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So, we knowx² + 2x + 1 = 0

( x + 1)² = 0

x = -1

Therefore this set have only one element -1

Set is { -1}

So, it is singleton

option (D) is correct

p(x)=x^3+3(x)^2-5(x)+8; x=-1/3 ; p(-1/3)=(-1/3)^3-3(-1/3)-5(-1/3)+8=(-1/27)+1+(5/3)+8= -1+27+45+72/27= 26+45+72/27=144/27=5.3e

x^3+3x^2-5x+6,; x=1/2; (1/2)^3+3(1/2)^2-5(1/2)+6= 1/8+3/4-5/2+6=1+6-20+48/8=7-20+48/8=7+28/8=35/8

x^3+3x^2-5x+8when x+1=0 , x= -1(-1)^3+(-1)^2-5(-1)+8= -1+1+5+8=13 not equal to 0when 2x-1=0 , x= 1/2(1/2)^3+3(1/2)-5(1/2)+8= 1/8+3/4-5/2+8= 1+3-5+64/868-5/8 not equal to 0when x+2=0, x= -2(-2)^3+3(-2)^2-5(-2)+8= -8+12+10+8=38not equal to 0it means option D is right

Find prime factors of 100

100 = 2*2*5*5

Thus prime factors of 100 are2, 2, 5, 5

Circumference of circle= 2*pi*r

Where r = radius of circle

Given, r = 10/2 = 5 cm

Circumference = 2*3.14*5 = 3.14*10 = 31.4 cm

42/5 is the correct answer of the given question

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a answer A is the correct

0.090.14 is the best answer

0.090.14 is the best answer

0.09 0.14 is the best answer

0.09 & 0.14 is the right answer

1. 0.092. 0.14

is the correct answer

1. 0.092. 0.14 is correct answer.

1

2

3

x=2and y=3 is correct answer

3 is the correct answer

3 is the correct answer of the following question.

The correct answer is 3

3 is the correct answer

29/7-1/7-4= 29-1-28/4= 0Answer

(900/121)^1/2 = 30/11 ANS...

cos^-1{cos(π-π/3)}+ sin^-1{sin(π-π/3)}=cos^-1{cos(-π/3)}+sin^-1(sinπ/3)=-π/3+π/3=0

this is part 1

this is part 2

LHS = cos^3A cos3A + sin^3A sin3A = cos​^3A (4cos^3A - 3cosA) + sin^3A (3sinA - 4sin^3A) (using identities of cos3A and sin3A) = 4cos^6A - 3cos^4A + 3sin^4A - 4sin^6A = 4 (​cos^6A -​sin^6A) + 3 (​sin^4A -​cos^4A) = 4 ( (cos^2A)^3- (sin^2A)^3) + 3 ( (sin^2A)^2- (cos^2A)^2) = 4 [ (​cos^2A -​sin^2A) (​cos4A +​cos^2A​sin^2A +​sin^4A)] + 3 [(sin^2A+cos^2A)(sin^2A - cos^2A)]

using a^3- b^3= (a-b)(a^2+ab+b^2) and a^2-b^2=(a-b)(a+b)

= 4 [ cos2A ((sin^2A+cos^2A)^2- cos^2Asin^2A) ] + 3 [ 1 (-cos2A)]= 4 [cos2A(1 - ​​cos^2Asin^2A )] - 3 cos2A= 4cos2A - 4cos2A ​cos^2A​sin^2A - 3cos2A = cos2A- 4cos2A​cos^2Asin^2A = cos2A (1 - 4​cos^2A​sin^2A )= cos2A (1 - sin^2A) ​(Since2sinAcosA=sin2A)= cos2A cos^22A= cos^32A= RHS

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Volume= 15*8*h= 540h= 540/120= 54/12= 18/4now for 18/4 height = 540 m^3 now for 4.5 mnow for 2/3 of 540= 360 m= 4.5/540*360= 3m

I = ∫ [ 1 / ( 1 + tan x ) ] dx

= ∫ { 1 / [ 1 + ( sin x / cos x ) ] } dx

= ∫ [ cos x / ( sin x + cos x ) ] dx

= (1/2) • ∫ [ ( 2 cos x ) / ( sin x + cos x ) ] dx ... Note This Step

= (1/2) • ∫ { [ ( sin x + cos x ) + ( cos x - sin x ) ] / ( sin x + cos x ) } ... Note This Too

= (1/2) • [ ∫ 1 dx + ∫ ( 1/u ) du ], ... u = sin x + cos x

= (1/2) [ x + ln |u| ] + C

= (1/2) [ x + ln | sin x + cos x | ]+C

LHS = cos(π/4 - x).cos(π/4-y)-sin(π/4 -x).sin(π/4-y)

Let ( π/4 - x) = A (π/4 - y) = B

Then, LHS = cosA.cosB -sinA.sinB But we know, cos(A + B) = cosA.cosB - sinA.sinB

use this, cos(A + B) = cos{(π/4 -x) + (π/4 -y)}=cos(π/2 - (x +y)}

We know, Cos(π/2 - ∅) = sin∅ use this , = sin(x + y)

Hence proved

∫sin(2x) / (a^2Cos^2(x) + b^2sin^2(x)) dx=1/2 ∫ 1/(a^2Cos^2(x) + b^2sin^2(x)) d(sin^2 x)=1/2 ∫ 1/(a^2(1-sin^2(x)) + b^2sin^2(x)) d(sin^2 x)=1/(2(b^2-a^2)) ∫ 1/(a^2 + (b^2-a^2)sin^2(x)) d(a^2+(b^2-a^2)sin^2 x)=1/(2(b^2-a^2)) ln|a^2+(b^2-a^2)sin^2 x|+C

thnxx

f(x)= √ sinxd/dx= 1/2(sinx)^-1/2*cos xthanks

Volume =l*b*depthhencedepth=2000/25*20=4m

Let r be the radius of hemisphere & Cylinder and h be the height of the Cylinder, H be the height of the Total building.GIVEN :Volume of air = 880/21 m³Internal diameter (d) = HInternal Diameter = 2r = HTotal Height of the building (H) = 2r……(1)Height of the building = height of the cylinder + radius of the hemispherical DomeH = h + r 2r = h +r [from eq 1]2r -r = hr = h ……………..(2)Volume of air inside the building = Volume of cylindrical portion + Volume of hemispherical portionπr²h + (2πr³/3)= 880/21π(h)²h + (2π(h)³/3)= 880/21[From eq 2, r= h]πh³ + ⅔ πh³ = 880/21πh³(1+⅔) = 880/21πh³[(3+2)/3] = 880/21πh³[5/3] = 880/2122/7 × h³ × 5/3 = 880/21h³ = (880 ×3 ×7) / 21 × 22 × 5h³ = 40 /5 = 8h³ = 8h = ³√8 = ³√2×2×2h = 2 mh= r = 2 m [From eq 2, r= h]Total height of the building( H) = 2r = 2×2 = 4 mHence, the Total height of the building is 4m.

Write tanx as sinx/cosx and cotx as cosx/sinx

I= √((sin^2x/sinxcosx) + √(cos^2x/sinxcosx))dx

I= (sinx+cosx dx)/√(sinxcosx)

sinx-cosx=t

(sinx+cosx)dx=dt

(sinx-cosx)^2=t^2

1–2sinxcosx=t^2

sinxcosx=(1-t^2)/2

Therefore,

I=dt/√((1-t^2)/2)

I=(√2)sin^-1(t) + C

I=(√2)sin^-1(sinx-cosx)

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