use the Laplace transform to solve the given initial-value problem.
use the Laplace transform to solve the given initial-value problem.
Step 1
Given, the initial value problem
step 2
The Laplace transform of the two derivatives
Where y(0) and y’(0) are initial conditions.
Step 3
Now,
when
when
Step 4
Hence the solution is
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at
vv
A second hand car dealer has ten cars for sale. He decides to investigate the link between the
ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars
are shown in the table below.
Age, x years
2 2.5 3 4 4.5 4.5 5 3 6 6.5
Mileage, y thousand miles
22 34 33 37 40 45 49 30 58 58
(a) Construct a well labeled scatter diagram in the graph paper provided to present the
information. (3 marks)
(b) Find Sxx and Sxy. (3 marks)
(c) Find the regression equation in the form y = α + βx. (4 marks)
(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line
appropriately. (2 marks)
(e) Give a practical interpretation of the slope β. (1 mark)
(f) Using your answer in (c), fifind the mileage for a 6 year old car.
A second hand car dealer has ten cars for sale. He decides to investigate the link between the
ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars
are shown in the table below.
Age, x years
2 2.5 3 4 4.5 4.5 5 3 6 6.5
Mileage, y thousand miles
22 34 33 37 40 45 49 30 58 58
(a) Construct a well labeled scatter diagram in the graph paper provided to present the
information. (3 marks)
(b) Find Sxx and Sxy. (3 marks)
(c) Find the regression equation in the form y = α + βx. (4 marks)
(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line
appropriately. (2 marks)
(e) Give a practical interpretation of the slope β. (1 mark)
(f) Using your answer in (c), fifind the mileage for a 6 year old car.
A second hand car dealer has ten cars for sale. He decides to investigate the link between the
ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars
are shown in the table below.
Age, x years
2 2.5 3 4 4.5 4.5 5 3 6 6.5
Mileage, y thousand miles
22 34 33 37 40 45 49 30 58 58
(a) Construct a well labeled scatter diagram in the graph paper provided to present the
information. (3 marks)
(b) Find Sxx and Sxy. (3 marks)
(c) Find the regression equation in the form y = α + βx. (4 marks)
(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line
appropriately. (2 marks)
(e) Give a practical interpretation of the slope β. (1 mark)
(f) Using your answer in (c), fifind the mileage for a 6 year old car
Let