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Sholpan [36]
4 years ago
13

A roller coaster starts from a deck at an elevation of 20 feet above the ground. On the first hill it climbs 83 feet and then dr

ops 42 feet. On the second hill the coaster climbs 128 feet and then drops 90 feet. How far above the ground is the coaster after the second hill?
please help me
Mathematics
1 answer:
Fantom [35]4 years ago
5 0
Initially started 20 feet from the ground .
Went uphill 83 feet.
So: 20 + 83 = 103. The coaster is 103 ft above at this point.

Went down 42 feet
So: 103 - 42 = 61.

Went up 128 feet
So: 61 + 128 = 189

Finally, went down 90 feet
So: 189 - 90 = 99

99 ft above ground.
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\large\boxed{-\dfrac{8}{\sqrt{63}}}

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\csc\theta=\dfrac{1}{\sin\theta}\\\\\cos\theta=-\dfrac{1}{8}\qquad\text{use}\ \sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta+\left(-\dfrac{1}{8}\right)^2=1\\\\\sin^2\theta+\dfrac{1}{64}=1\qquad\text{subtract}\ \dfrac{1}{64}\ \text{from both sides}\\\\\sin^2\theta=\dfrac{64}{64}-\dfrac{1}{64}\\\\\sin^2\theta=\dfrac{63}{64}\to\sin\theta=\pm\sqrt{\dfrac{63}{64}}\\\\180^o

\csc\theta=\dfrac{1}{-\frac{\sqrt{63}}{8}}=-\dfrac{8}{\sqrt{63}}

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