Math Answers

The equation of motion of a body is given by d²y/dt² + 4dy/dt + 13y = e^2tcost , where y is the distance and t is the time.

Determine a general solution for y in terms of t.

Determine the unique solution of the following differential equations by using Laplace transforms:

a. y"(t) - 6y'(t) + 9y(t) = t²e^3t if y'(0) = 6 and y(0) = 2

b. y"(t) - 2y'(t) + 3y(t) = e^-3t if y'(0) = 0 and y(0) = 0

Use two different methods to determine L^-1 {(11 - 3s)/ (s² + 2s -3)} Show that your answers are equal.

Find the slope and the equation of the tangent of the curve at the given point. Show your solution.

1) y = 2x² -x + 2 (-1, 5)

2) y = x² + x + 1 at (-2, 3)

Find the slope of the curve at the given point. Show your solution.

1) y = 4 - 3x² at (-1, 1)

2) y = x² – 5 at (1, -4)

3) y = 2x² – 5 at (2, 3)

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that the height of a child picked at random is less than 104cm?

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?

The weights of male students are normally distributed with a mean of 150 lbs. and a standard deviation of 25 lbs. What is the probability that 25 randomly selected make students will have a mean weight of more than 155 lbs?

A test taken by five people has a maximum score of 100. Their scores are 78, 65, 86, 91 and 68. 

1. Compute for the mean of the population.

2. Compute for the variance of the population.

3. List all the possible samples of size 3 that can be drawn from the population and compute for the mean of each sample. Use SRSWOR method.

4. Construct the probability distribution of the sample means.

5. Compute the mean of the sampling distribution of the sample means.

6. Compute the variance of the sampling distribution of the sample means

The probabilities that a traffic inspector will discover violations of the Traffic Code in Davao City are given in the following table.

Number of Violations (X)

Probability P(X)

0.41

1

2

3

0.22

0.17

4

5

0.13

0.05

0.02

a. Solve for the mean and variance. b. Interpret the mean and the variance of the problem.