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we know that sum of squares of direction cosines of a vector is 1

so cos²A + cos²B +cos²C = 1

=> 1-sin²A + 1-sin²B + 1 - sin²C = 1=> 3 - (sin²A +sin²B+sin²C ) = 1=> (sin²A +sin²B+sin²C ) = 3-1 = 2

and cos2A = 1-2sin²A

so, cos2A +cos2B +cos2C = 1-2sin²A +1-2sin²B +1-2sin²C = 3-2(sin²A +sin²B+sin²C ) = 3-2(2) = -1.

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Using Basic proportionality theorem,AX/XB = AY/YC AX/3 = 5/2 AX = 15/2 = 7.5 cm

Using Basic proportionality theorem,AX/XB = AY/YC AX/3 = 5/2 AX = 15/2 = 7.5 cm

2y-x=02y=x10x+15y=10510(2y)+15y=10520y+15y=10535y=105y=3x=2y=6

a1/a2= b1= b2here = √2/√5= √6/15= √2/5so no solution is there

(ii) If the graphs of two equations of a system are two parallel lines, the system is said to haveno solution,i.e., the system isinconsistent

√45×√20=√5*9×√4*5=√(5*9*4*5√9=3√4=2√5*√5=5

So, √(5*9*4*5=3*2*5=30

It is rational number

Acompositenumber has more than two factors. The number 1 is neitherprimenorcomposite. Theprimenumbers between2and 31 are2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 since each of these numbers has only two factors, itself and 1.

hence, 2 is a prime number

2 is a prime number

for the function to be continuous, value of function at x = -1 should be same around it's nearby

so, a(-1)²+b = 4 => b+a = 4

also, value at 0 should also be same

so, a(0)²+b = cos0 => b = 1

so, a = 4-b = 4-1 = 3

for the function to be continuous, value of function at x = -1 should be same around it's nearby

so, a(-1)²+b = 4 => b+a = 4

also, value at 0 should also be same

so, a(0)²+b = cos0 => b = 1

so, a = 4-b = 4-1 = 3

thanks for solve it

perimeter=49

sum of lengthof parallel

sides=perimeter-sum of non-parallel side =49-8 =41

area of trapezium =1/2 *distance between parallelsides *sum of parallel sides

=1/2*0.5*41 =10.25

area of trapezium=10.5square cm

sir y u took 0.5

let me know if don't understand

thanks sir

5x - 1/3 (x + 1) = 6 (x + 1/30)

5x - x/3 - 1/3 = 6x + 1/5

5x - x/3 - 6x = 1/5 + 1/3

-x - x/3 = (3 + 5)/15

(-3x - x)/3 = 8/15

-4x = 8*3/15

x = 8/5*-4

x = - 2/5

sine is between -1 and 1 , and also take value -1 and 1

for cosine is between -1 and 1 , and also take value -1 and 1

yes because both have same denominator so we will just compare numerator therefore 40< 141 so 40/ 29 < 141/29

area=16*7+9*7 =112+63 =175 m²

32(3/5) = 163/516(2/3) = 50/3area of park = area of rectangle = (163/5) × (50/3) = 1630/3 = 543(1/3) cm²

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Perimeter of trapezium = 104 m

Length of Non-parallel sides = 18 m and 22 m

Altitude = 16m

Area of Trapezium = 0.5 * (sum of parallel sides)*altitude ------ (1)

Sum of parallel sides = Perimeter - (sum of non-parallel sides) = 104 m - (18+22)m = 104-40 m = 64 m

From (1), Area of Trapezium = 0.5*64*16 = 512 m^2

Ans: Area of trapezium = 512 m^2

x+y=10x-y=20=9x-2y=20

so easy30X67 = 30+630x 67=36

thanks

Old remainder = 32

Divisor = 7

When we divide old remainder by divisor

ie) 32÷7

we get new remainder

ie) 4

x=3 is the root of the equation. Therefore,it should satisfy the quadratic equation.Substituting x=3;(3)^2-2k(3)-6=09-6k-6=06k=3k=3/6=1/2So,the value of k is 1/2.

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ABcz U, V, W, X, Zas same 32-3=29-3=26-3=23-3=20-3=17

(b) w17,z26.

tan 65=90-25/cot25=90-65

area of rectangular =16x9=144m^2now area of square is side^2=144hence side=√144=12cmhence perimeter =4*side=4*12=48m

ty

Thank you so much