Math Answers

Solve:

• dy/dx - 2y = 5y²

Suppose a population of insects according to the law of exponential growth/decay. There were 130 insects after the third day of the experiment and 380 insects after the 7th day. Approximately how many insects were in the original population?

Solve the ODE by Linear ODE method:

x dy/dx + 3y = 6x

Evaluate the line integral: ∫𝒖(𝑥,𝑦,𝑧)×ⅆ𝒓,

where 𝒖(𝑥,𝑦,𝑧)=(𝑦^2,𝑥,𝑧) and the curve 𝑪 is described by 𝒛=𝑦=𝑒^𝑥 with 𝑥∈[0,1].

Find the equation of the circle(x - 5)² + (y + 3)² = 25  translated through a vector

(-2,-2). Also Sketch it.

In the following ordered data, the mean is 6 and the median is 5.

2,b, 3, a, 6, 9, 10, 12 Find each of the following (a) the value of a;

(b) the value of b;

Q1: Use the matrix

9 1

7 2 

(a)  Obtain the Hill cipher for the plaintext message

                                              PAK ARMY

by letting  A=1,B=2,C=3,.......,Y=25 and Z=26

(b)  Decode Hill 2- cipher which was encrypted by this matrix.

Suppose a recurrence relation

an=4an−1−4an−2

where a1=14 and a2=40

can be represented in explicit formula, either as:

Formula 1:

an=pxn+qnxn

or

Formula 2:

an=pxn+qyn

where

x

and

y

are roots of the characteristic equation.

Determine

p

and

q

.

You are required to prepare a 15-minute presentation aimed towards new students engaged under a technology company’s graduate scheme.

Your presentation will include evidence of:

1. An explanation that adequately explains why group theory is taught to computing students.

2. The application of group theory within public key cryptography. All work should be appropriately and accurately referenced

The probability that a person has a certain disease is 0.05. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually​ present, the probability that the medical diagnostic test will give a positive result​ (indicating that the disease is​ present) is 0.88. If the disease is not actually​ present, the probability of a positive test result​ (indicating that the disease is​ present) is 0.03.

If the medical diagnostic test has given a positive result​ (indicating that the disease is​ present), what is the probability that the disease is actually​ present?