Other Math Answers

QUESTION 6
Suppose we have functions f, g and h, defined as follows
f (x) = log4(x + 3) − log4(x − 2)
g (x) = 5x − 2xsqaured
h (x) = 2x / √3 − x

6.1 (a) Write down Df .

(b) Solve f (x) = 1/2

6.2 (a) Find Dg and Rg.
(b) Solve g (x) ≤ 2.

6.3 (a) Write down Dh.
(b) Solve h (x) = 1.

QUESTION 4

4.1 Two aeroplanes leave two different airports, 1000km apart from each other, at 9h00 in the morning. They fly towards each other. The one flies at a speed of 250km/h and the other at 350km/h. At what time will they pass each other?

4.2 Find the amount of interest that a person will earn if he invests an amount of R9000 for 30 months, at an interest rate of 6% per annum, with the interest compounded semi-annually. (Leave your answer as an expression in exponential form as you may not use a calculator.)

QUESTION 5

The population of a country grows according to the formula N = N0ekt where N is the population (in millions) at time t (in years). N0 is the intial population (in millions) and
k is a constant.

5.1 If the initial population was 40 million and after 120 years it is 360 million, find an expression for k in terms of ln.

5.2 Use this expression for k and the other information given above, to find how long it takes for the population to double.

QUESTION 2

2.1 Three students, Thando, Busi and Peter, painted a room together. They spent 5 hours, 3 hours

and 2 hour, respectively, on the task. They earned R500 in total, for the job. How much should
each of them receive? (3)

2.2 A trader made a profit of 50% on merchandise that he sold for R10000. Calculate the original total price of the goods. (3)

QUESTION 3

3.1 The fourth, fifth and sixth terms of a geometric sequence are x − 4, x + 2 and 3x + 1 respectively. Determine:

(a) the possible values for x. (3)

(b) the value for the first term in the sequence if x < 0 (i.e. x is negative). (4)

3.2 The first term of an arithmetic sequence is 10 and the sixth term is 85. Find the first three terms of the sequence. (4)

Suppose A = {x ∈ R : x > −3} and B = (−4; 5].

1.1 Sketch each of A and B on a separate number line.

1.2 (a) Write A ∪ B in set builder notation.

(b) Sketch A ∪ B on a separate number line.

1.3 (a) Write A ∩ B in interval notation.

(b) Sketch A ∩ B on a separate number line.

QUESTION 1

Test marks for ten students are 2, 3, 6, 7, 7, x, 5, 5, 8, 9

(i) Given that the average mark is 6, find the value of x.

(ii) Calculate the standard deviation for these set of marks

QUESTION 2

Solve the following pair of equations by Cramer’s rule.

1) 3x + 5y = 2
2) 2x-7y = - 1

1.An aircraft flies into the north easterly direction at 750 km/h. There is a moderate Wind blowing at 5 km/h from west to east.

(i) Draw a vector diagram to represent the problem.

(ii) After travelling for two hours, find the distance travelled.

1.An aircraft flies into the north easterly direction at 750 km/h. There is a moderate Wind blowing at 5 km/h from west to east.

(i) Draw a vector diagram to represent the problem.

(ii) After travelling for two hours, find the distance travelled.

Solve the equation
3^-X = 243


Solve the following exponential equation
2^2X - 6(2^X ) + 8 = 0
3^2x - 4(3^x+1) + 27 = 0

Solve the following logarithmic equation
Log^3(x^2+7x 21=2
Log^8(x^2-8x+18)=1\3

Solve the equation
3-X = 243


Solve the following exponential equation
2^{2X}\:\:-\:6\left(2^X\right)^{\:}\:+\:8\:=\:0
3^{2x}\:\:-\:4\left(3^{x+1}\right)\:+\:27\:=\:0
• 32x - 4(3x+1) + 27 = 0

Solve the following logarithmic equation
Log3\:\left(\:x^2\:+\:7x\:21\:\right)\:=\:2
Log8\:\left(x^2\:-\:8x\:+\:18\right)\:=\:1/3

Show that 1n3 + 2n + 3n2 is divisible by 2 and 3 for all positive integers n.