Specialist 1/2 Question Thread!

[pans]

Hello,
Can someone pls explain 4E Q12, 13

[fun_jirachi]

Hey!

Q12 was answered here.

Q13a - each time you tear the pieces of paper, you double the number of pieces of paper. You start with 1, then after the first step you have 2. After two steps, you have 4. Is there a geometric series you can construct that will tell you how many will you have after 40 steps? If you stack each piece of 0.05mm paper, the stack should just be the number of pieces you have after 40 steps * 0.05mm.

Q13b - essentially, 384400 km = 3.844 x 10¹¹ mm. At what step does the number of pieces of paper exceed this number? use the same geometric series as part a).

Try this again and get back to us if you're stuck.

[pans]

can anyone help me with sequence and series hard Q!

[pans]

can someone also pls help me with these 3 sequence and series Q

[fun_jirachi]

Hey there!

Please try not to double post - you can edit your additional questions into the previous one

What have you tried? Ideally, I'd love to help you by giving you more hints, but at some point, it does become a bit counterintuitive as you won't be getting hints at school and in exams - it would help you learn more if you told us what you've tried, then in response, we point you in a better direction. Hopefully, this makes sense!

[Rachelrachel]

I've been stuck on this for a while:

If z₁ and z₂ are the two complex solutions to the quadratic equation ax² + bx + c = 0, and P₁ and P₂ are the corresponding points on an Argand diagram, what is the cosine of the angle between P₁, P₂, and the origin in terms of a b and c?

[fun_jirachi]

A few hints:
- If \(z_1, z_2\) are complex roots to a quadratic equation, how are they related?
- Can you express the points \(P_1, P_2\) in terms of \(a, b, c\)?
- If possible, graph the origin and these two points on the Argand plane (does require you get the first hint) - what do you notice about the position of these points?
- Connect each point to the origin so you have segments \(OP_1\) and \(OP_2\). Is there a relationship between these segments and the angles they make with the coordinate axes?
- You can use the fact that \(\cos (\angle P_1OP_2) = \frac{P_1 \ \bullet \ P_2}{|P_1||P_2|}\) - but is there an easier method?  (Think geometrically rather than algebraically)

Hope this helps

[Rachelrachel]

Thank you very much for the help, fun_jirachi.

To be honest, it is the geometric part that I'm having difficulty with. I know that the angle between P₁ and P₂ would be twice the argument of z₁, but I don't understand how to find the cosine of an angle in geometric terms.

[fun_jirachi]

Got everything apart from that, which is great! If you have the coordinates of a point on the Argand plane, how would you usually calculate the argument? You're right in that \(\cos (P_1OP_2) = \cos (2\text{arg}(z_1))\). Right-angled trig should be handy (which is what I meant when I said think geometrically (awful wording, in hindsight - sorry! that one's on me )).

[Ruchir]

Hey guys need help with this question
I got part a, but I am stuck with part b.


Let A and B be the points defined by the position vectors a=i+3j   and b=i+j
respectively. Find:
a the vector resolute of a in the direction of b
b a unit vector through A perpendicular to OB

[S_R_K]

Hey guys need help with this question
I got part a, but I am stuck with part b.


Let A and B be the points defined by the position vectors a=i+3j   and b=i+j
respectively. Find:
a the vector resolute of a in the direction of b
b a unit vector through A perpendicular to OB

1. The vector resolute of \(\mathbf{a}\) perpendicular to \(\mathbf{b}\) is given by: \(\mathbf{a}\) - the vector resolute of \(\mathbf{a}\) in the direction of \(\mathbf{b}\).

2. The unit vector in the direction of a vector v is given by \(\frac{1}{\lvert \mathbf{v} \rvert} \mathbf{v}\)

[mabajas76]

Hi hope all is well.
I have really been struggling with chapter 23 statics in the cambridge text book...my teacher didn't give the best explanation and home learning has really got me down.
Could somebody please explain how this question is answered carfully? I am just kinda confused on why they do what they do.
Cheers.

[fun_jirachi]

Here's a relevant diagram:


There are a fair amount of assumptions in that diagram, but logically it makes sense. The most important one that you should note is that the block does not move ie. the net horizontal force is zero, and the net vertical force is also zero.

Guiding questions:
- First, determine the angle denoted x in the diagram. You already know how much force rope one exerts horizontally. Is there a trigonometric ratio that could help you here?
- Then, determine the downwards force of the block by recalling that the net vertical force is zero. This will be equal to the combined upwards force exerted by the two men. Is there another trigonometric ratio that could help you? Don't forget that you want the mass of the block at the end, not the downwards force of the block.

Hope this helps

[Ryan Heng]

Hey guys I need help with this question (vectors)

The position vectors of three points A, B and C relative to an origin O are a, b and ka respectively.

The point P lies on AB and is such that AP = 2PB.The point Q lies on BC and is such that CQ = 6QB.

a) Find in terms of a and b,the position vectors of P and Q

[fun_jirachi]

Here are some hints to help you complete the question
\(\vec{OA} + \vec{AB} = \vec{OB}\).
\(\vec{AP} = \frac{1}{3}\vec{AB}\).
\(\vec{OA} + \vec{AP} = \vec{OP}\).