Math, asked by tannushree2986, 1 year ago

answer plz its urgent plz

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Answered by Varun1870
1

a+b+c=0

b+c=-a

a+b=-c

c+a=-b

Putting these in the question

a²/bc+b²/ac+c²/ab

a³+b³+c³/abc

It is an identity that if a+b+c=0 then a³+b³+c³=3abc

3abc/abc = 3


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Answered by Anonymous
5

(c) Parallel sides are 25 cm and 46 cm

Let x be the distance between the height and the apex of the trapezium

The other side the distance will be 46  - ( 25  + x )

                                                 = 21  - x

Let height be h

By Pythagoras theorem :

h² = 20² - ( 21 - x )²

==> h² = 400 - ( 441 + x² - 42 x )

==> h² = 400 - 441 - x² + 42 x

==> h² = - 41 - x² + 42 x ......................(1)

Also :

h² = 13² - x²

==> h² = 169 - x²........................(2)

From (1) and (2) :

==> - 41 - x² + 42 x = 169 - x²

==> 42 x = 169 + 41

==> 42 x = 210

==> x = 210/42

==> x = 5

By Pythagoras theorem :

h² = 13² - 5²

==> h² = 169 - 125

==> h² = 144

==> h = 12

Area = 1/2 × (25 + 46 ) × 6

==> 3 × 71

==> 213

The height is 12 cm and area is 213 cm²

( d ) 4/3 cot²30° + 3 sin²60° - 2 cosec²60° - 3/4 tan²30° + sin 15°/cos 75°

==> 4/3 × (√3)² + 3 × (√3)/2² - 2 × 2²/(√3)² - 3/4 × 1/(√3)² + sin 15°/sin 15°

==> 4/3 × 3 + 3 × 3/4 - 2 × 4/3 - 3/4 × 1/3 + 1

==> 4 + 9/4 - 8/3 - 1/4 +1

==> 4 + 8/4 - 8/3 + 1

==> 4 + 2 - 8/3 + 1

==> 5 - 8/3

==> ( 15 - 8 )/3

==> 7/3

The value is 7/3


( c ) Let the value that B gets be x

A gets 33+1/3 % more

       = 100/3 % more

A gets x + 100/3% × x

        = x + 100 x / ( 3 × 100 )

        = x + x/3

        = 4 x/3

C gets 60% more than A and B

         = ( 4 x/3 + x )+ 60/100 × ( 4 x/3 + x )

        ==> 7 x/3 + 3/5 × 7 x/3

        ==> 7 x/3 + 7 x/5

        ==>  ( 35 x + 21 x ) / 15

       ==>  56 x / 15

A + B + C = Rs 45,500

==> x + 4 x/3 + 56 x/15 = Rs 45,500

==> ( 15 x + 20 x + 56 x ) / 15 = Rs 45,500

==> 91  x = Rs 45,500 × 15

==> 91 x = Rs 682500

==> x = Rs 682500/91

==> x = Rs 7500

B gets Rs 7500

A gets 4/3 × Rs 7500

==> Rs 10,000        

C gets 56 x/15

==> Rs 56 × 7500/15

==> Rs 28,000

A gets Rs 10,000 , B gets Rs 7,500 and C gets Rs 28,000

Question - 7

(a)

( b ) Let the first boy be A

A got 30% and failed for 12 marks .

Let the total marks be x

Let the pass marks be y

30 x/100 = y - 12

==> 30 x = 100 y - 1200

==> 3 x = 10 y - 120

==> 3 x - 10 y + 120 = 0 .......................(1)

For B :

B got 40 % marks

B got 28 more than the pass marks

40 x/100 = y + 28

==> 40 x = 100 ( y + 28 )

==> 4 x = 10 ( y + 28)

==> 4 x = 10 y + 280

==> 2 x = 5 y + 140

==> 2 x - 5 y - 140 = 0 ..............................(2)

Multiplying (2) by 2 we get :

==> 4 x - 10 y - 280 = 0 ........................(3)

Subtracting (3) and (2) we get :

==> x = 280 + 120

==> x = 400

Put this value in 2 we get :

==> 2×400 - 5 y - 140 = 0

==> 800-140 = 5 y

==> 5 y = 660

==> y = 660/5

==> y = 132

The pass mark is 132

The full marks is 400

( c ) a + b + c = 0

==> a + b = - c ....................(1)

==> a + c = - b ...................(2)

==> b + c = - a....................(3)

Now :

( a + b )² / ab + ( b + c )²/bc + ( a + c )² / ac

From (1) , (2) and (3) we get :

( - c )² / ab + ( - a )² /bc + ( - b )² / ac

==> c² / ab + a²/ bc + b² / ac

==> ( c³ + a³ + b³ ) / abc

==> ( a³ + b³ + c³ ) / abc..........................(4)

Now :

a + b + c= 0

==> ( a + b ) = - c .................(5)

Cubing both sides :

==> ( a + b )³ = -c³

==> a³ + b³ + 3 ab ( a + b ) = -c³

==> a³ + b³ - 3 abc = -c³ [ From ( 5 ) ]

==> a³ + b³ + c³ = 3 abc ...............................(6)

Putting this value of (6) in (4) we get :

==> ( a³ + b³ + c³ ) /abc

==> 3 abc / abc

==> 3

Answer : 3

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