Vitamin D.

-Answered by Himanshi Verma On 10 March 2019:04:41:55 PM

 Since 2 is one root of the quadratic equation,

We substitute X=2

k(2)^2 - 14(2) +8= 0

4k-28+8=0

4k-20=0

4k=20

k=5

-Answered by Himanshi Verma On 10 March 2019:04:48:03 PM

 ABC is a right angle triangle at B and BD is a perpendicular from B on to AC, the diagonal.

Triangles ABC and BDC are similar, as:

     . angle DBC = 90 - angle C = angle A

     . angle ABC = angle BDC = 90

Ratios of corresponding sides are equal.

     AB / BD = BC / DC = AC / BC

    So we get  BC² = AC * DC     --- (1)

Triangle ABC amd ADB are similar, as:

    . angle DBA = 90 - (90 - C) = angle C

    . angle ABC = 90 = angle ADB

so ratios of corresponding sides are equal

         AB / AD = BC / BD = AC / AB 

       So we get  AB² = AD * AC  --- (2)

  Add (1) and (2) to get:

       AB² + BC² = AC * ( AD + DC) = AC * AC = AC²

So the theorem is proved.

-Answered by Himanshi Verma On 01 March 2019:03:38:26 PM

-Answered by Shalu Shukla On 01 March 2019:03:47:38 PM

 Let us draw a line segment AM ⊥ BC.

We know that,

Area of a triangle = 1/2 x Base x Altitude

It is given that DE = BD = EC.

⊥ Area (ΔADE) = Area (ΔABD) = Area (ΔAEC)

It can be observed that Budhia has divided her field into 3 equal parts.

-Answered by Himanshi Verma On 09 February 2019:04:40:18 PM

 If an event is impossible its probability is zero. Similarly, if an event is certain to occur, its probability is one. The probability of any event lies in between these values. It is called the range of probability and is denoted as 0 ≤ P (E) ≤ 1.

-Answered by Himanshi Verma On 09 February 2019:04:32:27 PM

 बेलन के पानी का आयतन = गोले का आयतन 

   πr²h   = 4/3 πr³

   14×14×h = 4\3×7×7×7

          h   = 4/3 × 343/196

          h  = 7/3cm

-Answered by Shalu Shukla On 11 February 2019:05:45:38 PM

 Considering AB = Base;

Area = Base x Height

⇒ 1470 cm2 = AB x DL

⇒ 1470 cm2 = 35cm x DL

Or, DL = 1470 ÷ 35 = 42 cm

Now considering AD = Base;

Area = Base x Height

⇒ 1470 cm2 = AD x BM

⇒ 1470 cm2 = 49 cm x BM

Or, BM = 1470 ÷ 49 = 30 cm

Hence, DL = 42 cm and BM = 30 cm

-Answered by Himanshi Verma On 09 February 2019:04:21:59 PM

  8 8 8

     8 8

        8

        8

+      8

= 1000 

-Answered by Himanshi Verma On 05 February 2019:05:36:22 PM

 Given

Ratio of side =3:2

Perimeter =60cm

Altitude =5cm

So let take one side as 3x and other is 2x

Then perimeter of parallelogram 

=3x+2x+3x+2x

=10x 

According to question perimeter =60cm 

Then 

10x=60cm 

X=60/10=6cm

Then one side is =6 x 3=18

And other is =2x6=12

So base=18cm 

Area of parallelogram =bxh

=18x5=90cm²

Altitude corresponding to smaller side 

90=12xh

H=7.5cm 

-Answered by Himanshi Verma On 05 February 2019:05:26:39 PM

 Diameter is the greatest chord of circle.

-Answered by Himanshi Verma On 05 February 2019:04:58:06 PM

 9+8+8+7+7=39,

9+9+8+3=29,

7+2=9

We write last nine of the three solution so, we get 777+888+999=999 

Hence, proved.

