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vovangra [49]
3 years ago
12

Two cyclists start at the same point and travel in opposite directions. one cyclist travels 10 /mi h slower than the other. if t

he two cyclists are 96mi apart after 4 hours, what is the rate of each cyclist?
Mathematics
1 answer:
Tcecarenko [31]3 years ago
3 0
We write the cinematic equation for each cyclist.
 We have then:
 Cyclist A:
 ra = v * t
 Cyclist B:
 
rb = - (v-10) * t
 After 4 hours we have:
 ra-rb = 4v - (-4 (v-10))
 96 = 4v - (-4 (v-10))
 Rewriting:
 96 = 4v + 4 (v-10)
 96 = 4v + 4v - 40
 96 = 8v - 40
 v = (96 + 40) / (8)
 v = 17 mph
 Cyclist A: v = 17mph
 Cyclist B: v-10 = 17-10 = 7mhp
 Answer:
 
the rate of each cyclist is:
 
Cyclist A: v = 17mph
 
Cyclist B: v-10 = 7mhp
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Step-by-step explanation:

By arc sum Postulate of a circle:

2 x + 3x + 4x = 360°

9x = 360°

x = 360°/9

x = 40°

3x = 3* 40° = 120°

By inscribed angle theorem:

m\angle 1= \frac {1}{2} \times 3x\\\\\therefore m\angle 1= \frac {1}{2} \times 120°\\\\\huge \red {\boxed {\therefore m\angle 1= 60°}}

By tangent secant theorem:

m\angle 2 = \frac {1}{2} \times 3x\\\\\therefore m\angle 2 = \frac {1}{2} \times 120°\\\\\huge \purple {\boxed {\therefore m\angle 2 = 60°}}

Since, measure of central angle is equal to the measure of its corresponding minor arc.

m\angle 3 = 3x\\\\\huge \pink {\boxed {\therefore m\angle 3 = 120°}}

By angle sum Postulate of a triangle:

m\angle 3 + 2 m\angle 4 = 180°\\\\120° + 2 m\angle 4 = 180° \\\\2 m\angle 4 = 180°- 120° \\\\2 m\angle 4 = 60° \\\\m\angle 4 = \frac {60°}{2} \\\\\huge \orange {\boxed {m\angle 4 =30°}}

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Answer:

Im confused is this a question

Step-by-step explanation:

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