'The terms numeracy and mathematics are often used interchangeably, but in fact they are very different concepts' (Grimley, 2016).

Your essay should be informed by your understanding of the two concepts: mathematics and numeracy. Weeks 1–4 of your learning materials will give you an understanding of both concepts and how they are crucial to one’s understanding of the world around us. You are required to support your discussion with examples of everyday (maths) phenomena and identify where mathematical and numeracy skills are used in everyday life.

Essay structure

1. Introduction: Write a clear introduction that frames the essay (approximately 10% of the word count).
2. Main body: Identify and briefly discuss the quote to scaffold the following sections of the essay:
   • What are the two concepts? Define and describe both concepts (maths and numeracy).
   • How and why are they different? Explore the similarities and differences between the concepts.
   • Where and when are they seen in the world around us? Support your discussion with a minimum of one everyday (maths) phenomena and at least one example where numeracy skills are used in everyday life, found in Weeks 1–4 learning materials. 
3. Conclusion: Conclude with a brief explanation of the importance of understanding the two different concepts and the impact this has for educators (approximately 10% of the word count).
4. Reference list: All resources that you have cited in-text in the essay need to be referenced in APA style.

Consider the following vectors {1 + x + x^2, 1 - x^2, x + 2, 1 - x}.
a) Test or refute if the vector set is linearly independent?
b) Construct a linearly independent set of dimension 2, describe the
shape of the generated space.
c) Construct a linearly independent set of dimension 3, describe the
shape of the generated space.
d) For the base you chose in part c), find a linear combination for
p (x) = 3 + 11x + 8x^3

Determine whether it is linear or nonlinear system:

1. y(t) = 3 + x(2t)

2. y(t) = x(4t)

3. y(t) = -4t[x(2t)]

4. y(t) = e^2[x(2t)]

5. y(t) = x^5(t)

6. y(t) = cost[x(2t)]

Use MATLAB to solve graphically the planar system of linear equations

x +4 y = −4

4x +3 y =4

to an accuracy of two decimal points.
Hint: The MATLAB command zoom on allows us to view the plot in a window whose axes are one-half those of original. Each time you click with the mouse on a point, the axes’ limits are halved and centered at the designated point. Coupling zoom on with grid on allows you to determine approximate numerical values for the intersection point.

A company produces and sells 2,500 sets of silverware each year. Each production run has a fixed cost of 200 dollars and an additional cost of 5 dollars per set of silverware. To store a set for a full year costs 4 dollars. What is the optimal number of production runs the company should make each year? Do not include units with your answer.

Discuss and describe the factors affecting spatial resolution (SR) in multiple ring PET systems

Answer the following questions in order to approximate the value of sin(0.8).

Note that π/ 4 ≈ 0.785 radians.

(a) Do you have enough information to use right triangles to estimate sin(0.8)? Why?

(b) Estimate sin(0.8) using values of sin(x) that you know from part (2).

(c) Estimate sin(0.8) using the graph of y = sin(x) from part (3).

(d) Estimate sin(0.8) using the 5th degree Taylor polynomial for sin(x) at a = 0 (I will accept either the Taylor polynomial up to n = 5 or the Taylor polynomial up to the x^5 term). Find the error bound from the Alternating Series Estimation Theorem (using the next nonzero term of the Maclaurin series), and explain what it tells you about the actual value of sin(0.8).

Mullet Technologies is considering whether or not to refund a $75 million, 12% coupon, 30-year bond issue that was sold 5 years ago. It is amortizing $5 millions of flotation costs on the 12% bonds over the issue’s 30-year life. Mullet’s investment banks have indicated that the company could sell a new 25-year issue at an interest rate of 10% in today’s market. A call premium of 12% would be required to retire the old bonds, and flotation costs on the new issue would amount to $5 million. Mullet’s marginal tax rate is 40%.

a. What is the cash outlay at the time of the refunding?

b. What is the net change in the annual flotation cost tax savings?

c. What is the after-tax annual interest savings?

d. What is the bond refunding’s NPV? What is the decision?

Differential Equations: Find the general solution by using infinite series centered at a.

5. xy′′− 2y′− 2y = 0, a=0.

Differential Equations: Find the general solution by using infinite series centered at a.

4.xy′′+ y′− y = 0, a=0.

Differential Equations: Find the general solution by using infinite series centered at a.

2. (x² +1)y′′ + xy′ + y = 0, a=0.

Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)

Consider a nonhomogeneous differential equation

?′′ + 2?′ + ? = 2? sin?

(a) Find any particular solution ?? by using the method of undetermined coefficients.

(b) Find the general solution.

(c) Find the particular solution if ?(0) = 0 and ?′(0) = 0.

My instructor doesn't have the most intelligible answer keys. Could you explain how to solve this?

Math 266, Quiz 15: Answers due today, April 22, by 1:00 PM via email.

1. Let g(t) be given by

?(?) = {

0, 0 < ? < 1

? − 1, 1 < ? < 2

3 − ?, 2 < ? < 3

1, ? > 3

Rewriting ?(?) using the unit step function gives:

a) ?(?) = (? − 1)?(? − 1) + (4 − 2?)?(? − 2) + (? − 2)?(? − 3)

b) ?(?) = (? − 1)?(? − 1) − (? − 1)?(? − 2) + (? − 3)?(? − 2) − (? − 3)?(? − 3) + ?(? − 3)

c) ?(?) = (? − 1) − (? − 1)?(? − 2) + (3 − ?)?(? − 2) − (3 − ?)?(? − 3) + ?(? − 3)

d) ?(?) = (? − 1)?(? − 1) + (1 − ?)?(? − 2) − (? − 3)?(? − 2) + (? − 3)?(? − 3)

e) None of the above.

2. Use Laplace transforms to solve ?′′ + ? = ?(? − 1) − ?(? − 2) with ?(0) = 0, ? ′ (0) = 1