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Sia ? 6 years, 4 months ago
Given: {tex}\Delta ABC \sim \Delta PQR{/tex}
Since we know that ,the ratio of area of two similar triangles is equal to the square of ratio of their corresponding sides. Thus,
{tex}\frac{\text { ar } \triangle \mathrm{ABC}}{\text { ar } \triangle \mathrm{PQR}}{/tex} = {tex}\frac{\mathrm{AB}^{2}}{\mathrm{PQ}^{2}}{/tex} = {tex}\left(\frac{1}{3}\right)^{2}{/tex} = {tex}\frac{1}{9}{/tex}
Posted by Rishika Verma 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Let {tex} \alpha{/tex} and {tex} \frac { 1 } { \alpha }{/tex} be the zeros of (a2 + 9)x2 + 13x + 6a.
Then, we have
{tex} \alpha \times \frac { 1 } { \alpha } = \frac { 6 a } { a ^ { 2 } + 9 }{/tex}
⇒ 1 = {tex} \frac { 6 a } { a ^ { 2 } + 9 }{/tex}
⇒ a2 + 9 = 6a
⇒ a2 - 6a + 9 = 0
⇒ a2 - 3a - 3a + 9 = 0
⇒ a(a - 3) - 3(a - 3) = 0
⇒ (a - 3) (a - 3) = 0
⇒ (a - 3)2 = 0
⇒ a - 3 = 0
⇒ a = 3
So, the value of a in given polynomial is 3.
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Sia ? 6 years, 6 months ago
Suppose x litres of 50% solution be mixed with y litres of 25% solution.
According to the question,
50% of x + 25% of y = 40% of 10
{tex}\Rightarrow \frac { 50 } { 100 } x + \frac { 25 } { 100 } y = \frac { 40 } { 100 } ( 10 ){/tex}
{tex}\Rightarrow{/tex} {tex}50x + 25y = 40(10){/tex}
{tex}\Rightarrow{/tex} {tex}2x + y = 16{/tex}..........(i)
The amount of each solution adds to {tex}10\ litres{/tex},
{tex}x + y = 10{/tex}.......(ii)
Subtract (ii) from (i),
{tex}\Rightarrow{/tex} {tex}x = 6{/tex}
Substituting {tex}x = 6{/tex} in (i), we get {tex}y = 4{/tex}
{tex}\therefore{/tex}{tex}6\ litres{/tex} of 50% solution is to be mixed with {tex}4\ litres{/tex} of 25% solution
Posted by Aman Bhatt 5 years, 8 months ago
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Sia ? 6 years, 6 months ago
We have,
3x2 + 2x + 3
Here, a = 3, b = 2 and c = 3
{tex}\therefore{/tex} {tex}D = b^2 - 4ac{/tex}
= (2)2 - 4 {tex}\times 3 \times 3{/tex}
= 4 - 36
= 32 > 0
{tex}\therefore{/tex} D > 0
So, the given equation has real and distinct roots.
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