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3. a) A function h is defined by: h(q) = aq³+q² + bq - 240 When h(q) is divided by (4 - q), the remainder is 72. Also, (2q - 5) is a factor of h(q). i. ii. Calculate the values of a and b. Hence or otherwise, determine all the factors of h(q).

3. a) A function h is defined by: h(q) = aq³+q² + bq - 240 When h(q) is divided by (4 - q), the remainder is 72. Also, (2q - 5) is a factor of h(q). i. ii. Calculate the values of a and b. Hence or otherwise, determine all the factors of h(q).

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3. a) b) A function h is defined by: h(q) = aq³+q² + bq - 240 When h(q) is divided by (4 - q), the remainder is 72. Also, (2q - 5) is a factor of h(q). i. ii. Calculate the values of a and b. Hence or otherwise, determine all the factors of h(q). Massy Store makes a $10,500 investment at Republic Bank Ltd on January 1, 2019. At the end of December 31, 2023, Massy Store is expected to accumulate an amount of $17166.25? i. Calculate the interest rate needed to procure this investment? ii. How long will it take for the initial amount invested to be doubled, given that interest is compounded annually at the rate in (i) above? c) At the end of eight years Susan had $6,000.00 in an investment account. The investment account pays interest at 7% p.a. compounded annually. How much money did Susan invested into the account at the start.
Transcribed Image Text:3. a) b) A function h is defined by: h(q) = aq³+q² + bq - 240 When h(q) is divided by (4 - q), the remainder is 72. Also, (2q - 5) is a factor of h(q). i. ii. Calculate the values of a and b. Hence or otherwise, determine all the factors of h(q). Massy Store makes a $10,500 investment at Republic Bank Ltd on January 1, 2019. At the end of December 31, 2023, Massy Store is expected to accumulate an amount of $17166.25? i. Calculate the interest rate needed to procure this investment? ii. How long will it take for the initial amount invested to be doubled, given that interest is compounded annually at the rate in (i) above? c) At the end of eight years Susan had $6,000.00 in an investment account. The investment account pays interest at 7% p.a. compounded annually. How much money did Susan invested into the account at the start.
2. a) b) A firm's revenue function from the sale of S21 is R(x) = 2x² - 9x 221 and the firm's total cost function is given by C(x) = -x² + 4 where x represents the level of demand for S21. i. ii. How many S21 would the firm be required to produce and sell to record total revenue of zero? Write an algebraic expression to represent the profit function for the firm. Figure 1 below shows the graphical representation of a straight-line m -6 -5 V. -4 -2 -1 2 0 -2 -4 1 2 From the diagram above; i. Describe the straight-line m (the line-colored orange). 11. Identify two clear and distinct points on the straight-line m. iii. Calculate the gradient of the straight-line m. iv. Determine the equation of the straight-line m. Straight line z passes through the origin and is perpendicular to straight line m, determine the equation of the straight-line z.
Transcribed Image Text:2. a) b) A firm's revenue function from the sale of S21 is R(x) = 2x² - 9x 221 and the firm's total cost function is given by C(x) = -x² + 4 where x represents the level of demand for S21. i. ii. How many S21 would the firm be required to produce and sell to record total revenue of zero? Write an algebraic expression to represent the profit function for the firm. Figure 1 below shows the graphical representation of a straight-line m -6 -5 V. -4 -2 -1 2 0 -2 -4 1 2 From the diagram above; i. Describe the straight-line m (the line-colored orange). 11. Identify two clear and distinct points on the straight-line m. iii. Calculate the gradient of the straight-line m. iv. Determine the equation of the straight-line m. Straight line z passes through the origin and is perpendicular to straight line m, determine the equation of the straight-line z.
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