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Write a Matlab program using Matlab script le for the estimation of the projectile motion of a ball. The projectile motion equation is given below. Write a script le that prompt the user to enter the input and computes:

a) how long does the ball take before it hits the water;

b) how far is it from the base of the cliff to the point of impact.

c) Plot the impact point against the angle. For the angle (theta) that varies from

5o – 50o with the increment of 5o.

d) Plot the graph for the vertical and horizontal location of the projectile against

the time. For a xed angle of 20o and different initial speed from 5 – 10 m/s with 0.5 m/s speed increment.

Save the results obtained in the external output le containing its input entry and student particular as well.

vOx=vocosθo vOy=vosinθo x−xo=vOx t

y−yo=vO t−1gt2=(vosinθo)t−1gt2 y22

vx=vocosθo vy=vosinθo−gt v2y=(vo sinθo)2−2 g(y−yo)

a) how long does the ball take before it hits the water;

b) how far is it from the base of the cliff to the point of impact.

c) Plot the impact point against the angle. For the angle (theta) that varies from

5o – 50o with the increment of 5o.

d) Plot the graph for the vertical and horizontal location of the projectile against

the time. For a xed angle of 20o and different initial speed from 5 – 10 m/s with 0.5 m/s speed increment.

Save the results obtained in the external output le containing its input entry and student particular as well.

vOx=vocosθo vOy=vosinθo x−xo=vOx t

y−yo=vO t−1gt2=(vosinθo)t−1gt2 y22

vx=vocosθo vy=vosinθo−gt v2y=(vo sinθo)2−2 g(y−yo)

I have detected the mouth on image using the viola jones algorithm on MATLAB, I need the codings to apply different colors on the detected mouth.

I need to develop a digital makeup system using MatLAB GUI, I have already detected the face,eyes and mouth on image using the Viola Jones algorithm. I need the codings for the detection of the cheeks and apply different colors on the cheeks, can help me with the codings?

Write a matlab script to display currency conversion for US dollar, british pound, euro with singapore dollar as the base currency. your output should show the equivalent values for USD, GBP, EURO for ever singapore dollar in increments of 1 dollar until 25 dollars.

Sample Output to be as follows:

SGD USD GBP EURO

1 - - -

2 - - -

3 - - -

. .

. .

25 - - -

I don't understand how to do this.

Sample Output to be as follows:

SGD USD GBP EURO

1 - - -

2 - - -

3 - - -

. .

. .

25 - - -

I don't understand how to do this.

Diode Forward Characteristic

Write a general matlab program for growing a binary tree and use it to train a tree fully

using the data from the three categories in the table, using an entropy impurity.

(a) Use the (unpruned) tree to classify the following patterns: {A,E, I, L,N},

{D,E, J,K,N}, {B,F, J,K,M}, a nd {C,D, J, L,N}.

(b) Prune one pair of leafs, increasing the entropy impurity as little as possible.

(c) Modify your program to allow for non-binary splits, where the branching ratio

B as is determined at each node during training. Train a new tree fully using a

gain ratio impurity and then classify the points in (a).

using the data from the three categories in the table, using an entropy impurity.

(a) Use the (unpruned) tree to classify the following patterns: {A,E, I, L,N},

{D,E, J,K,N}, {B,F, J,K,M}, a nd {C,D, J, L,N}.

(b) Prune one pair of leafs, increasing the entropy impurity as little as possible.

(c) Modify your program to allow for non-binary splits, where the branching ratio

B as is determined at each node during training. Train a new tree fully using a

gain ratio impurity and then classify the points in (a).

Write a matlab program to implement the Perceptron algorithm.

(a) Starting with a = 0, apply our program to the training data from ω1 and ω2.

Note the number of iterations required for convergence.

(b) Apply our program to ω3 and ω2. Again, note the number of iterations required

for convergence.

(c) Explain the difference between the iterations required in the two cases.

(a) Starting with a = 0, apply our program to the training data from ω1 and ω2.

Note the number of iterations required for convergence.

(b) Apply our program to ω3 and ω2. Again, note the number of iterations required

for convergence.

(c) Explain the difference between the iterations required in the two cases.

Use K-means algorithm with K=3 to

classify the Iris dataset with all four features (4

dimensions). Plot a figure to visualize the

sample data and the classifica=ons due to Kmeans

and the ground-truth

classify the Iris dataset with all four features (4

dimensions). Plot a figure to visualize the

sample data and the classifica=ons due to Kmeans

and the ground-truth

K-Mean Algorithm

1. Initialize

• Select initial m cluster centers

2. Find associations

• For each xi, assign the cluster with nearest center

• Find A to minimize J(X; C, A) with fixed C

3. Find centers

• Compute each cluster center as the mean of data in

the cluster

• Find C to minimize J(X; C, A) with fixed A

4. Stopping criterion

• Stop if clusters stay the same. Otherwise go to step 2

prove that this algorithm is always convergent

1. Initialize

• Select initial m cluster centers

2. Find associations

• For each xi, assign the cluster with nearest center

• Find A to minimize J(X; C, A) with fixed C

3. Find centers

• Compute each cluster center as the mean of data in

the cluster

• Find C to minimize J(X; C, A) with fixed A

4. Stopping criterion

• Stop if clusters stay the same. Otherwise go to step 2

prove that this algorithm is always convergent

Generate 1000 sample points in 3-d space, where

each x, y, and z is uniformly distributed between 0 and

1. Write code to perform K-means of these points with

K=2, where the initial cluster centers also follow

uniform distribution. Run your code 3 times and plot

three 3-D figures. Print and submit your figures along

with your observations. In particular, what K-means

tells you? What is the truth?

each x, y, and z is uniformly distributed between 0 and

1. Write code to perform K-means of these points with

K=2, where the initial cluster centers also follow

uniform distribution. Run your code 3 times and plot

three 3-D figures. Print and submit your figures along

with your observations. In particular, what K-means

tells you? What is the truth?