-Answered by Nishant Verma On 03 February 2019:05:23:34 PM

 9+8+8+7+7=39,

9+9+8+3=29,

7+2=9

We write last nine of the three solution so, we get 777+888+999=999 

Hence, proved.

-Answered by Himanshi Verma On 05 February 2019:04:51:38 PM

 The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius. ... This give a geometric justification that the area of a circle really is "pi r squared".

-Answered by Himanshi Verma On 02 February 2019:01:33:01 PM

 (secA+tanA-(sec^2 A - tan ^2A)) )/tanA-secA+1) as sec^2 A= 1 + tan ^2 A so 1= sec^2 A - tan ^2 A 

= (sec A + tan A - (sec A + tan A) ( sec A - tan A)) / ( tanA-secA+1) 

= ( sec A + tan A ) ( 1- (sec A - tan A)/ ( tanA-secA+1) 

= (sec A + tan A)/(+ tan A - sec A)/(tan A- sec A+ 1) 

= (sec A + tan A) 

= 1/cos A + sin A/ cos A 

= (1+ sin A)/ cos A 

= (1 + sin A )(1- sin A)/(cos A (1- sin A)) 

= (1- sin ^2 A/(cos A (1- sin A)) 

= cos ^2 A / (cos A (1- sin A)) 

= cos A /(1- sin A) 

proved

-Answered by Himanshi Verma On 02 February 2019:01:40:14 PM

 Length (l) of garden = 90 m

Breadth (b) of garden = 75 m

Area of garden = l × b = 90 × 75 = 6750 m2

From the figure, it can be observed that the new length and breadth of the garden, when path is also included, are 100m and 85m respectively.

Area of the garden including the path = 100 × 85 = 8500 m2

Area of path = Area of the garden including the path − Area of garden

= 8500 − 6750 = 1750 m2

1 hectare = 10000 m2

Therefore, area of garden in hectare

=6750/10000

=0.675

-Answered by Himanshi Verma On 02 February 2019:01:49:33 PM

 A=6400m²

-Answered by Himanshi Verma On 03 February 2019:04:19:42 PM

 The given quadratic will be a perfect square if it has two real and equal roots. To have two real and equal roots the discriminant must be zero.

i.e., b²-4ac=0

or, (2k+4)²-4(4-k)(8k+1)=0

or, 4k²+16k+16-4(32k-8k²+4-k)=0

o², 4k²+16k+16-128k+32k²-16+4k=0

or, 36k²-108k=0

or, 36k(k-3)=0

either 36k=0

or, k=0

or, k-3=0

or, k=3

∴, k=0,3 Ans.

-Answered by Himanshi Verma On 02 February 2019:01:43:20 PM

 Consider, abx2 +(b2-ac)x-bc = 0

-Answered by Himanshi Verma On 02 February 2019:01:44:13 PM

ON solving the above equation we have a quadratic equation  

(a+b)x^2+(a+b)^2x+ab(a+b)

on solving the above equation by formula -b+root over(b^2-4ac) and -b-root over(b^2-4ac)

we got -a and -b as roots.

According to me this is much easier then others when compared.

-Answered by Himanshi Verma On 10 March 2019:04:49:29 PM

 : (11 + 9) + (3) + (7) = 30

ANOTHER: (13 + 15) + (1) + (1) = 30

OR: (7 + 9) + (1) + (13) = 30

-Answered by Himanshi Verma On 21 January 2019:04:52:39 PM

 Cscϕ/secϕ = (1+cotϕ)/(1+tanϕ) 

LHS = (1+cotϕ)/(1+tanϕ) 

where cotϕ=cosϕ/sinϕ and tanϕ = sinϕ/cosϕ 

= (1+(cosϕ/sinϕ))/(1+(sinϕ/cosϕ)) 

= ((cosϕ+sinϕ)/sinϕ)/((cosϕ+sinϕ)/cosϕ) 

