Higher Maths 2014-2015 :: Discussion Thread

Help please am stuck

Find the equation of the parallel line to the given line 2y - 3x + 1 = 0
the parallel line passes through (1,3)

worked out that m = 3/2

but using y-b = m(x-a) i am getting 2y - 3x = 3 which is incorrect

help please
Functions

h(x)=x^{2 -} 2x

Show that

h(2x) = 4x(x-1)

How are multiple bracketed terms to the same power integrated?

e.g. "integrate (2x + 9)^5 with respect to x"

How are multiple bracketed terms to the same power integrated?

e.g. "integrate (2x + 9)^5 with respect to x"

Have you covered the chain rule in differentiation yet?


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In 22a), once we deduce that kcosa = 1 and ksina = 3sqroot, how can we find k?

ksina/kcosa = tana

Use that to find a, then find k.


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I tried that: ktana = 3sqroot.
tan60 = 3sqroot
But aren't we wrongly assuming k to be 1 here?

Can anyone help me with these questions please?

g(x) = x3 – 3x + 5.
What is the remainder when g(x) is divided by (x + 2)?
I know how to do this one, but I cannot get the remainder to work out right. It should be 3.

Find the range of values of k such that the equation kx2 – x – 1 = 0 has no real roots.

What is the value of cos 5pi/3 - tan 7pi/4? (non calculator)

Any help would be much appreciated, thanks in advance!

Can anyone help with these questions? So stuck ahaha


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We're not assuming k=1. It's k/k = 1.


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1. Take the transformation a step at a time. In y = -f(x+1) + 4, what we've done is:
- flipped across the x-axis, meaning every y-coord is multiplied by -1
- THEN moved 1 unit to the left, meaning every x-coord subtracts 1
- THEN moved the whole graph up by 4 units, meaning every y-coord adds 4

I like to think of it this way: if you do something OUTSIDE the bracket, you're affecting the y-coords in some way - if you do something INSIDE the bracket, you're affecting the x-coords.



2. Log functions are the inverse of exponential functions. You should already be aware that, with exp. functions/graphs such as y = a^x, when x = 0, y will equal 1, and when x = 1, y will equal a.

Inverse graphs have the straight line y = x as their axis of symmetry. So, essentially to get the inverse of a graph, you will be flipping the x and y coords of every point. With log graphs, the previous noteworthy points in the exp. graphs become such that (0, 1) ---> (1, 0), and (1, a) ---> (a, 1). This means, in the form loga-x, when x = 1, loga-x = 0, and when x = a, loga-x = 1.

This means you can immediately identify a in your question. For b, notice that log graphs will cut the x-axis at x = 1 when there is no b variable - from this information you can identify b.

For the second part of the question: you need to know that in any log function, the variable you're applying the "log to the base of" must be greater than 0. Look at your graph. Simply put, as the y-coord decreases, x will continue to get nearer and nearer the y-axis, but it will never touch it - so x > 0 (this is the exact opposite of an exponential graph where y > 0). In your question, solve the inequality x - b > 0.


3. A case of taking care when multiplying out brackets and collecting like terms. Take your time, and the "relationship" part most likely refers to the fact that the functions are the inverse of each other, in which case they return x as the output.

Thanks for that.

Still confused about the first one though. Could the 4-f(x+1) not be stretched? Also, does it matter the order in which you complete the transformations? Because if I do -flip, move left, add four, and get a different answer to doing -add four, flip, move left. Which was round do I do it?


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Would the answer to 2b be x > -1 ? Not sure I've done it correctly...


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