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-1+ihencer=√(-1)^2+(1)^2=√1+1=√2and angle will be tan^-1(-1/1)=-π/4hencepolar formr(costheta+isintheta)√2(cos(-π/4)+isin(-π/4)

Let the number be x

One third is x/3One fifth is x/5

x/3=x/5 +4x/3-x/5=4

5x-3x/15=42x=4*152x=60x=60/2=30

Number is 30

yes the product is less than the fractions being multiplied. as both the fractions is less than 1.

(i) Total cards =100 The numbers those are divisible by 9 and are perfect squares are 9, 36, 81.

Therefore probability that the number on the selected card is divisible by 9 and is a perfect square is 3/ 100

(ii) Total cards =100 The prime numbers greater than 80 are, 83, 89, 97

Therefore probability that the number on the selected card is a prime number greater than 100 is 3 ./100

(i) 50.63° = 0.8836 radians(ii) -10.68° = -0.1863 radians

Suppose numbers are x and x + 36 x + x + 36 = 48 2x = 12 x = 6 numbers are 6 a d 42

y=e^x+1y'=e^xy''=e^xso y''-y'=e^x-e^x=0Hence Proved

option (i), (ii) are in proportion

Here we will tin-plate the inside of the hemisphere So, We need to find the curved surface area of hemisphere

Radius of hemisphere = r = /2 = (10.5/2) cm = 5.25 cm

Curved surface area of the hemisphere = 22 = (2×22/7×5.25×5.25) cm2 = 173.25 cm2

Cost of tin-plating 100 cm2 = Rs 16Cost of tin-plating 1 cm2 = Rs 1/100 × 16Cost of tin-plating 173.25 cm2 = Rs 1/100 × 16 × 173.25 = Rs 27.72∴ Cost of tin-plating the hemisphere is Rs 27.72

answer

Ans..169|144

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In mathematics and signal processing, theZ-transformconverts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. Itcanbe considered as a discrete-time equivalent of the Laplacetransform.

In mathematics and signal processing, theZ-transformconverts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. Itcanbe considered as a discrete-time equivalent of the Laplacetransform.

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Let one number be xthen the other number is x+36Sum of two numbers = 48x + x + 36 = 482x + 36 = 482x = 48-362x = 12x = 12/2=6

The other number = 6+36 = 42

Therefore, the two numbers are 6 and 42

Let AB be the tower with height h.Let AC and AD be the shadows when elevation of sun are 60 degrees and 45 degrees.As per given, CD=10mlet us assume CA=xIn triangle ACB,tan60°=opposite side /adjacent side√3=h/AC√3=h/xx=h/√3 ------ equation (1)

In traingleDAB,

tan45°=AB/AD=h/(AC+DC)1=h/(x+10)x+10=h-----equation(2)

By substituting the value of x in equation 2 we get:

h/√3+10=h

h-h/√3=10

h√3-h=10√3

h(√3-1)=10√3

h=10√3/√3-1

Rationalizing factor is√3+1

h=10√3(√3+1)/[(√3-1)x(√3+1)]

h=10√3(√3+1)/(3-1)

h=10√3(√3+1)/2

h=5√3(√3+1) m

h=5(3+√3)

=15+5*√3

=15+5*1.732

=15+8.660

=23.66 m

∴ Height of tower is 23.66m

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Let the no. be x. Then,x/5= 10 +( x/7)

Taking the LCM ,x/5 = ( 70 + x)/ 7Cross multiplying,

7x = 350 + 5x2x = 350x = 175

the answer is Let common multiple be xwe know,x/5 = (70+x) / 7Taking the LCM ,x/5 = (70 + x ) / 7By cross multiplying ,7x = 350 + 5x2x = 350x = 175

Assuming that individual rings are not to be distinguishable from eachother… there are 9 possible Combinations

6 on one finger, none on the rest (6 0 0 0)

5 on one finger, 1 on another (5 1 0 0)

4 2 0 0

4 1 1 0

3 3 0 0

3 2 1 0

3 1 1 1

2 2 2 0

2 2 1 1

Each combination has its own quantity of permutations

(6 0 0 0) 4 permutations because 4 fingers to choose to place the 6 rings.

(5 1 0 0) 12 permutations

(4 2 0 0) 12 permutations

(4 1 1 0) 12 permutations

(3 3 0 0) 6 permutations

(3 2 1 0) 24 permutations

(3 1 1 1) 4 permutations

(2 2 2 0) 4 permutations

(2 2 1 1) 6 permutations

Total 84 different ways to put 6 rings on 4 fingers.

6=2×372=2×2×2×3×3120=2×2×2×3×5

HCF=2×3=6LCM=2×2×2×3×3×5=8×9×5=40×9=360

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To find the inner cost of plating it, we must find the CSA of the bowl=2πr2radius=0.105m=0.105*100 cm=10.5 diameter

radius=10.5/2= 5.25now CSA=2*22/7* 5.25 * 5.25

=173.25cm square

cost of tin plating=rs.16 /100cm squarecost for 173.25 cm square =173.25* (1/ 100) *16=27.72thus the cost of tin plating it inside = 27.72 rs

Answer will be 15 and 16.

पेहले determinant = x(x)-36 =x^2-36Second determinant= 6(6)-18(2) So x^2-36=36-36x^2=36x=6/-6

let x be the smaller number then the larger number is x+3x+(x+3)=272x+3=272x=27-32x=24x=24÷2x=12so smaller number is 12 andlarger number is 12+ 3= 15

Let be number xanother number be

The number will be 3 digit as its differs 3 digit(594)

Let original number be 100x+10y+z

Reverted number is 100z+10y+x

At the question

Original Number=Reverted number+594

which means,

original number-reverted number=594

ON PUTTING VALUES

100x+10y+z-(100z+10y+x)=594

100x+10y+z-100z-100y-x=594

99(x-z)=594

Therefore x-z=6

This means ones and hundred digits have difference of 6

Therefore we can substitute any values of x&z to satisfy the condition and y=any value

Like if x=9 therefore x=3

903–309=594 {9–3=6}

812–218=594

862–268=594

The possible remainder are 0,1,2,3,4.

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8sin x - cos x = 4

Therefore,

8sin x - 4 = cos x

We Know,

sin^2 x + cos^2 x = 1…(Trigonometric Identity)

Thus,

sin^2 x + (8sin x - 4)^2 = 1

sin^2 x + 64 sin^2 x -64 sinx + 16 = 1

…(Since (a + b)^2 = a^2 + 2ab + b^2)

Therefore,

65sin^2 x - 64 sin x + 16 = 1

65sin^2x - 64 sin x + 15 = 0

Solving this quadratic equation, we get,

sin x = 3/5 and sin x = 5/13

Thus, possible values of sin x are:

sin x = { 3/5 , 5/13}

As given conditionx - (-7) = - 8x + 7 = - 8x = - 15

Therefore,Possible value of x = - 15

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