maths a level

Hi
I am a bit confused

when you have an expression such as (3+12x)/x=4 why do you multiply by x^2

and when are the cases when you don't do that

Reply 1

Itsmikeysfault

Why would you multiply by x^2. Multiply both sides by x would give you the correct answer.

You would only multiply by x^2 If its an inequality

Reply 2

davros

Original post by Sclaremonths

Hi
I am a bit confused

when you have an expression such as (3+12x)/x=4 why do you multiply by x^2

and when are the cases when you don't do that

You don't do that in this case! If you multiply that equation by x^2 then you will introduce the spurious solution x = 0 which doesn't satisfy your original equation :smile:

Reply 3

username5586810

Original post by Itsmikeysfault

Why would you multiply by x^2. Multiply both sides by x would give you the correct answer.

You would only multiply by x^2 If its an inequality

ohhh okay thank you so much!

Reply 4

username5586810

Original post by davros

You don't do that in this case! If you multiply that equation by x^2 then you will introduce the spurious solution x = 0 which doesn't satisfy your original equation :smile:

i also wanted to ask when asked to find the equation of the tangent/normal, why do we sometimes take the negative reciprocal of the gradient, and in other occasions we don't

Reply 5

LemonCake1234

Original post by Sclaremonths

i also wanted to ask when asked to find the equation of the tangent/normal, why do we sometimes take the negative reciprocal of the gradient, and in other occasions we don't

You only take the negative reciprocal for the normal not for the tangent

Reply 6

username5586810

Original post by LemonCake1234

You only take the negative reciprocal for the normal not for the tangent

okay thank you!

Reply 7

LemonCake1234

Original post by Sclaremonths

okay thank you!

No worries ask if you need more help!

Reply 8

username5586810

Original post by LemonCake1234

No worries ask if you need more help!

https://crashmaths.com/wp-content/uploads/2018/09/AS-M-BRONZE-P1-B-MS.pdf

Hi,
here we take the negative reciprocal of the gradient despite the question asking for the tangent. Why?

tangent1.PNG92.0KB

Reply 9

Driving_Mad

Original post by Sclaremonths

https://crashmaths.com/wp-content/uploads/2018/09/AS-M-BRONZE-P1-B-MS.pdf

Hi,
here we take the negative reciprocal of the gradient despite the question asking for the tangent. Why?

The gradient is of the centre and point on the circle, so the radius. The tangent’s gradient is perpendicular to the radius, so you take the negative reciprocal.

Reply 10

Matcccc

Original post by Sclaremonths

https://crashmaths.com/wp-content/uploads/2018/09/AS-M-BRONZE-P1-B-MS.pdf

Hi,
here we take the negative reciprocal of the gradient despite the question asking for the tangent. Why?

You take the negative reciprocal when ever you want something that is perpendicular

Reply 11

username5586810

Original post by Driving_Mad

The gradient is of the centre and point on the circle, so the radius. The tangent’s gradient is perpendicular to the radius, so you take the negative reciprocal.