Math Answers

Reduce the following PDE to a set of three ODEs by the method of separation of
variables.
∂²u/∂r² + (2/r) ∂u/∂r + (1/r²) ∂²u/∂θ² + (cosθ/r²) ∂u/∂θ + (1/r² + sin²θ) ∂²u/∂φ² = 0

integrate by substitution ∫ (√1+x^2) x^5 dx
integrate by substitution ∫ secx dx, u = secx + tanx

Obtain all the first and second order partial derivatives of the function:
f (x, y) = x² sin y+ y² cos x

Use the Frobenius method to obtain one solution of the following ODE:
4 yx ′′ + 2y′ + y = 0

Solve the initial value problem :

d²x/dt² -6dx/dt + 9x = 0 , x(0) =6 ,x(0) = -1 .

For a normal distribution with mean,μ=2, and standard deviation, σ=4 what proportion of observations take values greater than 4?

QUESTION 3/SOALAN 3
Table 2: Mathematics Score/Jadual 2: Skor Matematik
27 37 30 28 39 25 45 28
32 28 26 38 31 30 47 41




a) Based on Table 2, organize the data into a frequency distribution by taking 25 as the lower limit of the first class and 5 as the class width. (4)
b) Construct a “less than or equal” ogive for the frequency distribution established in (a) and then approximate the number of candidates who scores below 35. (6)

QUESTION 1

Suppose you are working for a company in the music business. They make stereos, musical instruments and produce CD’s. They decide to do a survey on dance preferences by college students. Basically, they wanted to know about college students’ interests and practices on dance music. A survey was administered to a random sample of 37 students and recorded in Table 1:
A – Ironic dance B – Pro dance C – Sway dance
D – Dad-dance E – Twerk dance

Table 1
Male Female Male Female Male
A A A A E
C E C C A
A A C B E
A C A D D
A A B A A
C D E B B
D A D D A
D A




















Based on Table 1 in Question 1:
a) Prepare a multiple frequency table for dance preferences of both genders. (2)

b) Using your frequency table, draw a multiple bar chart to represent the information.
(4)
c) Briefly discuss and compare the percentage of favorite and least favorite dance preferences of both genders. (4)
[Total: 10 marks]

Dawn Corporation has 12 employees who hold managerial positions. Of them, 7 are female and 5 are male. The company is planning to send 3 of these 12 managers to a conference. If 3 managers are randomly selected out of 12, Find the probability that at most 2 of them are female.

Q. Which of the following curves are regular?
(i) γ(t) = (cos^2 t, sin^2 t) for -∞<t<∞
(ii) γ(t) = (cos^2 t, sin^2 t) for 0<t<π/2
(iii) γ(t) = (t, cosh t) for -∞<t<∞
Find unit speed reparametrisation of regular curve(s).