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Post mathematic related questions here

OP
rst

rst

Youngling
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NEW OBJECTIVE QUESTION


kxef.png


Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋
 
OP
rst

rst

Youngling
----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION


kxef.png


Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

Put x=0,then we get
e=|0 -1 3|
|1 0 -4|
|-3 4 0|

e=0
 
OP
rst

rst

Youngling
----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION


s327.png


Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋
 
OP
rst

rst

Youngling
----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION


s327.png


Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

cosα+2cosβ+3cos γ=0-----(1)

sinα+2sinβ+3sinγ=0
isinα+2isinβ+3isinγ=0(multiplying both sides by iota)--------(2)

Adding (1) and (2),we get
e^iα+2e^iβ+3e^iγ=0.

using a³+b³+c³−3abc=(a+b+c)(a²+b²+c²−ab−bc−ca).
e^i3α+8e^i3β+27e^i3γ=6e^i(α+β+γ)=−6

Comparing imaginary parts,we get
sin3α+8sin3β+27sin3γ=0
 

theterminator

Wise Old Owl
I have one confusion:
In the question
48÷2*12.

will we do the division first or multiplication first & by what rule??

being from comp sci background , i know that multiplication & division are in the same level of priority but the operation will be performed first when encountered upon going from left to right. Some say to follow BODMAS rule to solve...in that case , what will be the answer to this question
48*2÷12
 

theterminator

Wise Old Owl
48*2÷12 = 48 *(1/6)=8
but in computer program, multiplication will be performed first coz order of precedence is from left to right in case of operators of same level ( * and / are of same level )

Did you first looked for ÷ sign in your keyboard? :-D
 
OP
rst

rst

Youngling
but in computer program, multiplication will be performed first coz order of precedence is from left to right in case of operators of same level ( * and / are of same level )

Well,its also correct
By doing so,you will get the same answer
48*2÷12 =96 ÷12 =8
---------------------------------------------
From left to right you can do any "D" or "M"
Similar is for addition and subtraction
 
Last edited:
OP
rst

rst

Youngling
sec²x dx/(sec x + tan x )^9/2

put tanx =t
then sex²x dx= dt

∫dt/[t+ √ (1+t²)]^9/2--------(1)

Now let t+ √ (1+t²) =u
clearly 1/u =√ (1+t²) -t

So t =1/2 [u - (1/u)]
dt =1/2 [1+ (1/u²)]du

Using in (1),we get
(1/2)∫du [u ^(-9/2) + u ^(-13/2)]du

Now its easy to solve
 

Niilesh

Padawan
I have one confusion:
In the question
48÷2*12.

will we do the division first or multiplication first & by what rule??

being from comp sci background , i know that multiplication & division are in the same level of priority but the operation will be performed first when encountered upon going from left to right. Some say to follow BODMAS rule to solve...in that case , what will be the answer to this question
48*2÷12

Since there is no bracket 48÷2*12 = 24*12 = 288 = 48*12÷2 = 12÷2*48
 
OP
rst

rst

Youngling
View attachment 12070
With AO || CD, find area of shaded region.

∠O=<D=θ (corresponding angles)
Then <ODC= π-θ
The area of the shaded region = the area of the sector OCB - the area of the
triangle OCD

Let <BOC =x and <OCD =y

sin(π−θ)/R=siny/ℓ
sinθ/R=siny/ℓ
y= arcsin(ℓsinθ/R)

x+y+(π−θ)=π
x=θ-y
x=θ-arcsin(ℓsinθ/R)

A(ΔOCD)=(1/2)Rℓsinx
 
OP
rst

rst

Youngling
----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION


exgv.png


Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋
 
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