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The first terms of an A.P and G.P are each 2/3. Their common and difference and

common ratio are each X and the sum of their first three terms are also equal.

Find the two possible values of X


Simply and express your answer in a form that is free of radicals in the denominator

3/2+√3-4/1-√2


The first term of a geometric progression is √ 3+1 and the sum of the first three

terms is 3( √ 3-1) . Find the common ratio of the progression.

(4marks).


A person's height is measured to be 67.50 in.what is this height in centimeters


If Phumza and Nathi eat together, they can eat 480 hamburgers in 6 hours. However, eating alone, Nathi takes 16 hours longer than Phumza would eat 480 hamburgers.
How long does it take Phumza to eat 480 hamburgers?

solve the following quadratic equations. Leave surds in your answers.

a) (x-3)^2-3=0

b) (3x-7)^2 =8


2a) x^4-5x^2+4=0

b) x-8=2squareroot x


Equation x^3 + 27x^2 + p = 0 has three different real solutions that form an arithmetic progression. Find the smallest value of parameter p.


y=3(x-13)^2+23



If m, n and p are the roots of the polynomial x3+5x-8 and sum of the roots is 0

0, then find the value of m3+n3+p3.



.



The volume of a box V, varies with some variable x as V(x)=x^3 - 12x ^2 + 44x -48 cubic metres. If (x - a) metre is the measurement of one side of the box, then find the value for a.