Mathematics: Post your doubts here!

[qwertypoiu]

Ummmmm hey is there any rule, in vectors, that if a.b is negative, the angle is obtuse?

I imagine so, since:
a•b = |a|*|b|*cos(theta)
The magnitude of the two vectors will each be positive in all cases, and cosine of an obtuse angle is negative, so it would make sense that the dot product producing a negative result would indicate an obtuse angle in between them.

 

[sj0007]

I imagine so, since:
a•b = |a|*|b|*cos(theta)
The magnitude of the two vectors will each be positive in all cases, and cosine of an obtuse angle is negative, so it would make sense that the dot product producing a negative result would indicate an obtuse angle in between them.

Thanks!

 

[AnonymousX9]

Which is the best textbook for practice and good examples/explainations for Pure Math 1?

 

[Maayee]

Can anyone help me with this http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_33.pdf
Question 2

 

[qwertypoiu]

Can anyone help me with this http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf
Question 2

ln(2x + 3) = 2 ln x + ln 3
ln(2x + 3) = ln x^2 + ln 3 (raising the power rule)
ln(2x + 3) = ln (3x^2) (the sum law of logarithms)
2x+3 = 3x^2 (since its an equation we can remove the log from both sides)
3x^2 - 2x - 3 = 0 (rearrange)
x = -0.721, 1.387 (solve the quadratic equation using the formula)

 

[nehaoscar]

For this question part ii
I have the final equation for the answer as:
2cos²x - 3cosx - 1 = 0
This is correct according to the mark scheme as well
Then to find x you use the formula -b +- √b² - 4ac divided by 2a...
So by using that I'm getting
1/4(3+√17) AND 1/4(3-√17)
Now it says that the first one i.e 1/4(3+√17) is invalid since the range is from 1 to -1
I don't understand how you know the range for x?? Like how and why is it 1 to -1
Please explain! :S

 

[qwertypoiu]

View attachment 57051
For this question part ii
I have the final equation for the answer as:
2cos²x - 3cosx - 1 = 0
This is correct according to the mark scheme as well
Then to find x you use the formula -b +- √b² - 4ac divided by 2a...
So by using that I'm getting
1/4(3+√17) AND 1/4(3-√17)
Now it says that the first one i.e 1/4(3+√17) is invalid since the range is from 1 to -1
I don't understand how you know the range for x?? Like how and why is it 1 to -1
Please explain! :S

You got:
cosx = 1/4(3+√17) and cosx = 1/4(3-√17)
Let's focus on the invalid one:
cosx = 1/4(3+√17)
cosx = 1.7807764...
Now you've learnt that the range of cosx is from -1 to +1. You can do cos of ANY angle you want to try and it will NEVER be greater than 1. So for cos(x) to be 1.78... We know that's impossible.

 

[nehaoscar]

You got:
cosx = 1/4(3+√17) and cosx = 1/4(3-√17)
Let's focus on the invalid one:
cosx = 1/4(3+√17)
cosx = 1.7807764...
Now you've learnt that the range of cosx is from -1 to +1. You can do cos of ANY angle you want to try and it will NEVER be greater than 1. So for cos(x) to be 1.78... We know that's impossible.

Oh i see! Thankyou!
I don't know why but I was thinking that those values were of x and not cos(x) that's why I was wondering why x has a range
Thankyou!

 

[Maayee]

ln(2x + 3) = 2 ln x + ln 3
ln(2x + 3) = ln x^2 + ln 3 (raising the power rule)
ln(2x + 3) = ln (3x^2) (the sum law of logarithms)
2x+3 = 3x^2 (since its an equation we can remove the log from both sides)
3x^2 - 2x - 3 = 0 (rearrange)
x = -0.721, 1.387 (solve the quadratic equation using the formula)

Thank you so much

 

[manya]

can someone plz tell me y do we have to multiply by 7c3 in the end

 

[nehaoscar]

View attachment 57063 View attachment 57064
can someone plz tell me y do we have to multiply by 7c3 in the end

Because the way in which the red sweets can be picked out can have different combinations
For example in the answer above you have found out the probability of picking 3 red sweets in the first 3 chances
It may be that you pick out a red sweet in the 2nd , 4th and 6th chance etc...
So you multiply by 7C3 in order to obtain the different possible chances of picking red sweets in the different orders

 

[Sarosh Jameel]

PLZZ help me with this !!!

 

[The Sarcastic Retard]

PLZZ help me with this !!!

https://answers.yahoo.com/question/index?qid=20150821061035AAz12N4

 

[Shujaat Khan]

PLZZ help me with this !!!

Just make sure you understood that convergent means |r|< 1.
Why?
Because convergent means narrowing down to a definite value(intersecting you may call)
What gives a definite value for sum to infinity in a geometric progression is when |r|<1

 

[Sarosh Jameel]

Thanks !

Just make sure you understood that convergent means |r|< 1.
Why?
Because convergent means narrowing down to a definite value(intersecting you may call)
What gives a definite value for sum to infinity in a geometric progression is when |r|<1

 

[manya]

Because the way in which the red sweets can be picked out can have different combinations
For example in the answer above you have found out the probability of picking 3 red sweets in the first 3 chances
It may be that you pick out a red sweet in the 2nd , 4th and 6th chance etc...
So you multiply by 7C3 in order to obtain the different possible chances of picking red sweets in the different orders

oh i got it. thans alot

 

[forever_chocoholic]

pk this is a really dumb question
ive done this before
but i completely forgot how to solve this
can anyone explain me how to find the inverse of a cubic function?
ex: y = 5x^3 - 9x^2 - 2

 

[manya]

plz help me with part 2

 

[qwertypoiu]

pk this is a really dumb question
ive done this before
but i completely forgot how to solve this
can anyone explain me how to find the inverse of a cubic function?
ex: y = 5x^3 - 9x^2 - 2

Well cubic equations are not one-one functions in general. So it seems to me that your function cannot possibly have an inverse function unless you restrict the domain. If the domain IS restricted, there's probably a way but I feel that this requires solving a cubic equation, which I think isn't in our syllabus. Do you have a past paper question like this?

 

[RadzMau]

Can someone please help me with this M1 question?

The top of a cliff is 40 metres above the level of the sea. A man in a boat, close to the bottom of the cliff, is in difficulty and fires a distress signal vertically upwards from sea level. Find (i) the speed of projection of the signal given that it reaches a height of 5 m above the top of the cliff, [2]
(ii) the length of time for which the signal is above the level of the top of the cliff. [2]

The man fires another distress signal vertically upwards from sea level. This signal is above the level of the top of the cliff for 17 s.
(iii) Find the speed of projection of the second signal.