= cosϕ/sinϕ 

wkt cosϕ=1/secϕ 

and sinϕ=1/cosecϕ 

= cscϕ/secϕ 

LHS = RHS 

Hence Proved

-Answered by Himanshi Verma On 22 January 2019:05:15:48 PM

 Total no. of times tossing a coin= 1000

no. of head comes= 425

no. of tail comes= 1000-425= 575

probability   p(e)= 575/1000 

-Answered by Himanshi Verma On 20 January 2019:04:27:24 PM

 Let three spheres are S1, S2 & S3

having radii r₁ = 3cm, r₂ = 4cm & r₃ = 5cm respectively.

Let the radius of new Big sphere S is R.

A/Q,

Volume of new Sphere  S = Sum of volumes three Spheres S1, S2 & S3

⇒ 4/3πR³ = 4/3π(r₁)³ + 4/3π(r₂)³+4/3π(r₃)³

⇒ 4/3πR³ = 4(r₁³ +r₂³ + r₃³)/3π

⇒ R³ = r₁³ +r₂³ + r₃³

⇒  R³ = 3³ +4³ + 5³ = 27 + 64 + 125

⇒ R³ =  216

⇒ R = ∛216

⇒ R = 6cm

Therefore radius of new Sphere is 6 cm.

-Answered by Himanshi Verma On 20 January 2019:05:15:36 PM

  slant height of cone is : 10 

Radius of the base is : 8 cm

Total surface area of cone is : πr(l+r)

227 ×8(10+8) 

227 ×144

= 452.57

-Answered by Himanshi Verma On 20 January 2019:04:27:57 PM

 Total surface area= 2πr(r+h) -πr²

curved surface area = 2πrh+πr²

-Answered by Himanshi Verma On 03 February 2019:04:44:16 PM

  Let ABCD, the square garden of side= 30 m.

PQRS is the region inside the garden.

so,

PQ = (30 -1-1 ) = 28 m

also

PS = ( 30 – 1 – 1 ) = 28 m 

(i) Area of the path = Area of ABCD – Area of PQRS 

= [( 30 x 30) – (28 x 28)]

= 900 – 784 

= 116 sq.m 

(ii) Area of the remaining portion in which the grass is planted = Area of square PQRS 

= 28 x 28 

= 784 sq.m 

cost of planting the grass in the region PQRS =  area x cost = 764 x 40

 =31,360

-Answered by Himanshi Verma On 18 January 2019:05:16:10 PM

 An integer that is divisible by 2 is called Even Number.

-Answered by Himanshi Verma On 17 January 2019:05:28:03 PM

 Counting numbers are numbers you can use to count whole items. You can use the positive integers to count marbles, for example. Whether 0 is a counting number or not, that's a big debate you may or may not be interested in 

-Answered by Harshita Rathore On 17 January 2019:05:31:45 PM

 We know,

---> if a + b + c = 0 ; a³ + b³ + c³ = 3abc

We observe,

( a² - b² ) + ( b² - c² ) + ( c² - a² ) = 0

=> ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ = 3( a² - b² )( b² - c² )( c² - a² )

Similarly, 

( a - b ) + ( b - c ) + ( c - a ) = 0

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

Now, [ ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ ] / [ ( a - b )³ + ( b - c )³ + ( c - a )³ ]

== 3( a² - b² )( b² - c² )( c² - a² ) / 3( a - b )( b - c )( c - a )

= ( a + b )( b + c )( c + a ) <---- Answer..

-Answered by Himanshi Verma On 03 February 2019:04:45:43 PM

 1

-Answered by Himanshi Verma On 17 January 2019:05:27:08 PM

 The Hindu-Arabic numerals are the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). They are descended from Indian numerals, and the Hindu-Arabic numeral system by which a sequence of digits such as "406" is read as a whole number was developed by Indian mathematicians.

