Answer:
[2 , ∞)
Step-by-step explanation:
y = sqrt( x-2)
The domain is the values that x can take
Since we have a square root
Domain: [2 , ∞) since the square root must be greater than or equal to zero
The range is the values that y can take
The square root starts at 0 and increases
Range [0,∞)
The inverse swaps the domain and range
Range: [2 , ∞)
Domain [0,∞)
The negative 16 in the second line should be positive 16.
See attached picture:
Answer:
(a) 0.107 million per year
(b) 0.114 million per year
Step-by-step explanation:
(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, 
and in 2014, 
. Mathematically,
(b) The instantaneous rate of change is determined by finding the differential derivative at that year.
The result of differentiating functions of the firm 
(where 
is a constant) is 
. Let's use in this in finding the derivative of 
.
In the year 2014, .
Factor r 4 t 4 out of 5 r 8 t 5 − 3 r 4 t 4 . r 4 t 4 ( 5 r 4 t − 3 )
(a) Yes all six trig functions exist for this point in quadrant III. The only time you'll run into problems is when either x = 0 or y = 0, due to division by zero errors. For instance, if x = 0, then tan(t) = sin(t)/cos(t) will have cos(t) = 0, as x = cos(t). you cannot have zero in the denominator. Since neither coordinate is zero, we don't have such problems.
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(b) The following functions are positive in quadrant III:
tangent, cotangent
The following functions are negative in quadrant III
cosine, sine, secant, cosecant
A short explanation is that x = cos(t) and y = sin(t). The x and y coordinates are negative in quadrant III, so both sine and cosine are negative. Their reciprocal functions secant and cosecant are negative here as well. Combining sine and cosine to get tan = sin/cos, we see that the negatives cancel which is why tangent is positive here. Cotangent is also positive for similar reasons.
