Search & Filtering
You are given with a list of positive integers nums, return whether there exist integers a, b, and c such that a ** 2 + b ** 2 = c ** 2.
Let vector A=a1i +a2j + a3k and B=b1i + b2j + b3k ne on the same plane. Fine the unit vector perpendicular to both A and B.
Find the position vector of the point in space P that lies on the line AB such that |AP|/|PB|= m/n with m, n is a real number. Find the position vector of P if vector A=(1,2,1), B(3,-1,2), m=3 and n=2
Solve for the determinant in the equation below. (10)
1.7.1.
4 −3 2
1 2 −2
2 −1 −4
1.7.2
2 −2 1
2 2 1
4 1 3
As urvey unofficially claimed that in every five young executives, only one practices good reading habits.
What is the probability that out of 10 young executives, two executives practice good reading habits? （b) What is the probability that at least five out of 20 young executives practice good reading habits?
If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10)
A = {90, 92, 94, 96, 98, 100},
B= {91, 93, 95, 97, 99},
C = {90, 94, 98}
1.4.1 What is (A ∩ C)c
1.4.2 What is(B ∪ C)c
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)
Learning Task 2
Write the equilibrium constant expression for each of the following reactions.
1. H2(g) + I2(g) ⇌ 2HI(g)
2. 3O2(g) ⇌ 2O3(g)
3. 2CO2(g) ⇌ 2CO(g) + O2(g)
4. CH3COOH(aq) + C2H5OH ⇌ CH3COOC2H5(aq) + H2O(l)
5. AgCl(s)
⇌
Ag+
(aq) + Cl-
(aq)
1. Are Integers Created Equally?
by CodeChum Admin
It's time to find out if something is true or false. Let's test your capabilities by creating a program that checks if two integers are equal!
Instructions:
- Input two integers in one line.
- Print the two integers in one line, and separate them with a space.
- Print a string message "Equal" on a new line, if both inputted integers are equal.
Input
1. First integer
2. Second integer
Output
The first two lines will contain message prompts to input the two integers.
The next line will contain the inputted integers.
The last line will contain a string which is the result, if the condition were true.
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
