1. Determine each of the following set of vectors is linearly independent or dependent.

(a) S1 = {(1, 2, 3),(4, 5, 6),(6, 9, 12)}.

(b) S2 = {(1, 2, 3, 4),(5, 6, 7, 8),(3, 2, 1, 0)}.

(c) S3 = {(1, 2, 3, 4),(5, 6, 7, 8),(9, 10, 11, 12)}

Passwords on an ancient computer are required to be 4-5 characters long and made up of lower case letters only (a..z : there are 26 possibilities). Please answer each of these questions below, giving numerical answers. You should also explain how you got each answer, for full or partial credit.

a) Assume that letters may NOT be repeated, and passwords are 4-5 letters long. How many passwords are possible?

b) Assume that letters MAY be repeated, and passwords are 4-5 letters long. How many passwords are possible?

c) Assuming that letters MAY be repeated, what proportion of the total number of passwords in fact *do* have at least one letter used more than once?

d) Letters may be repeated but the following extra rules exist:

• The password cannot be 4 or 5 identical letters like xxxx or bbbbb
• The password cannot be on a list of 71 common 4-5 letter words (none of them are like xxxx or bbbbb!)

How many passwords are possible now?

Note: since this is a practice test question, the answers can be seen in the question comment after you turn in your quiz. Canvas can't grade "essay" type questions for correctness, so you will get a 0 grade whatever you write.

Explain in detail Multilevel Structural Equations Modelling. Discuss your answer in 1000 words

f(x)= x^3-5sinx-23 use Newton iteration to estimate the root Find A, R, Theoritically and Numerically

Some say that Engineering is not a profession
What is the argument they use to support this position?
(Be brief and precise in your answer)

Draw all possible border pieces of a puzzle, each having a different shape.

Border-pieces are puzzle pieces that have at least one smooth edge.

1. Solve the given third-order differential equation by variation of parameters. y''' − 2y'' − y' + 2y = e^3x

MAT 117 Problem Set 1                               Name: ___________________________

Directions: Show all work and explain your thinking as you solve these problems or write the explanations. Each problem is worth five points.

1. Below are definitions of different math number concepts. Write the concept that goes with each description. (no explanation needed for this problem only).

2. Explain the difference between the expressions 6x⁰ and (6x)⁰. If there is no difference, explain why.

Grading: 2 points: Worked out Problem Mathematically; 3 points: Explanation

3. For a recent year, the United States consumed about 1.0 x 10⁴ of petroleum per second. (Source: U.S. Energy Information Administration)

How many gallons of petroleum did the United States use that year?

Show work for all intermittent steps and Explain each step used to get your answer.

Grading: 1 point: Correct Answer; 2 points: Work; 2 points: Explanation

4. State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial. Give an example proving your answer is correct.

Grading: 2 points: Correct Answer; 2 points: Explanation; 1 point: Example

5. Explain why x+ 7 is a polynomial, but x+7 is not a polynomial.

Grading: 5 points: Complete explanation

Given the below relational algebra expressions, use domain and tuple relational calculus to specify them:

a. σ_x=z ( R(a,b,c) )

b. π_x,y ( R(x,y,z) )

c. R(x, y) / S(x)

d. R(a,b,c) ∪  S(a,b,c)

e. R(a,b,c) – S(a,b,c)

f. R(d,e,f) ∩ S(d,e,f)

g. R(x,y,z) × S(f,g,t)

Find all x ∈ Z such that x≡2 mod 221 and x≡5 mod 184.

The reader understands derivatives, and knows the definition of instantaneous velocity and knows how to calculate integrals but is struggling to understand them. Use students’ prior knowledge to provide an explanation that includes the concept and physical meaning of the integral of velocity with respect to time. (Give an example)

Reminder: The user is comfortable with the calculations, but is struggling with the concept. To fully address the prompt, emphasize the written explanation in English over the calculation.

Do not copy paste Please type and attach graph or figures(Draw) for better understanding.

Use the Laplace transform to solve the given initial value problem:

y''+3y'+2y=1 y(0)=0, y'(0)=2