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Two towns P and Q are 144km apart by rail and 150km by road .A car takes t hours for the journey from P and Q and a train takes 24 minutes longer.
(a)Write down, in terms of t, expressions for the average speed of
the car and the train
(b)If a train average is 15kmh^-1 less than the car for the journey, write down an equation in t.
(c)By solving your equation in (b), find the average speed of the car and of the train
(a)Write down, in terms of t, expressions for the average speed of
the car and the train
(b)If a train average is 15kmh^-1 less than the car for the journey, write down an equation in t.
(c)By solving your equation in (b), find the average speed of the car and of the train
1(a) A number is written as 37 in base.Twice the number is written as 75 in base x.Find the value of x
(B)A garden ,in front of a square is surrounded by a path which is 1m wide on two opposite sides and 1/2m wide on the two opposite sides.If the area of the path is 17m^2,
calculate the :
1.perimeter of the garden
2.area of the space covered by the garden and the path
(B)A garden ,in front of a square is surrounded by a path which is 1m wide on two opposite sides and 1/2m wide on the two opposite sides.If the area of the path is 17m^2,
calculate the :
1.perimeter of the garden
2.area of the space covered by the garden and the path
If y= e ax cos 3 x sin 2 x find dy/dx
Find the Taylors expansion of f(x)=sin x at x=0.
Taylors expansion of f(x) = Sin x at x = 0.
Question 1:
For the following transfer function:
H(S)= (s^2-1)/(s^2+s+1)
Plot the poles and zeros in the s-plane and determine and sketch the inverse Laplace transform h(t ) using Matlab..
Question 2:
For the following transfer function:
H(S)=3+((S+4)/(S^2+3S+2))
Find and sketch the inverse Laplace transform h(t) using Matlab..
Question 3:
Solve the following second order differential equation:
y"+4y' +3y=4e^-3x
, given that y(0)=1 and y'(0)=-1
and sketch the output y(t) using Matlab.
For the following transfer function:
H(S)= (s^2-1)/(s^2+s+1)
Plot the poles and zeros in the s-plane and determine and sketch the inverse Laplace transform h(t ) using Matlab..
Question 2:
For the following transfer function:
H(S)=3+((S+4)/(S^2+3S+2))
Find and sketch the inverse Laplace transform h(t) using Matlab..
Question 3:
Solve the following second order differential equation:
y"+4y' +3y=4e^-3x
, given that y(0)=1 and y'(0)=-1
and sketch the output y(t) using Matlab.
A bank is interested in studying the number of people who use the
ATM located outside its office late at night.On average, 1.6 customers
used the ATM during any 10 minute interval between 9 pm and
Midnight.
i. What is the probability of exactly 3 customers using the ATM
during any 10 minute interval?
ii. What is the probability of 3 or fewer customer using the ATM
during any 20 minute interval?
ATM located outside its office late at night.On average, 1.6 customers
used the ATM during any 10 minute interval between 9 pm and
Midnight.
i. What is the probability of exactly 3 customers using the ATM
during any 10 minute interval?
ii. What is the probability of 3 or fewer customer using the ATM
during any 20 minute interval?
Let X be a normal random variable with its mean equal to 65 and
standard deviation equal to 12. Find the probabilities for normal
distribution.
1)p(x>48)
2)p(35<x<43)
3)p(x<37)
standard deviation equal to 12. Find the probabilities for normal
distribution.
1)p(x>48)
2)p(35<x<43)
3)p(x<37)
If electricity power failures occur according to a Poisson distribution
with an average of 3 failures every twenty weeks, calculate the
probability that:
i. at most one failure during a particular week.
ii. exactly 4 failures within ten weeks.
with an average of 3 failures every twenty weeks, calculate the
probability that:
i. at most one failure during a particular week.
ii. exactly 4 failures within ten weeks.
For certain population of students in university, the total students for first,
second and third semester listed according to the faculty, are shown in the
Table 1 below:
Table 1: Total students
Faculty Semester
First Semester Second Semester Third Semester
Engineering 200 150 350
Business 320 110 270
Education 400 340 360
(a) If a students is selected at random, find :
i. The probability of the students from the engineering faculty.
ii. The probability of the students second semester and from
education faculty.
iii. The probability that students from business faculty given that the
students third semester.
second and third semester listed according to the faculty, are shown in the
Table 1 below:
Table 1: Total students
Faculty Semester
First Semester Second Semester Third Semester
Engineering 200 150 350
Business 320 110 270
Education 400 340 360
(a) If a students is selected at random, find :
i. The probability of the students from the engineering faculty.
ii. The probability of the students second semester and from
education faculty.
iii. The probability that students from business faculty given that the
students third semester.
