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Sia ? 6 years, 5 months ago
According to the question, {tex}\sin (A - B) = \frac{1}{2}{/tex}, therefore, {tex}A - B ={/tex} 30o ........ (1)
{tex}\cos (A + B) = \frac{1}{2}{/tex}, therefore, A + B = 60o ........ (2)
Solving (1) and (2), we get
A = 45o and B = 15o
Posted by Masood Raza 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Posted by Yatharth S 7 years, 8 months ago
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Yatharth S 7 years, 8 months ago
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Sia ? 6 years, 6 months ago
{tex}12576 = 4052 \times 3 + 420{/tex}
{tex}4052 = 420 \times 9 + 272{/tex}
{tex}420 = 272 \times 1 + 148{/tex}
{tex}272 = 148 \times 1 + 124{/tex}
{tex}148 = 124 \times 1 + 24{/tex}
{tex}124 = 24 \times 5 + 4{/tex}
{tex}24 = 4 \times 6 + 0{/tex}
HCF of 12576 and 4052 is '4'.
Posted by Samiksha Khandelwal 7 years, 8 months ago
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Posted by Manu Kamboj 7 years, 8 months ago
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Sia ? 6 years, 6 months ago
The given equation is 4x2 - 4x + 1 = 0
Here a = 4, b = - 4, c= 1
{tex}\therefore D=b^2-4ac = (-4)^2-4(4)(1) = 16-16=0{/tex}
So, the given equation has equal roots
{tex}x = {-b \pm \sqrt{D} \over 2a} = {-(-4) \pm0 \over 2(4)}{/tex}
{tex}\implies x={4 \over 8}= {1 \over2}{/tex}
{tex}Hence,\, x={1 \over 2}, \,{1 \over 2}{/tex}are the required roots.
Posted by Ekaansh Jain 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
Given, {tex}3x -{/tex} {tex}\frac{y+7}{11}{/tex} {tex}+ 2 = 10{/tex}
{tex}\Rightarrow \frac{33 x-(y+7)+22}{11}=10{/tex}
{tex}\Rightarrow{/tex} {tex}33x - y - 7 + 22 = 110{/tex}
{tex}\Rightarrow{/tex} {tex}33x - y = 95{/tex} ..(i)
Also, {tex}2 y+\frac{x+11}{7}{/tex} = 10
{tex}\Rightarrow \quad \frac{14 y+x+11}{7}{/tex} = 10
{tex}\Rightarrow{/tex} {tex}14y + x + 11 = 70{/tex}
{tex}14y + x = 59{/tex}
{tex}14y = 59 - x{/tex}
{tex}\Rightarrow{/tex} y = {tex}\frac{59-x}{14}{/tex}
eq. (i) becomes
33x - {tex}\left(\frac{59-x}{14}\right){/tex} = 95
{tex}\Rightarrow \quad \frac{462 x-59+x}{14}{/tex} = 95
{tex}\Rightarrow{/tex} 463x - 59 = 1330
{tex}\Rightarrow{/tex} x = 3
When x = 3 eq. (i) becomes
33(3) - y = 95
{tex}\Rightarrow{/tex} y =4
Posted by Khush Agarwal 7 years, 8 months ago
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Posted by Muddit Popli 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
Assume A has x mangoes and B has y mangoes.
As per given condition if B gives 30 then A will have twice as many as left by B.
(x + 30) = 2(y - 30)
{tex}\Rightarrow{/tex}x + 30 = 2y - 60
{tex}\Rightarrow{/tex} x = 2y - 90....(1)
And if A gives 10 mangoes to B, then B will have thrice as many as left by A.
3(x - 10) = (y + 10)
{tex}\Rightarrow{/tex} 3x = y + 40 ....(2)
{tex}\Rightarrow{/tex} 3(2y - 90) = y + 40 (using x from Eq. 1)
{tex}\Rightarrow{/tex} 6y - 270 = y + 40
{tex}\Rightarrow{/tex} 6y - y = 310
{tex}\Rightarrow{/tex} y = 62
Put y = 62 in (1)
So, x = 124 - 90 = 34
Therefore A has 34 mangoes and B has 62 mangoes.
Posted by Mass Poobesh 7 years, 8 months ago
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Posted by Tanay Garg 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
A real number x will be called a solution or a root if it satisfies the equation.

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Yatharth S 7 years, 8 months ago
1Thank You