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The sum of S of n successive odd natural number starting from 3 is given by the relation of S = n(n+2). DEtermine n, if the sum is 168

Posted by Mala Ramachandran 6 years, 11 months ago

CBSE > Class 10 > Mathematics

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If the sum of first p terms of an A.P is ap2 +bp,find its common difference

Posted by Sushant Thareja 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We are given that sum of first p terms of this AP
S_p= ap² + bp
Let the first term= x and common difference = d
{tex}{\mathrm S}_1=\mathrm a(1)^2+\mathrm b(1)=\mathrm a+\mathrm b{/tex}
So first term x = a+b
Now S₂ = a(2)² + b(2)
S₂ = 4a + 2b
,{tex}\mathrm{So}\;{\mathrm s}_2={\mathrm a}_1+{\mathrm a}_2=\mathrm x+\mathrm x+\mathrm d=4\mathrm a+2\mathrm b{/tex}
2x + d = 4a+2b
2(a+b)+d = 4a+2b
2a+2b+d=4a+2b
d=4a+2b-2a-2b
d = 2a
Therefore, the common difference of the given AP is 2a.

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If the median of the distribution given below is 28.5find the values of x and y

Posted by Vishal Singh 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

<th scope="col">Monthly Consumption</th> <th scope="col">

0-10	5	5
10-20	x	5 + x
20-30	20	25 + x
30-40	15	40 + x
40-50	y	40 + x + y
50-60	5	45 + x + y
Total	{tex}\sum f _ { i } = n = 60{/tex}

Here, {tex}\sum f _ { i } = n = 60{/tex}, then {tex}\frac { n } { 2 } = \frac { 60 } { 2 } = 30{/tex}, also, median of the distribution is 28.5, which lies in interval 20 – 30.

{tex}\therefore{/tex} Median class = 20 – 30

So, l = 20, n = 60, f = 20, cf = 5 + x and h = 10

{tex}\because 45 + x + y = 60{/tex}

{tex}\Rightarrow x + y = 15{/tex} ………...........(i)

Now, Median = {tex}l + \left[ \frac { \frac { n } { 2 } - c f } { f } \right] \times h{/tex}

{tex}\Rightarrow { 28.5 = 20 + \left[ \frac { 30 - ( 5 + x ) } { 20 } \right] \times 10 }{/tex}

{tex}\Rightarrow 28.5 = 20 + \frac { 30 - 5 - x } { 2 }{/tex}

{tex}\Rightarrow { 28.5 } = \frac { 40 + 25 - x } { 2 }{/tex}

{tex}\Rightarrow 2 ( 28.5 ) = 65 - x{/tex}

{tex}\Rightarrow 57.0 = 65 - x{/tex}

{tex}\Rightarrow x = 65 - 57 = 8{/tex}

{tex}\Rightarrow{/tex} x = 8

Putting the value of x in eq. (i), we get,

8 + y = 15

{tex}\Rightarrow{/tex} y = 7

Hence the value of x and y are 8 and 7 respectively.

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ABC is a right triangle right angled at A . Find the area of shaded region if AB_ 6cm , BC_ 10cm and O is the centre of circle of triangle ABC .(take _3.14)

Posted by Sri Charan 6 years, 11 months ago

CBSE > Class 10 > Mathematics

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How can we find the terminating and non terminating decimal expansion without doing any long division

Posted by Lionel Messi⚽️ 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Divya Garg 6 years, 11 months ago

If the denominator has the prime factors of 2 and 5 only then the fraction will be terminating but if the prime factorization contain any other prime number like 3,7,9etc. Then the fraction has a non terminating decimal expansion....

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