Search & Filtering
Three points with position vectors, b and c are said to be colinear. If the parallelogram with adjacent sides a - b and a - c has zero geometry area. Use this fact to check whether or not the following triples of points are collinear
(a) (2,2,3), (6,1,5) (2,4,3)
(b) (2,3,3), (3,7,5), (0,-5,-1)
(c) (1,3,2), (4,2,1), (1,0,2)
Given that vector A=3i + j + k, B=2i - j +2k and C=i + j + k
(a) Find a unit vector normal to the plane containing vector A+B and A+C
(b) Find the unit vector normal to the plane containing vector A+(A+B)B and C
(c) Why is the unit vector normal to the plane containing A and B parallel to the vector normal plane containing (A•B)A and (B•C)B
Problem 1: Use the tabular method to determine if the limits of the following functions exist:
a) lim𝑥→3 2/(𝑥−3)^2
b) lim𝑥→3 2/(𝑥−3)^3
Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by y=2x^2 and y=x^3 about the x-axis.
- If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.
a chip is placed at room temperature of 40°c after minutes its temperature changes from 80c to 60c the proportionallity constant in case is k=0.05 ln2 find temperture of chip after 40 minute.
Check whether 𝑇 ∶ ℝ2 → ℝ2
, defined by 𝑇 (𝑥, 𝑦) = (−𝑦, 𝑥) is a linear transformation.
Left-tailed test, variance unknown, 𝛼 = 0.01, n = 23
A population consists of the five numbers 2, 3, 6, 8, and 11.
Consider the samples of size 2 that can be drawn from this
population.
A. List all the possible samples and the corresponding mean.
B. Construct the sampling distribution of the sample mean.
1. Solve the following linear programming problem graphically:
Minimise Z = 200 x + 500 y
subject to the constraints:
x + 2y ≥ 10 ... (1)
3x + 4y ≤ 24 ... (2)
x ≥ 0, y ≥ 0 ... (3)
