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DanielleElmas [232]
3 years ago
8

A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22

Mathematics
1 answer:
Igoryamba3 years ago
3 0

The train travel 20 kilometers in the southward direction to reach its original location.

Step-by-step explanation:

          The given is,

                First train travels east for 50 kilometers, then

                Turns north and travels for 22 kilometers

                 It goes west for 50 kilometers

Step:1

       Let, A - Distance of train travels from its starting point in Eastern direction at pq point

              B - Distance train travels in northward direction at qr point

              C - Distance of train travels in western direction at rs point

              D - Distance of train travels in southward direction to reach its starting location at sp point

Step:2

           Refer the attachment,

           Distance of travel in northward direction and distance of travel in southward direction are equal.

           qr = sp.............. (1)                           ( ∵ Eqn (1) from the Diagram)

           20 km = 20 km

          sp = 20 km

Result:

       So, the distance of train travel to reach its original location in southward direction is 20 km.

           

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\bf \begin{array}{cccllll} \stackrel{\textit{point (0,-7)}}{-7=a(0)^2+b(0)+c}& \stackrel{point (7,-14)}{-14=a(7)^2+b(7)+c}& \stackrel{point (-3,-19)}{-19=a(-3)^2+b(-3)+c}\\\\ -7=c&-14=49a+7b+c&-19=9a-3b+c \end{array}

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\bf -19=9a-3b-7\implies -12=9a-3b\implies -12=9a-3(-1-7a) \\\\\\ -12=9a+3+21a\implies -15=9a+21a\implies -15=30a \\\\\\ -\cfrac{15}{30}=a\implies \blacktriangleright -\cfrac{1}{2}=a \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{and since we know that}}{-1-7a=b}\implies -1-7\left( -\cfrac{1}{2} \right)=b\implies -1+\cfrac{7}{2}=b\implies \blacktriangleright \cfrac{5}{2}=b \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{2}x^2+\cfrac{5}{2}x-7~\hfill

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