Which statement best describes f(x) = -2 square root x-7 +1?
2 answers:
Answer:
-6 is not domain of f(x) but is in range of f(x)
B is correct.
Step-by-step explanation:
Given:
Domain is input value of x where function is well defined.
Range is output value of f(x) for defined value of x.
Here, we have square function. As we know the value inside the square must be positive.
Therefore, x-7≥0
x≥7
Domain: x≥7 or [7,∞)
For range, we will put x=7 into function.
The maximum value of f(x) is 1.
Range: f(x)<1 or (-∞,1)
-6 is not belongs to domain.
-6 is belongs to range.
Hence, -6 is not domain of f(x) but is in range of f(x)
You might be interested in
We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.
The distance of a point to a line is the length of the perpendicular from the line to the point.
So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:
4x + 5y = 4(-1)+5(3) = 11
Those lines meet at the foot of the perpendicular, which is what we're after.
4x + 5y = 11
5 x - 4y = 10
We eliminate y by multiplying the first by four, the second by five and adding.
16x + 20y = 44
25x - 20y = 50
41x = 94
x = 94/41
y = (11 - 4x)/5 = 15/41
We want the distance from (-1,3) to (94/41,15/41)
Answer:
Light is moving at the speed = 77.78 km/min
Step-by-step explanation:
Given:
Distance between island and point P = 5 km
Moving along the the shoreline when it is 1 km from P.
So, x = 1
From the above statement light makes seven revolutions per minute.
Therefore,
Solution:
From the given figure.
Substitute x = 1
-------------------(1)
Now, first we differentiate both side with respect to t.
Using chain rule.
Substitute from equation 1.
Substitute
Applying cross multiplication rule.
Therefore, light is moving along the shore at the speed of 77.78 km/min
