MATHS ADVANCED (1 Viewer)

[CM_Tutor]

Is the first one just 2 times the natural log of x^2+3x

You are correct for the integral given as written. For the question to work, however, the integral should be:

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[Jerryclover]

A lot of the questions you posted have errors in them. I hope you're not trolling

 

[CM_Tutor]

How does one do part a?

If the middle term in the AP is , and we take , then the three sides of the triangle are, in increasing order, . Now, which of these must be opposite the angle given as 120^o? Draw a diagram and recognise that you can use the cosine rule...

 

[CM_Tutor]

A lot of the questions you posted have errors in them. I hope you're not trolling

If you have specific examples of errors, post them and I will check.

 

[Jerryclover]

If you have specific examples of errors, post them and I will check.

The 9th post. The entire question doesn't work. a.) should be 2ln(x^2+3x)+c.

The 10th post, M and N coordinates shout be (-1,1) and (1,1) respectively.

If i'm wrong please correct me, but i double checked on wolfram alpha

 

[Jerryclover]

The 10th post, M and N coordinates shout be (-1,1) and (1,1) respectively.

Nope, nevermind. Misread the 10th post. My bad, jumped to conclusions.

 

[CM_Tutor]

The 9th post. The entire question doesn't work. a.) should be 2ln(x^2+3x)+c.

The 10th post, M and N coordinates shout be (-1,1) and (1,1) respectively.

If i'm wrong please correct me, but i double checked on wolfram alpha

The 9th post has had a note added to note that there is a fault in it, as is posted above. The function should be

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The 10th post, M and N are two of the three points of intersection of the parabloa and the circle . The points and lie on the circle but not the parabola.

 

[Jerryclover]

The 10th post, M and N are two of the three points of intersection of the parabloa and the circle . The points and lie on the circle but not the parabola.

my bad. Apologies

 

[Jerryclover]

for b), i got stuck on , how can i write that in terms of sin?

+1

 

[Jerryclover]

View attachment 33696

Spoiler: Answer

just wanna say d.) is a beautiful question

 

[CM_Tutor]

for b), i got stuck on , how can i write that in terms of sin?

For an AP, we need

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from which we can find .

For (b), we have that the common difference is and so the next term after is

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as you found. To answer in terms of , we need to eliminate the term by using the result established above, that , so the term is

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[CM_Tutor]

+1

Solution posted above. You need to use the condition that was established in part (a) that links and and allows you to find the specific value of .

 

[Jerryclover]

Solution posted above. You need to use the condition that was established in part (a) that links and and allows you to find the specific value of .

Cheers. That connection was hard to find. Seems more like an ext1 question honestly

 

[CM_Tutor]

Cheers. That connection was hard to find. Seems more like an ext1 question honestly

It's more an illustration of the difficulty that can be worked into a question by mixing topics, IMO.