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Show that the inequality x^4 < 8x^2 + 9 is satisfied for when -3 < x < 3 .

(x^2 - 9)(x^2 + 1) &lt; 0 solving the equation to get solutions to the equality (x^2 - 9)(x^2 + 1) = 0 : x = +/- 3 or x = +/- 1 now consider points either side of these x-intercepts... for x&gt;3: equality i...
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Answered by Hakkihan T. • MAT tutor
1511 Views

Express cos(x) + (1/2)sin(x) in terms of a single resultant sinusoidal wave of the form Rsin(x+a)

cos(x) + (1/2)sin(x) : Rsin(x + a) = R{sin(x)cos(a) + cos(x)sin(a)} = (1/2)sin(x) + (1)cos(x) (comparing coeffs.) Therefore Rcos(a) = 1/2 and separately Rsin(a) = 1 So tan(a) = 2 and R^2 = 5/4. Answer: sqrt(...
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Answered by Hakkihan T. • Maths tutor
8149 Views

How can you tell whether a word is feminine or masculine?

There is no simple answer for this! In short, the gender of nouns in French must be learnt, rehearsed and repeated until you can't hear the word any other way. Although there are some shortcuts for this, for...
YG
Answered by Yemi G. • French tutor
3899 Views

Find the general solution, in degrees, of the equation 2 sin(3x+45°)= 1

A general way of solving these equations is getting them to the form sin(y)=k . In this case, to do so, we have to divide by 2 and then put y=3x+45° We then get sin(y)=1/2 . You should know which angles have...
CG
9255 Views

The quadratic equation 2x^2+ 6x+7 has roots a and b. Write down the value of a+b and the value of ab.

A general method would be to compute a and b with the general solution formula for quadratic equations. However, a special property of quadratic equations can make this a lot easier. In fact, given the equat...
CG
6234 Views