-Answered by Himanshi Verma On 17 January 2019:05:27:36 PM

  Lateral Surface Area of cube=256 cm²

-Answered by Himanshi Verma On 16 January 2019:06:04:58 PM

 l=5m    b=4m      h=3m 

The total area of cuboid = 2(lb+bh+hl)+l×b

                                  = 2(5×4+4×3+3×5)+5×4

                                  = 2(20+12+15)+20

                                  = 2(47) +20

                                  =    94+20

                                  =     114m²

The cost of white washing the wall and the ceiling of the room = 7.50 per m²

      The cost of 114m² of the walls and ceiling of the room= (7.50×114)Rs

                                                                                   = 855.00Rs.

-Answered by Himanshi Verma On 19 January 2019:05:10:07 PM

The total surface area of hemisphere= 3πr²

The ratio of total surface area of sphere and hemisphere= 4πr²/3πr²

                                                                                = 4:3

-Answered by Himanshi Verma On 20 January 2019:04:38:18 PM

   Total surface area of cube is 150sq. cm

Total surface area of cube : 6a²

^{To find perimeter of its one faces :  ?}

Total surface area of cube =150sq.cm

                           6a²  =150sq.cm

 = 1506 

= 25cm

=a² = √25cm

=a = 5 cm

Perimeter of its one face is = 4 × a

                                        = 4 × 5 cm

                                        = 20 cm Answer

-Answered by Himanshi Verma On 19 January 2019:04:39:34 PM

 The surface area of the cuboid= 1372 sq. cm 

  Let the dimensions =4x, 2x, 1x

     The total surface area of the cuboid = 2(lb+bh+hl)=1372

                                                        = 2(4x × 2x + 2x × 1x + 4x × 1x )=1372 

=2(8x²+2x²+4x²) =1372

=2(14x²)= 1372

=28x²=1372

= x²=1372/28

       = 49

x=7m

the dimensions are 4x=4×7=28m

                           2x=2×7=14m

                           1x=1×7=7m

-Answered by Himanshi Verma On 19 January 2019:05:17:58 PM

 Let the radii be 2x and 3x,

let the height be 5y and 3y.

so, ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27,

The ratio is = 20:27

-Answered by Himanshi Verma On 20 January 2019:05:11:58 PM

 Let the first and second angle be a and b respectively 

-Answered by Himanshi Verma On 20 January 2019:05:07:15 PM

 We know, 

-Answered by Jyoti Srivastva On 30 January 2019:04:32:47 PM

  Ans 1. Zero(0)

Ans 2. 0 and 1

Ans 3. 2

-Answered by Akki chauhan On 15 January 2019:09:06:44 AM

 Let 'x' be the number of boys and 'y' be the number of girls.

To find the total marks

The total marks of boys = 42x

The total marks of girls = 45y

Total number of boys and girls = x + y

To find the ratio

The total marks of boys and girls = 44(x + y)

Then we can write

44(x + y) = 42x + 45y

44x + 44y = 42x + 45y

2x = y

x/y = 1/2

Therefore the ratio of the number of boys to the number of girls is 1:2

-Answered by Himanshi Verma On 20 January 2019:05:29:47 PM

Let 'x' be the number of boys and 'y' be the number of girls.

To find the total marks

The total marks of boys = 42x

The total marks of girls = 45y

Total number of boys and girls = x + y

To find the ratio

The total marks of boys and girls = 44(x + y)

Then we can write

44(x + y) = 42x + 45y

44x + 44y = 42x + 45y

2x = y

x/y = 1/2

Therefore the ratio of the number of boys to the number of girls is 1:2

-Answered by Himanshi Verma On 22 January 2019:05:24:43 PM

   l=10cm r=8cm

The total surface area of cone=πr(l+r)

                                          =22/7×8(10+8)

                                          =22/7×8(18)

                                          =22/7×144

                                          =3168/7cm

-Answered by Akki chauhan On 15 January 2019:09:06:10 AM

r= 32

Volume of hemisphere= 23 πr³

                                = 23 ×22/7×3/2×3/2×3/2

                                 = 7.071

-Answered by khushi chauhan On 22 January 2019:05:23:49 PM

 The concentric circle are the circles with a common center the region between two concentric circle of different radii is called an annulus. 

