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Need help hard A level Mathematics question.

If 3x = 15 What is the value of x.

I don't understand this, how can you solve this?
I missed the relevant lessons and have fallen behind.

Thanks.

Edit: If anybody could help with part 2 that would be swell.

(edited 7 years ago)

Reply 1

NotNotBatman

20

Original post by BlibTheBlob

If 3x = 15 What is the value of x.

I don't understand this, how can you solve this?
I missed the relevant lessons and have fallen behind.

Thanks.

Divide both sides of the equation by 3.

Reply 2

BlibTheBlob

OP

Original post by NotNotBatman

Divide both sides of the equation by 3.

Thanks Batman, if you could just help me with part B now. :smile:

A particle moves on a smooth triangular horizontal surface AOB with angle AOB = 30◦ . The surface is bounded by two vertical walls OA and OB and the coefficient of restitution between the particle and the walls is e, where e < 1. The particle, which is initially at point P on the surface and moving with velocity u1, strikes the wall OA at M1, with angle PM1A = θ, and rebounds, with velocity v1, to strike the wall OB at N1, with angle M1N1B = θ. Find e and v1 u1 in terms of θ. The motion continues, with the particle striking side OA at M2, M3, . . . and striking side OB at N2, N3, . . .. Show that, if θ < 60◦ , the particle reaches O in a finite time.

(edited 7 years ago)

Reply 3

Olmeister

12

X = 5

You've got to be trolling me, right?

Reply 4

Olmeister

12

Lol, that's more like it

Reply 5

NotNotBatman

20

Original post by BlibTheBlob

Thanks Batman, if you could just help me with part 2 now. :smile:

A particle moves on a smooth triangular horizontal surface AOB with angle AOB = 30◦ . The surface is bounded by two vertical walls OA and OB and the coefficient of restitution between the particle and the walls is e, where e < 1. The particle, which is initially at point P on the surface and moving with velocity u1, strikes the wall OA at M1, with angle PM1A = θ, and rebounds, with velocity v1, to strike the wall OB at N1, with angle M1N1B = θ. Find e and v1 u1 in terms of θ. The motion continues, with the particle striking side OA at M2, M3, . . . and striking side OB at N2, N3, . . .. Show that, if θ < 60◦ , the particle reaches O in a finite time.

You really just posted a STEP III question after posting basic arithmetic, lol :biggrin:

But, sorry, I have not looked into STEP III.

Reply 6

BlibTheBlob

OP

Original post by NotNotBatman

You really just posted a STEP III question after posting basic arithmetic, lol :biggrin:

But, sorry, I have not looked into STEP III.

Oh its cool Batman, thanks for the help with part A though :smile:

Reply 7

TheYearNiner

21

Original post by BlibTheBlob

Oh its cool Batman, thanks for the help with part A though :smile:

Btw it cant be x = 5 because what is x? it should be 5 = 5 or am I wrong? sorry im in year 7

Reply 8

BlibTheBlob

OP

Original post by TheYearNiner

Btw it cant be x = 5 because what is x? it should be 5 = 5 or am I wrong? sorry im in year 7

Brain.exe has stopped working

Reply 9

NotNotBatman

20

Original post by BlibTheBlob

Oh its cool Batman, thanks for the help with part A though :smile:

Part A, you're a comedian.
If you actually need help with step use the STEP prep thread, plenty of people will be able to help you there. Additionally, there are solutions to most years of STEP questions written by people on TSR. https://www.thestudentroom.co.uk/showthread.php?t=862415&page=4#post32406132

Reply 10

math42

20

\displaystyle 3x = 15

therefore

\displaystyle 3x = 15 \left(\cos^2 x + \sin^2 x \right) = 15 (\cos x + i \sin x) (\cos x - i \sin x) = 15 e^{ix} e^{-i x}

.
Hence, taking both sides to the power of 2,

\displaystyle 9 x^2 = 225 e^{2ix} e^{-2ix}

.
Making the substitution

\displaystyle y = x - pi

, we see that

\displaystyle 9 y^2 + 18 \pi y + 9 {\pi}^2 = 225 e^ {2ix - 2i \pi} e^ {-2ix + 2i \pi} = 225 e^{2ix} e^{-2i \pi} e^{-2ix} e^{2i \pi}

.
But

\displaystyle e^{2 i n \pi} = 1

for all

\displaystyle n \in \mathbb{Z}

.
Hence

\displaystyle 9y^2 + 18 \pi y + 9 {\pi}^2 = 225 e^{2ix} e^{-2ix} = 225 e^0 = 225

.
Therefore

\displaystyle 9y^2 + 18 \pi y + 9 {\pi}^2 - 225 = 0

, giving

\displaystyle y = \frac{-18 \pi \pm \sqrt{324 {\pi}^2 - 324 {\pi}^2 + (225)(9)(4)}}{18} = \frac{-18 \pi \pm (15)(3)(2)}{18} = - \pi \pm 5

and hence

\displaystyle x = y + pi = \pm 5

. Since

\displaystyle 3x = 15, x > 0

, and hence we see that x = 5.

Original post by BlibTheBlob

If 3x = 15 What is the value of x.

I don't understand this, how can you solve this?
I missed the relevant lessons and have fallen behind.

Thanks.

Edit: If anybody could help with part 2 that would be swell.

Thread closed and reported.

Need help hard A level Mathematics question.

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