Certainly! Let's address these questions step-by-step.
1. Find the logarithm of 3.752
A. 0.152
B. 0.54
C. 0.5542
D. 0.574
To determine the correct logarithm value of 3.752, we typically use logarithmic tables or a calculator. The correct answer in this case is:
C. 0.5542
2. What is the order of the matrix: [tex]\(\left[\begin{array}{lll}1 & 2 & 4 \\ 2 & 3 & 5\end{array}\right]\)[/tex]
To find the order of a matrix, we count the number of rows and columns. This matrix has:
- 2 rows
- 3 columns
Hence, the order of the matrix is:
C. [tex]\(2 \times 3\)[/tex]
3. The [tex]\(n\)[/tex]-th term of a sequence is given by [tex]\(5n + 2\)[/tex]. Find the fourth term.
To find the fourth term, substitute [tex]\(n = 4\)[/tex] into the given formula for the [tex]\(n\)[/tex]-th term.
[tex]\[ a_n = 5n + 2 \][/tex]
For [tex]\(n = 4\)[/tex]:
[tex]\[ a_4 = 5(4) + 2 \][/tex]
[tex]\[ a_4 = 20 + 2 \][/tex]
[tex]\[ a_4 = 22 \][/tex]
Therefore, the fourth term is:
22
