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myrzilka [38]
3 years ago
7

Two trains leave stations 324 miles apart at the same time and travel toward each other. one train travels at 95 mph while the o

ther travels at 85 mph how long will it take for the two trains to meet
Mathematics
1 answer:
Lapatulllka [165]3 years ago
7 0
324/(95+85)=1.8 It will take 1 hour and 48 minutes
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Cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.
umka21 [38]

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

  tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

  tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

  tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

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* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

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Answer: here are a few ordered pairs

1. (0,-4)

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7 0
3 years ago
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Hope this helps! :)

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5 0
3 years ago
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castortr0y [4]

Answer:

3.14635164e91

Step-by-step explanation:

3 0
3 years ago
Please solve and graph each inequality x-7<-12
Keith_Richards [23]

For this case we must resolve the following inequality:

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x

Different signs are subtracted and the major sign is placed.

x

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The solution set is: (-∞, - 5)

Answer:

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