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OK. Say you take x = 5.7 say. Then this number is |5.7 + 1| = 1 + 5.7 = 6.7 away from the number -1, and |5.7 -5| = 0.7 away from the number 5; so it is = the constant 6 plus 2 x 0.7 from the 2 numbers. Remember, any x outside the closed interval [-1,5] is 6 + twice its distance from the nearer...

Say you choose any x between -1 and 5, x = 2, say. then |x+1| + |x-5| = |2+1| + |2 - 5| = 6. Choose another such number, say x = -0.7; then |x+1| + |x-5| = |-0.7 + 1| + |-0.7 -5| =0.3 + 5.7 = 6 (again). If you choose x = -3 (which is more than 0.5 to the left of -1), then |-3+1| + |-3-5| = 2 + 8...

Follow what i said. Draw a line and mark off -1 and 5. any number x between and including -1 and 5 will have |x+1| + |x-5| = 6 (a fixed sum - so we need at least 1 more for this sum) So x must be outside this interval; x now only needs to be more than 0.5 beyond the 2 numbers -1 and 5; i.e. at...

To me graphing is easier like this: Draw the number line and mark off the 2 numbers "-1" and "5". The distance between these 2 numbers = 5-(-1) = 6. Now read the inequality this way: the distance of the number x from "-1" plus the distance of x from the number "5" is greater than 7. Now x...

Yes! For someone doing MX2, your grasp of the fundamentals of trigonometry needs to be better.

It is. It is always true that: cos(\pi -\theta) = -cos \theta whatever the value of theta.

No.

In outline as LaTeXing is so tedious. \therefore b_2 = b_{1+1} = b_1(b_1 + 1) = 1(1+1) = 2\\ \\ \therefore b_2 = 2 = 1 + \sum ^1 _{r=1} b_r ^2 = 1 + 1^2 Therefore true for k = 1. Now assume true for n = k (k >= 1) \therefore b_{k+1} = 1 + \sum ^k _{r=1} b_r ^2 \\ \\ b_{k+2} = b_{k +1}(b_{k...

Australia likes to boast about world-class universities. All those university ranking bodies like the Times Higher Education World University rankings that appear annually shouldn't be taken too seriously. To give a bonus point for a Band 3 in (the so-called - what a misnomer) Advance Maths is a...

I recall having a chat with a stranger about 10 years ago who told me he was doing Electrical Engineering at USyd, but did not study Physics for his HSC. They let him do it. May well have eventually completed his B Eng(Electrical). Miracles do happen! Scott Morrison is right after all.

Bad! Unis are nowadays often run by bureaucrats (Scott currently at USyd) - not by administrators with an academic background. I think it is a retrograde step and, as you have said, sends a wrong message. When I went to uni long long ago, there were no such thing as ATARs. Each course has its...

If anyone is seriously interested in a highly experienced 1-on-1 Maths Ext 1 and/or Maths Ext 2 tutor, please message me. I'm not a recent HSC graduate. I tutor from my place: about 10 to 15 minutes walk from Epping Station. If you want a good coaching centre, you have the Dr Du, Kurt, Matrix...

I'm not familiar with the questions asked. Can you show the type of questions asked?

The Bernoullis were a famous family of outstanding mathematians.

sin3x-sinx = (3sinx - 4sin^3x) - sinx = 2sinx - 4sin^3x

I can.

Is the area 8, by any chance?

It's not necessarily true you will excel in MX1 if you work hard. Appreciate that wollongong warrior is trying to be helpful and to encourage you. But do give MX1 your best effort and see how you go, before deciding.

What subject is he offering?

If p implies q, then consider the truth table of p => q: p q | p=>q ______________________ T T | T T F | F F T | T F F | T Out of the 4 p:q possibilities, only the T:F case is F(False) In this question, we have p:q as...