This one is straightforward

You can see that in getting from O to P, we move 2 units to the right and 7 units downwards.

We represent this as OP--> = (column vector with 2 on top and -7 below).

(I write that OP with an arrow on top as OP-->)

Similarly, OQ--> = (column vector with 8 on top and 3 below)

I let you try for PQ and OM

If OPRQ is a diagram, then the movement from Q to R will be identical to the movement from O to P (because OP and QR will be on opposite ends of the parallelogram having the same length and direction).

O to P, as mentioned before, is a movement 2 units to the right and 7 units downwards.

Q to R will be the same, with 2 units to the right and 7 units downwards.

R will eventually be (10, -4).

You must link the ideas of coordinate geometry to this, as they are closely linked. Vectors is basically like physically counting grids on a graph paper (eg moving 2 grids to the right etc).

thx :)

hi Mr Eric, why is it
3/(x-4)^2 - 1/4-x
= 4/(x-4)^2 + 1/x-4 and not 4/(x-4)^2 + (-1/x-4)?

You must check whether you have flipped the denominator and changed the signage yet.

So,

3 / (x - 4)^2 - 1 / (4 - x)
= 3 / (x - 4)^2 + 1 / (x - 4)
= (make denominator (x - 4)^2)
= (numerator becomes 3 + x - 4)
= (x - 1) / (x - 4)^2

The error with your “not” version in this case is that the connector suddenly changed from “-“ to “+” when you brought in the negative sign to the second term and flipped the fraction at the same time. In doing so, you made three changes to the signages the same time.

One, in changing the connector of - into + for the two fractions.

Two, in introducing the - sign in front of the second fraction when there was no - sign previously.

Third, hidden as the conversion of 4 - x into x - 4.

As such, there are three changes to the negative signs, bringing about an imbalance to the equality of the expressions between your working steps.

flipping the denominator already means taking out the negative sign, and that theres no need to touch the numerator anymore?

by the way what does the "n" in n(AnB) represent tho, is it in the syllabus? as i have never seen it before

Yes, because 4 - x = - (x - 4)

(Hence, the idea of flipping)

n (A n B)

The n outside the brackets represents the number of elements in the set A n B.

So let’s say A n B = {2, 5, 10}.

Then n (A n B) = 3 because there are three elements 2, 5 and 10 inside the set.

It’s well within your syllabus.

thx :) what is the difference between the drying agents concentrated sulfuric acid and fused calcium chloride tho

These are just different substances capable of extracting water content from other substances (due to their own lack of water content) to dry these other substances

Their functions are primarily the same, but it works for specific classes of gases

is it true that both concentrated sulfuric acid and fused calcium chloride dry any type of gases? my notes said so, however it is weird as both have the same usage...

Of course not the same gases, but at least for your syllabus, it happens to be the same.

Concentrated sulfuric acid should work for most gases which are non-basic or non-alkaline. It will not be able to dry ammonia gas.

Calcium chloride works for many gases, but I know that ammonia is one of them which fails.