MATH 2326 Lecture 15: Triple integrals, Volumes constrained by planes and lines

The third term of (2x + y)^8 is ax^6 y^2. What's the value of a? The first three terms of a geometric sequence is 9, 3, 1. Use general term formulas to find the 9th term. Find the infinite sum sigma_n=1^infinity 1/2^n Write in summation notation 2/1 + 1^2 + 4/1 + 2^2 + 6/1 + 3^2 + 8/1 + 4^2 + 10/1 + 5^2 Evaluate (a) P(8, 3) B) C(8, 3) How many ways can we arrange 6 pictures on the wall from left to right, if the left most picture is already chosen? How many ways can we form a four letter word using letters in {a, b, c, d, e}, if the first and the last letter must be different? How many ways can we choose two candidates to run tor president it there are five male candidates and two female candidates? In a club of 12 members, howe many ways can we choose the presided, the vice president and the treasurer for the club? How many bit strings (with only 0's and 1's) of length eight have equal number of 0's and 1's?

2. Find the integral 1 of the function F(a, y, 2) -1- z over the graph of the function hr.) 3. Find the average valuo of 4. A metallic surface S is in the shape of a hemisphere z- VR-y2, where (x, y) satisfies 2 with 2S 1. the function f(z, y, z) ao +r +2 on the curve C parameterized as e(t) = (cos t, sin t,t), 0 st 21. %2,2+y2 . A2, and it has the mass density 6(nzuz)三Z2+ 1,2. Find the centre of gravity of s. Find the surface integral I C

Solve Equations Solve the following equations. Remember that equations may have no solution or infinitely many solutions. 2x + 3x + 5(2x - 3) = 30 4x^2 + 7x - 2x(2x - 5) = 17 (x - 2)(x + 4) = 0 (x - 2)(x + 4) = 2x (x - 2)(x + 4) = - 8 x(x - 2)(x + 4) = 0 4x(x - 2)(x - 2) = 0 2x(y + 2) - 2y (x + 2) = 0 (x + 2)(y + 2) = 0 (x + 2)(y + 2) + (x - 3) (y + 2) = 0 (x - 2)(x + 4) - 2 (x - 4) = 0 (x + 2)^2 + (x - 2)^2 = 0 (x + 2)^2 - (x - 2)^2 = 0 x(x^2 + 2) = 0 x/3 - x/2 = 2/3 x/3 = 2x 2/x - 3/2x = 1 4x(x - 4)(x + 3.8)/x^4 - 4x^3 + 7x^2 - 5x + 102 = 0 (-12P/P)(3P/2 = P/2) = 480 2/Q = 0 (25/x)/x = 1 (5Q/P + 2)/(1/P + 2) = 20 10 - 1/10! = 0 4x + 8(x - 2) = x - 1.5 3x(x - 2) = 0 (x - 2)^2 = 4 100(1 - x) (1 + x) = 0 100(1 - x)(1 + x) = 100 x/5 + 2x/5 - 6/5 = 3 7/2x - x/9 = x x - 3/5 + 2/x - x/5 = 3/10 Refer to exchange rates given in Table 1.1 to answer questions 34 to 40. Give answers correct to two decimal places. An iPad is priced at 400 Canadian dollars. Calculate the price of the iPad in (a) Euros, (b) rupees and (c) ringgits. How many Euros are equivalent to (a) 800 US dollars, (b) 800 zlotys? A flight is priced at 240 South African rand. What is the equivalent price in Brazilian reals?