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it's answer is 5✓2 it's the correct answer

3+3√2-3+2√2=(3-3)+(3√2+2√2)=0+5√2=5√2

5√2 is the correct answer

5√2 at the end it will remain

Let us assume that 3√2 is rational

ie,3√2=a/bwhere a and b are co-prime numbers

√2=(a/b)(1/3)=a/3bHere √2 is irrational and a/3b is rational

Thus our assumption is wronghence 3√2 is irrational

let 3 root 2 be rational number.3 root 2 = p/qroot 2 = p/3 q............. (1)

from equation 1, we conclude thatp/3 q are integers but root 2 is not a integer.so, our supposition is wrong.hence, 3 root 2 is irrational number.

Given √2 is irrational

Let assume 5+3√2 be rational.

5 + 3√2 = p/q

3√2 = p/q -5

√2 = (p - 5q)/5

So, LHS is irrational and RHS is rational.So, 5+3√2 is irrational

We know that,cos²B - sin²A = cos(A + B) * cos ( A - B)

Now, cos²67° - sin²23° = cos(67 + 23 ) * cos( 67 - 23 )= cos ( 90 ) * cos45= 0 * 1/√2 .= 0

cos²67 -sin²23 = 0 .

Quick Alternative : [ cos²67-sin²23 = cos²(90-23) - sin²23 = sin²23 - sin²23 = 0 ]

[ cos²67-sin²23 = cos²67-sin²(90-67) = cos²67-cos²67 = 0 ]

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It is wrong

please send the question again is it square of (sin A + sec A) ordouble of (sin A + sec A)

⬜ square

Given d = 7,22nd term =149 ,⇒ a+21d = 149⇒a+21(7) = 149⇒a+147 = 149⇒a=149-147=2Sn = (n/2)(2a+(n-1)d)S₂₂ = (22/2)(2×2+(22-1)7)S₂₂ = 11(4+21(7))S₂₂ = 11(4+147)S₂₂ = 11(151)S₂₂ = 1661.

Latent heat is thermal energy released or absorbed, by a body or a thermodynamics system, during a constant-temperature process — usually a first-order phrase transition.

If we think about substances at a molecular level, gaseous molecules have more vibration than liquid molecules. So when you add heat to a liquid, you are actually causing the molecules to vibrate. The latent heat is the energy required to change the molecular movement. Each substance has a unique latent heat value.

state of matter transforms from gas to liquid and from liquid to solid if the latent heat is given off.

646-64+164+55-5484=865-5548= -4619 is correct answer.

sqrt[(7 + 3(5)^1/2 * (7 - 3(5)^1/2)]

Using (a + b)(a - b) = a^2 + b^2

= sqrt(7^2 - 3^2×5)

= sqrt(49 - 45)

= sqrt(4)

= 2

2 is the correct answer of the given question

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the answer therefore is 40

a is 3 root 5 b 8s -3root 5

photo is not clear and it is of icic.board

it will be -3 not sure

Hence, we gota= -49/41b= -21/41

We need to find the values ofaaandbb, such that the polynomialx3−10x2+ax+bx^3-10x^2+ax+bis exactly divisible byx−1x-1as well asx−2x-2

Assume that :f(x)=x3−10x2+ax+bfx=x3-10x2+ax+b

Using remainder theorem, we know that if a polynomialf(x)f(x)is divided byx−cx-c, the remainder isf(c)f(c)x−1=0⇒x=1x-1=0⇒x=1

Applying the factor theorem, we know that:

f(x)will be exactly divisible by(x−1)iff(1)=0fxwill be exactly divisible byx-1iff1=0.

Hence, we have:

f(1)=13−10×12+a×1+b=(1−10+a+b)=−9+a+bf1=13-10×12+a×1+b=1-10+a+b=-9+a+b∴f(1)=0⇒a+b=9...(1)f1=0⇒a+b=9...1

The same method must be applied for the second factor as well,x−2=0⇒x=2x-2=0⇒x=2

Similarly, applying the factor theorem gives us:

f(x)will be exactly divisible by(x−2)iff(2)=0fxwill be exactly divisible byx-2iff2=0.

Hence, we have:

f(2)=23−10×22+a×2+b=(8−40+2a+b)=−32+2a+bf2=23-10×22+a×2+b=8-40+2a+b=-32+2a+b∴f(2)=0⇒2a+b=32...(2)f2=0⇒2a+b=32...2

Solving simultaneously, by subtracting (1)from (2),we have:a=23Solving simultaneously, by subtracting (1)from (2),we have:a=23

Substituting the value ofainto11or22, we get the value ofbwhich is−-14.∴a= 23 andb=−-14

hence,wegot-49/41a -21/41

a= -49/41b= -12/41it is the right answerhope it helps u

a=-49/41

b= -21/41 this is the answer

a is 3 root 5b 8s-3root 5

a is 3 root 5b 8s -3root 5

first of all 2 + 3√5------------ = a + b√52 - 3√5

then2 + 3√5 2 + 3√5------------ x ---------- = a + b√52 - 3√5 2 + 3√5

4+ 45 +12√5------------------- = a + b√5 4 - 45

49 12√5---- - ----- = a + b√5-41 41

now comparison the both sides

a = -49/41b = -12/41

A is 3 root 5 B is 8 -3 root 5 this is very right answer

a= -49/45. and b=-12/41 this is write answer

value of a is 49and value of b is 12

a=(-49/41)B=(-21/41)

STEPS: 1: On a numberline mark AB = 9.3 unit & BC= 1 unit.

