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Posted by Puja Guru 6 years, 5 months ago
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Sia ? 6 years, 5 months ago
If A(- 4,8), B(- 3, - 4), C(0, - 5) and D(5,6) are the vertices of a quadrilateral ABCD,then we have to find its area.
Here , x1=-4, y1=8, x2=-3,y2=-4, x3 =0, y3 = -5, x4 = 5, y4 = 6
Area of quadrilateral
{tex}= \frac { 1 } { 2 } \left[ \left( x _ { 1 } y _ { 2 } - x _ { 2 } y _ { 1 } \right) + \left( x _ { 2 } y _ { 3 } - x _ { 3 } y _ { 2 } \right)\right.{/tex} {tex}\begin{array} { c } { + \left( x _ { 3 } y _ { 4 } - x _ { 4 } y _ { 3 } \right) } {+ \left( x _ { 4 } y _ { 1 } - x _ { 1 } y _ { 4 } \right) ] } \end{array}{/tex}
Here co-ordinates are:
A(-4, 8), B(- 3, - 4), C(0, - 5), D(5, 6)
Area = {tex}\frac { 1 } { 2 } [ \{ - 4 \times ( - 4 ){/tex}- (- 3) (8)} + {(- 3) (- 5) - 0
{tex}× ( - 4 ) \} + \{ 0 \times 6 - 5 ( - 5 ) \} + \{ 5 \times 8 - ( - 4 ) ( 6 ) \}{/tex}]
= {tex}\frac { 1 } { 2 }{/tex}[16 + 24 +15 - 0 + 0 + 25 + 40 + 24]
= {tex}\frac 12{/tex}[40 + 15 + 25 + 40 + 24]
= {tex}\frac { 1 } { 2 } \times 144{/tex} = 72 sq units.
Posted by Ijjkgg Rgfddggjhh 7 years, 9 months ago
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Foram Desai 7 years, 9 months ago
Victor The Victorious 7 years, 9 months ago
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Anurag Chopra 7 years, 9 months ago
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Posted by Rahul Gupta 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
According to question,two pipes are used to fill a swimming pool.Pipe with larger diameter is used for 4 hours and pipe with smaller diameter is used for 9 hours.
Let x hours be the total time taken by the larger pipe to fill the tank
so in 1 hour it would fill {tex}\frac{1}{x}{/tex} part of the tank.
Similarly, y hours are needed for the smaller pipe,
then in 1 hour it would fill {tex}\frac{1}{y}{/tex} part.
So, y=10+x .........(1)
{tex}\frac{4}{x}{/tex} + {tex}\frac{9}{y}{/tex} = 1/2
using (1), {tex}\frac{4}{x}{/tex} + {tex}\frac{9}{10+x}{/tex} =1/2 ............(2)
solve (2), to get
x2 -16x - 80=0
(x-20)(x+4)=0
since value of x cannot be -ve
therefore x=20 and y=30
Larger diameter pipe fills in 20 hours, Smaller diameter pipe fills in 30 hours. Therefore it would take 20 hours and 30 hours respectively.
Posted by Devash Sharma 7 years, 9 months ago
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Aryan Kaushik 7 years, 9 months ago
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