Mathematics Question Thread

[jamonwindeyer]

Thanks very much!  :)Hopefully i will remember in my exam tomorrow!

Similarity proofs in exams are way more commonly equiangular proofs rather than the ones involving proportional sides, so at the least, make sure you remember that one! Prove two angles equal for similarity

[RuiAce]

Similarity proofs in exams are way more commonly equiangular proofs rather than the ones involving proportional sides, so at the least, make sure you remember that one! Prove two angles equal for similarity

Whilst I only came across one "all 3 sides in proportion" I swear 33% of the time I've seen two sides prop+angle and 66% of the time equiangular

[Kekemato_BAP]

I'm stuck on this question on exponentials..
"The line y=mx is the tangent to the curve y=e^3x. Find m"
Any help with step by step

[jamonwindeyer]

I'm stuck on this question on exponentials..
"The line y=mx is the tangent to the curve y=e^3x. Find m"
Any help with step by step

Hey! So since it is a tangent, the gradients of the line and the curve are the same, so we know that:



Further, they have to meet at the point where the gradients are the same, so:



This is a set of simultaneous equations. Via substitution:



Does that make sense?

[Kekemato_BAP]

Thank you jamon!! This makes sense now!!

[Kekemato_BAP]

How would I do this question?
I have a maths log/exp exam tomorrow

[RuiAce]

(Image removed from quote.)
How would I do this question?
I have a maths log/exp exam tomorrow

[Fahim486]

Hey how would you solve y=2sin5(pi symbol)/3 - 5(pi symbol)/3 in exact form?

[RuiAce]

Hey how would you solve y=2sin5(pi symbol)/3 - 5(pi symbol)/3 in exact form?

Assuming you meant to simplify?



Side note: If you just type "pi" we will understand

[Fahim486]

I understand what you mean by 5pi/3 is a fourth quadrant angle but when you say "with related angle pi/3" what do you mean by that?

[RuiAce]

[Fahim486]

oohhhh yes now that makes sense. Thank you!!!!!

[kiiaaa]

hello,
i was doing a past paper and this question appeared and i like lowkey know what to do but was slightly confused so i went to the solutions and their solutions they gave even confused my poor brain more. could you please help me out. it is question dii)

thank you

[jakesilove]

hello,
i was doing a past paper and this question appeared and i like lowkey know what to do but was slightly confused so i went to the solutions and their solutions they gave even confused my poor brain more. could you please help me out. it is question dii)

thank you

We know that


Now, we want to find


Note that the integral is ALMOST the same as the result of part i) (which is obviously not accident!). In fact, if we rearrange the above, we find that



If we then integrate both sides, we would get to the answer required. ie.


Note that the second term is literally the integral of a differential. ie. first, differentiate xtan(x), then integrate it. Obviously, you'll just get xtan(x) again, but with some constant C added to it. We can also perform the first integral, as it is just the negative natural logarithm relation.


As required! Does that make sense?

[kiiaaa]

We know that


Now, we want to find


Note that the integral is ALMOST the same as the result of part i) (which is obviously not accident!). In fact, if we rearrange the above, we find that



If we then integrate both sides, we would get to the answer required. ie.


Note that the second term is literally the integral of a differential. ie. first, differentiate xtan(x), then integrate it. Obviously, you'll just get xtan(x) again, but with some constant C added to it. We can also perform the first integral, as it is just the negative natural logarithm relation.


As required! Does that make sense?

heyy, im sort of confused on where did the 'cos' come from. your explanation made everything else make sense except where did the 'ln(cos)' come from

thank you so much!