Solve for x. 4x - 36 3x + 10
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Answer:
.
Step-by-step explanation:
From Mathematics we remember that the domain of a functions corresponds to the set of values of the independent variable ( in this case) so that images exist and the range of a function is the set of images.
In this case, we know the domain and range of and we must find the domain and range of
.
Domain
The domain of is the domain of
. That is,
.
Range
We have to define the bounds of the range of , given that range
is modified by streching and horizontal translation operations:
Lower bound ()
Upper bound ()
In consequence, the range of is
We can find the height of the altitude by the ratio of sin. See my attachment.
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance
If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.
Find the height of first pilot
height/distance = sin x
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200
Find the height of second pilot
height/distance = sin x
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192
So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance
If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.
Find the height of first pilot
height/distance = sin x
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200
Find the height of second pilot
height/distance = sin x
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192
So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°