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Mathematics: Post your doubts here!

InnocentAngel

InnocentAngel

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Hey parthrocks I like the questions u’ve been asking. There’s always something I learn from them. They are not like the questions ive been working till now.
I could answer only part a. L Please others help us.
It is easier to convert radians into degrees to manipulate the values.
Sin (π/12)
= sin 15
= sin (45- 30)
= sin45 cos30 –cos45 sin30
=( 1/√2 X (√3)/2 ) – ( 1/√2 X ½ )
=( √3 – 1 ) / 2√2

Tan (π/12)
= tan( 45-30)
= (tan 45 – tan30) / (1 + tan45 tan30)
=(1 – 1/√3) / (1 + 1/√3)
Simplify and get
= (√3 -1 ) / (√3 +1 )
 
parthrocks

parthrocks

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smzimran said:
View attachment 14425

Q8:
What roots did you get ?

Q6:
A chord is a straight line joining two points on the circumference of a circle

Arc is NOT a line, its a curved part of a pizza slice shaped sector of a circle!
Click to expand...
hey bt id u look at the question in that is clearly says that we have to find the length of the chord PQ,,,which means that PQ is also the arc correct??so both are same...??is it
smzimran
 
C

celoth

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shanky631 said:
View attachment 14432

plz someone help me.
Click to expand...

(i)
x^4 -2x^3 -2x^2 + a = (x^2 -4x +4)Q(x)
f(x) = (x-2)(x-2) Q(x) , since factorisation of (x^2 -4x +4) is (x-2)^2

so let x=2, f(2)=0 then you will be able to find a already.
a is 8.

(ii)
by using long division,
f(x)
=(x-2)(x-2)(x^2 + 2x +2) , by doing completing the square on (x^2 +2x +2)
= (x-2)^2 ((x+1)^2 +1)

we can see that for any number of x,
it is positive,
because any square number multiplies with any square number + 1,
it will never be negative.
 
parthrocks

parthrocks

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celoth said:
(i)
x^4 -2x^3 -2x^2 + a = (x^2 -4x +4)Q(x)
f(x) = (x-2)(x-2) Q(x) , since factorisation of (x^2 -4x +4) is (x-2)^2

so let x=2, f(2)=0 then you will be able to find a already.
a is 8.

(ii)
by using long division,
f(x)
=(x-2)(x-2)(x^2 + 2x +2) , by doing completing the square on (x^2 +2x +2)
= (x-2)^2 ((x+1)^2 +1)

we can see that for any number of x,
it is positive,
because any square number multiplies with any square number + 1,
it will never be negative.
Click to expand...
hey hii celoth for the 2nd part cant we find out the derivative and show that all the 3 points are minima???any idea about that method?does it work?
 
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celoth

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parthrocks said:
hey hii celoth for the 2nd part cant we find out the derivative and show that all the 3 points are minima???any idea about that method?does it work?
Click to expand...

it will be 2 minima and 1 maxima....
and then you can find the coordinates for every turning points,
you will find that all points are above x-axis,
so i think it will works too
 
parthrocks

parthrocks

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celoth said:
it will be 2 minima and 1 maxima....
and then you can find the coordinates for every turning points,
you will find that all points are above x-axis,
so i think it will works too
Click to expand...
Hey can u show me how did u get one maxima for 0??
 
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