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Find the roots of the equation
2x^3-x^2-22x-24=0
if two of them are in the
ratio 4:3 .
Obtain the discriminant of the equation 2x^3-23x^2+82x-78=0
Hence provide the nature of its roots.
Find the polynomial over R of least degree which has i−3 and √7+5i as its
roots.

Give examples, with justification, of the following:
ii) two non-singular 2× 2 matrices C and D , with |C| =√2 |D|
Give examples, with justification, of the following:
i) two non-zero, 3×3 matrices A and B , with |A|=0, |B|=(5/7)i
Write an odd natural number as a sum of two integers m1 and m2 in a way that m1m2 is maximum.
x/5=80%. Which number makes this true?
An ant lives on the surface of a cube with edges of length 7cm. It is currently
located on an edge x
cm from one of its ends. While traveling on the surface of the cube,
it has to reach the grain located on the opposite edge (also a
t a distance xcm from one of its ends)
.
(i) What is the length of the shortest route to the grain if x = 2cm? How many routes of
this length are there?
(ii) Find an x for which there are four distinct shortest length routes to the grain.
Terry is buying juice. He needs 3 L. A half liter of juice cost $2.39. A 250 mL container of juice c Play needs 3 L. A half liter of juice cost $2.39. A 250 mL container of juice costs $1.69.What should Terry buy so he gets 3 Liters at the lowest price? Explain
The waveform of a voltage in an electrical circuit has the following parameters:
 A continuous series of right-angled triangles, each with a base length equivalent to 3 ms, 9 V maximum
-Voltage ramps up over the 3 ms and then drops back to zero instantaneously
-Sketch the waveform and mark on the relevant parameters.
-Derive the function which defines the waveform.
-Using integral calculus, find the RMS value of the voltage.
The acceleration of a sliding component in a packaging machine is given by the following expression: (d^2 s)/(dt^2 ) =12t+3
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