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lana [24]
3 years ago
9

What is the range of possible sizes for side x? the other two sides are 8.0 and 8.5

Mathematics
1 answer:
kirza4 [7]3 years ago
8 0

Answer: 0.5 < x < 16.5.

Step-by-step explanation:

Given: Two sides of triangle: 8.0 units and 8.5 units

Measure of third side = x

According to the triangle's inequality,

  • Sum of any two sides > third side.    (i)
  • Difference between the sides < third side.    (ii)

If x is the third side, then

x < 8+8.5   [Using (i)]

i.e. x< 16.5  

Also, x > 8.5-8   [Using (ii)]

i.e. x> 0.5

Hence, Range of possible sizes for side x would be 0.5 < x < 16.5.

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Answer:

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Step-by-step explanation:

<u>Equation</u>

Let s represent the speed of the faster plane. Then its travel time is ...

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The difference in these times is 1.5 hours, so we have ...

  3600/(s -200) -3600/s = 1.5

<u>Solution</u>

Multiplying by (2/3)s(s -200), we get ...

  2400(s) -2400(s -200) = s(s -200)

  s^2 -200s -480000 = 0 . . . . . . . . . . rewrite in standard form

  (s -800)(s +600) = 0 . . . . . . . . . . . . . factor

The positive value of s that makes a factor zero is s = 800.

<u>Conclusion</u>

The speed of the faster plane was 800 km/h; of the slower plane, 600 km/h.

_____

<em>Check</em>

The travel time for the faster plane was 3600/800 = 4.5 hours. For the slower plane, 3600/600 = 6 hours, a difference of 1.5 hours.

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