Mathematics: Post your doubts here!

[parthrocks]

celoth
how do we solve if
y=cos2x - 2sin x
how do we find dy/dx and the stationary points and whether minima or maxima???

 

[GorgeousEyes]

Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .

*Gp:Geometric Progression .
Ap :Arithmetic progression .

Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3

I tried my best to reach the answers but i couldn't . So , please someone explain them for me

 

[celoth]

Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .

*Gp:Geometric Progression .
Ap :Arithmetic progression .

Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3

I tried my best to reach the answers but i couldn't . So , please someone explain them for me

no 1)

to find r,
we know that the ratio:
Sum of infinity : Sum of 1st 7 terms = 128:127
127 x Sum of infinity = 128 x Sum of 1st 7 terms
127 x (a/1-r) = 128 x (a(1-r^7)/1-r)
by getting rid of (a/1-r) ,
127 = 128(1-r^7)

r^7
= 1 - 127/128
= 1/128
= (1/2)^7

therefore, r= 1/2

 

[InnocentAngel]

Question 2:
since Z = cos π/6 + i cos π/3
therefore, arg(Z) = π/6
or you can try to sketch this thing out on cartesian plane.

mod Z
= √ ( cos^2 π/6 + cos^2 π/3 )
= √ ( (√3 / 2)^2 + (1/2)^2 )
= 1

Thanks friend

 

[shanky631]

how to integrate tan2x with respect to x

 

[GorgeousEyes]

no 1)

to find r,
we know that the ratio:
Sum of infinity : Sum of 1st 7 terms = 128:127
127 x Sum of infinity = 128 x Sum of 1st 7 terms
127 x (a/1-r) = 128 x (a(1-r^7)/1-r)
by getting rid of (a/1-r) ,
127 = 128(1-r^7)

r^7
= 1 - 127/128
= 1/128
= (1/2)^7

therefore, r= 1/2

Thankyouuu Wut about the two other questions ?

 

[celoth]

Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .

*Gp:Geometric Progression .
Ap :Arithmetic progression .

Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3

I tried my best to reach the answers but i couldn't . So , please someone explain them for me

no 2)

Given T5 = 2/81, then
ar^4 = 2/81 --- eq(1)

Given T3+T4 = 8/27, then
ar^2 +ar^3 = 8/27
ar^2 (1+r) = 8/27 --- eq(2)

just use eq(1) divide by eq(2) or vice versa,
then you can get rid of a and get a quadratic equation of r,
solve it then you will find the answer.

 

[celoth]

Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .

*Gp:Geometric Progression .
Ap :Arithmetic progression .

Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3

I tried my best to reach the answers but i couldn't . So , please someone explain them for me

no 3)

this question is interesting.

from the GP: 1, a, b
we can assume the ratio=a
because T2 = 1xa = a ,
then,
a x a = b
a^2 = b --- eq(1)

from the AP: 1, b, a
we can assume the difference is b-1,
since T2 = 1+(b-1) = b,
then,
b + (b-1) = a
2b-1 = a --- eq(2)

by putting eq(1) into eq(2) or vice versa,
you will be able to find a and b.

 

[celoth]

how to integrate tan2x with respect to x

change tan2x = sin2x/cos2x

 

[shanky631]

change tan2x = sin2x/cos2x

but how to do integration of division. can u plz show in steps.

 

[parthrocks]

change tan2x = sin2x/cos2x

And then we can use the substitution formula make cosx as u by i prefer not doing that cos it would be a nerve wrecking scenario!!
follow the formula

 

[GorgeousEyes]

ms

no 3)

this question is interesting.

from the GP: 1, a, b
we can assume the ratio=a
because T2 = 1xa = a ,
then,
a x a = b
a^2 = b --- eq(1)

from the AP: 1, b, a
we can assume the difference is b-1,
since T2 = 1+(b-1) = b,
then,
b + (b-1) = a
2b-1 = a --- eq(2)

by putting eq(1) into eq(2) or vice versa,
you will be able to find a and b.

Merci Celoth for ur help ,appreciate it .

 

[InnocentAngel]

To Parthrocks:

Answer to Question 10


Using chain rule :
d/dx (sin (a + x )) = cos (a+ x) .(1)
= cos( a + x)

Using addition formla then differentiating :
d/dx ( sina cosx + cosa sinx )
=( sin a . -sinx + cosx . cosa . 0 ) + ( cos a . cos x + sin x . -sin a . 0 )
= -sin a sin x + 0 + cos a cos x + 0
= cos a cos x - sin a sinx
(apply addition formula for the cos one again which gives you the follo. )
= cos ( a + x )

Conclusion : with both chain rule and addition formula the answer is cos ( a + x)

 

[InnocentAngel]

Please help me out with these buddies :

Maths P1
Question1 .

X² +6x + 11 > 0
Find the range of values for x.

ANS: x € R
ANS: x € R

 

[bamteck]

Please help for these 3 questions !

 

[Amy Bloom]

Hello there! Can somebody help me with this tweeny mini question.

smzimran celoth

 

[parthrocks]

Please help me out with these buddies :

Maths P1
Question1 .

X² +6x + 11 > 0
Find the range of values for x.

ANS: x € R
ANS: x € R

hey I hope u understood and hey ya thanks for answering my query which I posted you!!!thank you!

 

[parthrocks]

Please help for these 3 questions ! View attachment 14314View attachment 14315

Hello bro atlast got that....I hope u understood I think it would be like this:-


Attached!

 

[smzimran]

Hello there! Can somebody help me with this tweeny mini question.
View attachment 14317
smzimran celoth

 

[bamteck]

View attachment 14322

Would you mind helping me with these questions please ?