-Answered by Akki chauhan On 15 January 2019:09:05:48 AM

 √125 +2√27 +(-5√5 -√3)

=√5×5×5 +2√3×3×3 -5√5 -√3 

=5√5 +6√3 -5√5 -√3

=5√3

-Answered by Akki chauhan On 15 January 2019:09:05:29 AM

  ∠A + ∠C = 180 ....1

But ∠A = ∠C

So ∠A = ∠C = 90

Again 

  ∠B + ∠D = 180 ....2

But ∠B = ∠D

So ∠B = ∠D = 90

Now each angle of parallelogram ABCD is 90.

Hense ABCD is a rectangle

-Answered by Akki chauhan On 15 January 2019:09:05:05 AM

 2x-5=0

2x=5

x= 5/2

-Answered by Akki chauhan On 15 January 2019:09:04:26 AM

  x³ -23x²+142x-120 

=x³-x²-22x²+22x+120-120

=x²(x-1)-22x(x-1)+120(x-1)

=(x-1)(x²-22x+120)

=(x-1)(x²-12x-10x+120)

=(x-1)[x(x-12)-10(x-12)]

=(x-1)(x-10)(x-12)

-Answered by Himanshi Verma On 16 January 2019:05:57:48 PM

  When p(x) is divided by (x-2),

By remainder theorem,

Remainder= p(2)

p(2)=a*2^3 + 3*2^2 - 13

        =a*8+3*4-13

       =8a+12-13 = 8a-1

p(2) = 2*2^3-5*2+a

      =2*8-10+a

     =16-10+a = 6+a

Since the remainders of ax^3+3x^2-13 and 2x^3-5x+a are same when divided by x-2,

8a-1 = 6+a

8a-6+a=1

8a+8=1-6=-5

8a=-5-8 =-13

a=-13/8

-Answered by Himanshi Verma On 20 January 2019:05:29:25 PM

 (a+1/a)2=a2+1/a2+2

a2+1/a2=(a+1/a)2-2→ I

Now,

a=9-4root5

1/a=1/9-4root5

=(1/9-4root5)×9+4root5/9+4root5

=(9+4root5)

a+1/a=9-4root5+9+4root5

=81

Now,

a2+1/a2=(a+1/a)2-2 →(from I)

=(81)2-2

=6561-2

=6559

-Answered by Himanshi Verma On 22 January 2019:05:31:51 PM

 The first 10 prime numbers are : 2,3,5,7,11,13,17,19,23 and 29.

n=10

Median if n is even numbers

n2 th term = 5th term = 11

n2 + 1 = 5 + 1 = 6th term = 13

Median = 5th term + 6th term2 

Median = 11 + 132 

 = 242 = 12 Answer

-Answered by Akki chauhan On 15 January 2019:09:03:48 AM

 The number of times an observation occurs in the given data is called frequency of the observation.

-Answered by Rohit Rajput On 12 January 2019:08:59:05 AM

volume of the sphere = 43 πr³= 310.4cm³

                                4/3×22/7×r³=310.4

                                88/21×r³= 310.4

                                   r³=   310.4×21/88

                                      =   6518.4/88

                                   r³  = 74.0727272cm

-Answered by Himanshi Verma On 19 January 2019:04:56:34 PM

 Highest power of x in the algebraic expression is called the degree of the polynomials.

-Answered by Prince Rawat On 11 January 2019:10:08:00 AM

Given : In a circle C(O,r) , ∠AOB = ∠COD 

To Prove : Chord AB = Chord CD .