2: Mark O the mid point of AC

3: Draw a semicircle with O as centre & OA as radius

4: At B draw a perpendicular BD.

5: BD = √9.3 unit

6: Now, B as centre, BD as radius, draw an arc, meeting the numberline at E.

Now, with BD or BE = √9.3 as radius , with 0 ( origin) of the number line as centre, draw an arc on the the number line, intersecting at point ‘k’. And this point ‘k' lies between integers 3 & 4, & represents √9.3

JUSTIFICATION:

BD = √ {(10.3/2)² - (8.3/2)²}

=> BD = √{10.3²- 8.3²)/4 }

=> BD = √{(10.3+8.3)(10.3–8.3)/4}

=> BD = √{18.6*2/4}

=> BF = √{37.2/4}

=> BD = √9.3 = BE

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1) (3√3/5)^2 = 27/25

3√2 + 5√3 -2√5 +3√5 -√2 -2√3=2√2 +3√3 +√5

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L.H.S. = (sec 8A -1) / (sec 4A -1)=> [(1 - cos 8A)/ cos 8A] / [(1 - cos 4A)/ cos 4A]=> [2 sin² 4A / 2 sin² 2A] * [cos 4A / cos 8A]=> [(2 sin 4A * cos 4A) * sin 4A / cos 8A] / [2 sin² 2A]

=> [(sin 8A / cos 8A) * sin 4A] / [2 sin² 2A]=> tan 8A * (sin 4A / 2 sin² 2A)=> tan 8A * (2sin 2A * cos 2A / 2 sin² 2A)=> tan 8A * ( cos 2A / sin 2A)=> tan 8A * cot 2A

=> tan 8A / tan 2A ==> R.H.S.

root(5)x^2-5x-3x+3root(5)=0root(5)x(x-root(5))-3(x-root(5))=0(root(5)x-3)(x-root(5))=0so x=root(5) or 3/root(5)

64^1/6now2^6=64 64^1/6=232^1/5now2^5=32 hence 32^1/5=2

16^3/2=(16)^1/2)^3=4^3=64

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The products obtained in chlor - alkali process aresodium hydroxide,chlorinegas, andhydrogengas. # the gas liberated at anode ischlorineand gas liberated at cathode ishydrogen

7. Let the angles of quadrilateral be

x, 2x, 3x , 4x

sum of all angles of quadrilateral = 360°

x + 2x + 3x + 4x = 360°

10x = 360°

x = 360/10 = 36°

Ans. the four angles are :-

x = 36°2x = 2 × 36 = 72°3x = 3 × 36 = 108°4x = 4 × 36 = 144°

8. √2+1/√2-1

= √2+1/√2-1 * √2+1/√2+1

= (√2+1)²/(√2²-1²)

= √2² + 2√2 + 1/2-1

= 2+1+2√2

= 3+2√2

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the Laplace transform is an integral transform named after its inventor Pierre-Simon Laplace. It takes a function of a real variable t (often time) to a function of a complex variable s (complex frequency). The transform has many applications in science and engineering.

The Laplace transform is similar to the Fourier transform. While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are usually restricted to functions of t with t ≥ 0. A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable s. Unlike the Fourier transform, the Laplace transform of a distribution is generally a well-behaved function. Techniques of complex variables can also be used to directly study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory.

TanA=√2-1or, tanA=(√2-1)(√2+1)/(√2+1)or, tanA=(2-1)/(√2-1)or, tanA=1/√2-1∴, tanA+1/tanA=1/√2-1+√2-1or, (tan²A+1)/tanA=[1+(√2-1)²]/(√2-1)or, sec²A/tanA=(1+2-2√2+1)/(√2-1)or, (1/cos²A)/(sinA/cosA)=(4-2√2)/(√2-1)or, 1/sinAcosA=(4-2√2)(√2+1)/(√2-1)(√2+1)or, 1/sinAcosA=(4√2-4+4-2√2)/(2-1)or, 1/sinAcosA=2√2or, sinAcosA=1/2√2

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(√2 + 1)/(√2 - 1) = (√2 + 1)*(√2 + 1)/(√2 - 1)*(√2 + 1) = (2+1+2√2) / (2-1) = 3+2√2

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