NAPT - Navy Advanced Programs Advanced Mathematical Concepts Questions and Answers

Question 1

A submarine is on the surface, located 2,500 meters from a straight coastline.
It dives at a constant angle of depression of 15 degrees.
What is the submarine's depth below the surface, to the nearest meter, when it has traveled 1,000 meters horizontally towards the coastline?

Accepted Answer

268 meters

Answer

250 meters

Answer

966 meters

Answer

3,732 meters

Question 2

What is the derivative of the function f(x) = 4x³ - 7x² + 2x - 9 with respect to x?

Accepted Answer

12x² - 14x + 2

Answer

4x² - 7x + 2

Answer

12x³ - 14x² + 2x

Answer

x⁴ - (7/3)x³ + x² - 9x

Question 3

Which of the following is the correct solution for x in the logarithmic equation: log₂(x) + log₂(x - 4) = 5?

Accepted Answer

x = 8

Answer

x = -4

Answer

x = 4

Answer

x = 6

Question 4

A complex number operation is defined as (3 + 5i) * (2 - 4i). What is the resulting complex number in the form a + bi?

Accepted Answer

26 - 2i

Answer

6 - 20i

Answer

6 - 2i

Answer

26 + 2i

Question 5

In a manufacturing process, the failure rate of a specific component follows a geometric progression. The probability of failure in the first hour is 0.5, in the second hour is 0.25, in the third hour is 0.125, and so on. What is the total probability that the component will fail within the first 5 hours?

Accepted Answer

0.96875

Answer

0.9375

Answer

0.984375

Answer

1.0

Question 6

Given Matrix A = [[3, 1], [4, 2]] and Matrix B = [[5, 0], [1, 6]], what is the product A * B?

Accepted Answer

[[16, 6], [22, 12]]

Answer

[[15, 0], [4, 12]]

Answer

[[15, 6], [20, 12]]

Answer

[[8, 1], [5, 8]]