Proof : In △AOB and △COD 

AO = CO [radii of same circle]

BO = DO [radii of same circle]

∠AOB = ∠COD  [given]

⇒  △AOB ≅  △COD [by SAS congruence axiom]

⇒   Chord AB = Chord CD [c.p.c.t]

-Answered by Akki chauhan On 13 January 2019:01:04:33 PM

  Start with: -20 = -20

-Answered by Akki chauhan On 15 January 2019:09:03:13 AM

  21b - 32 + 7b - 20b

=(21b+7b -20b) - 32

=8b - 32 Answer

-Answered by Akki chauhan On 10 January 2019:10:54:03 AM

 3p²q² - 4pq + 5 + (-10p²q²) + 15 + 9pq + 7p²q² 

= 3p²q² + 7p²q² - 10p²q² + 9pq - 4pq + 5 + 15 

= 10p²q² - 10p²q² + 5pq + 20 

= 5pq + 20 Answer

-Answered by Akki chauhan On 10 January 2019:10:54:27 AM

                   =4

The value of b²= (-2²) = 4

 a²+b²= 4+4

         =  8

-Answered by Himanshi Verma On 22 January 2019:05:38:40 PM

 x+7+4(x-5)=2

x+7+4x-20=2

5x-13=2

5x=2+13

5x=15 

x=3

So, The value of x is 3. 

-Answered by Akki chauhan On 14 January 2019:10:15:24 AM

 a=5,      b=-3

2(5²+5×(-3))+3-5×(-3)

2(25+(-15))+3+15

2(25-15)+18

2×10+18

20+18

38

-Answered by Himanshi Verma On 10 March 2019:04:58:49 PM

    Mean is an average of some data which is calculated by dividing ∑Sum of data by total numbers of data

-Answered by Akki chauhan On 19 January 2019:10:46:10 AM

    x² + 2x + 1 

= x² + x + x + 1

= x(x + 1) + 1(x + 1) 

= (x + 1) (x + 1) 

-Answered by Akki chauhan On 10 January 2019:10:57:10 AM

 For finding the value of x first we find mean of 5, 10, 3 

sum of observation = 5 + 10 + 3 = 18

mean = 18 / 3 = 6 

Therefore, x = 6 

Now we have data for median 11, 12, 14, 18, 21, 23 

n = 6 { n is an even number} 

n/2 th trem = 14 

and (n/2 + 1)th trem = 18 

Median = (14 + 18)/2 = 32/ 2 = 16 Answer

-Answered by Akki chauhan On 14 January 2019:10:14:53 AM

 S7 = 7/2(2a + 6d) 

=> 49 = 7a + 21d

=> 7 = a + 3d   ------------ (i) 

S17 = 17/2 (2a + 16d) 

=> 289 = 17a + 136

=> 17 = a + 8d --------------  (ii) 

Substracting equation (i) from (ii) 

we have ... 

17 - 7 = a - a + 8d - 3d 

10 = 5d 

d = 10/5 

d = 2 

Putting the value in Equation (i) 

7 = a + 3d 

7 = a + 3 x 2 

a = 7 - 6 

a = 1 

Sum of first n terms = n/2 [2a + (n - 1) d]

= n/2 [2x 1 + (n - 1)2] 

= n/2 [2 + 2n - 2 ]

= n/2 (2n) 

= nxn = n2

-Answered by Akki chauhan On 14 January 2019:10:14:29 AM

 A.p= 9,17,25

a=9

d=17-9

=8

Sum of n terms=n÷2[2a+(n-1)d

636=n÷2[2(9)+(n-1)8]

636=n÷2[18+8n-8]

636=n÷2[10+8n]

1272=10n+8n^2

8n^2+10n-1272=0

2[4n^2+5n-636]=0

4n^2+5n-636=0

4n^2+53n-48n-636=0

n(4n+53)-12(4n+53)=0

(n-12)(4n+53)=0

n-12=0

n=12

12 terms must be given to sum of 636

-Answered by Himanshi Verma On 20 January 2019:05:32:22 PM