代写QTS0103 Business Mathematics代写Processing

BUSINESS MATHEMATICS (QTS0103)

CONTINUOUS ASSESSMENT 1

INDIVIDUAL ASSIGNMENT (30%)

Question 1 (10 marks)

(a)       Solve the following equation. Give your answer to 2 decimal places (if applicable).

4/x − 15 = −2x + 2/1

[2 marks]

(b)       Solve the following inequalities:

(i) −3 ≤ 3/x+1 ≤ 2

[2 marks]

(ii)       |2x − 5|  ≥ 10

[2 marks]

(c)       Given: f(x) = 3x  and g(x) = x2  − 1. Find the value of: fog(1)

[2 marks]

(d)       Determine the domain of the function: f(x) = x2-9/5

[2 marks]

(Total 10 marks)

Question 2 (10 marks)

(a)       Find the equation of the line that passes through the point (5, –5) and is parallel to the line with equation y = -2x – 1.

[3 marks]

(b)       Find the point of intersection(s) of the lines of the functions f(x) = 5x + 6 and g(x) = x 2  + 2x. Provide your workings and answer(s) to 2 decimal places when applicable.

(c)       Your firm had sales of $30,000 in its first year of operation. If sales increase by 10% per year thereafter, determine your company’s sales in the tenth year and its total sales over the twenty years of operation. Give your answers to the nearest dollar.

[4 marks]

(Total 10 marks)

Question 3 (10 marks)

(a)       Your firm manufactures office tables at cost of $50 per unit and sells them for $80 per unit. With a monthly fixed cost of $120,000, determine your firm’s monthly break-even quantity and break-even revenue.

[3 marks]

(b)       Solve the following equations for x. Provide your answer(s) to 3 decimal places when applicable.

(i)        2e4x-1  = 12

[2 marks]

(ii)       ln x 2   +  ln 3 = 5

[2 marks]

(c)       Your firm purchased a machine for $250,000. After 2 years, the value of the machine decreased to $150,000. If the machine’s value decreases exponentially, what will the machine’s value be after 10 years? Provide your workings to 3 decimal places and answer to the nearest dollar.

[3 marks]

(Total 10 marks)