the other vertices Spress 2 + /S and 1 -12 in potar torm and a 60 tex of the triangle is the point 3 -NS. Find the comps centre ot an epuailateral trang 2 Express the result in th e form a jo and in espoment form. nd the fnith roots of -3+3 in polar form and in esponential torm...
Could someone pls explain question 9 (e)? 9. Consider the set of matrices F = a) Show that AB BA for all A, B E F b) Show that every A E F\ {0} is invertible and compute A-. c) Show that F is a field d) Show that F can be identified with C e) What form of matrix in F corresponds to the modđulus-argument form of a complex number Comment on the geometric significance. Solution a) Let A...
By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
3 8 16 (0 complete) This Q Plot each point and form the triangle ABC. Show that the triangle ABC is a right triangle. Find its area. A (-2,11); B (5,7); C ( 1,0) Choose the correct graph below that shows points A, B, C, and triangle ABC. O A. O B. O C. OD. -14 14 Ha Show that the triangle ABC is a right triangle. Select the correct choice below and fill in the answer boxes to complete...
First page is solved and the answers are needed to answer the next 2 Name: Vectors Review Score: /22 Many of the quantities you will encounter in this course are vectors. You will need to be proficient at basic vector manipulations: addition, subtraction, dot products and cross products. This worksheet is a refresher. Chapter 3 of your textbook explains vectors at the level we will be using them in the course. Please review it Below is a list of six...
math final 172 Problems 16-17 are worth 8 credits each 1 Let fx)9 and let ga)-1. Specity the domain of f(x)/slz). 2. Draw the graph of y 3cos 2x from z0to x-2 3. Draw the graph of y 4-+2. 4Write an equation of the line perpendicular to the line y-2r-3 through (4,1) and sketch its graph. 5. Draw the graph of y- -2r-2 and label its maximum 6. Draw the graph of y-V-I 7. In triangle ABC, side a-8 in.,...
upson's Rule with n=4 #5 (9) Use Simpson's Rule wi intervals to estimate ex-l at 16 Find the exact value - A the error. drant of the integral linpartas) and the =0: #5, Use integration by. Seť Int de #7 (a) Evaluate St sin x cos x dic (6) If g(x) = 5 Je tidt, find g'(x) and g'(o). |#8 use partial fractions to find substitution to evaluate $3x(x-3) dx #0 (a). Find 52 sin o do (6) Find the...