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Further Mathematics
A Level

Solve the following, giving your answers in terms of ln a: 7 sechx - tanhx =5

7sechx - tanhx = 5 7/coshx - sinhx/coshx = 5 7 - sinhx = 5 cosh x 7 - 0.5(e- e-x) = 2.5(e+ e-x) 7 -0.5e+ 0.5e-x = 2.5e+...

Answered by Alex W. Further Mathematics tutor
6823 Views

How would go about finding the set of values of x for which x+4 > 4 / (x+1)?

Whenever you see a problem involving an inequality (greater than or less than sign) it is really important to pause for a second before you go breaking any rules of mathematics. ...

Answered by Tim H. Further Mathematics tutor
2062 Views

Use algebra to find the set of values of x for which mod(3x^2 - 19x + 20) < 2x + 2.

The initial quadratic can be either positive or negative so we must solve for both possibilities.

Solving for positive:

3x^2 - 19x + 20 < 2x + 2    =    3x^2 - 21x + 18 < 0

...
Answered by James M. Further Mathematics tutor
10105 Views

z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.

a) Need to multiply with conjugate to bring z to form a+ib. => z= z * (1-i)/(1-i) = (4-4i) / 2 = 2-2i

b) z^2 = (2-2i)^2 = 4-8i+4 i^2 = 4-8i-4 = 8i

since z is root of x^2+px+q=0 then z* (c...

Answered by Harry P. Further Mathematics tutor
5660 Views

Express cos5x in terms of increasing powers of cosx

De Moivre's theorem: (cos5x + isin5x) = (cosx + isinx)5 To get cos5x we will need to expand (cosx + isinx)5 and then take the real parts. Binomial expansion: (cosx + isinx)5

Answered by Chris S. Further Mathematics tutor
30275 Views

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