An interactive introduction to MATLAB

16 basic concepts

Exercise 2: Variables and arrays (continued)

4. continued
   b)

5x+3y−z= 10

3x+2y+z= 4

4x−y+3z= 12

c)

x 1 −2x 2 −x 3 +3x 4 = 10

2x 1 +3x 2 +x 4 = 8

x 1 −4x 3 −2x 4 = 3

−x 2 +3x 3 +x 4 = − 7

5. Create a vectortthat ranges from 1 to 10 in steps of 1, and a vector
   thetathat ranges from 0 toπand contains 32 elements. Now compute
   the following:

x=2sin(θ)

y=t−^1

t+ 1

z=sin(θ

(^2) )
θ^2

6. A discharge factor is a ratio which compares the mass flow rate at the
   end of a channel or nozzle to an ideal channel or nozzle. The discharge
   factor for flow through an open channel of parabolic cross-section is:

K=1.2x

[√

16x^2 + 1 +4x^1 ln

(√

16x^2 + 1 +4x

)]−^23

,

wherexis the ratio of the maximum water depth to breadth of the

channel at the top of the water. Determine the discharge factors forxin

the range 0.45 to 0.90 in steps of 0.05.

7. Points on a circle
   All points with coordinatesx=rcos(θ)andy=rsin(θ), whereris
   a constant, lie on a circle with radiusr, i. e. they satisfy the equation
   x^2 +y^2 =r^2. Create a column vector forθwith the values 0 ,π/4,π/2,
   3π/4,π, and5π/4. Taker= 2 and compute the column vectorsxand
   y. Now check thatxandyindeed satisfy the equation of a circle, by
   computing the radiusr=

√

(x^2 +y^2 ).