Answer:
28
Step-by-step explanation:
32 - 9 = 23,
24 + 4 = 28
We know that the x-ordinate of the vertex is x = 4, because the x-ordinate of the vertex will not change.
Now, the definition of a parabola in locus terms is that for any fixed point that lies on the parabolic shape, it is equidistant from the directrix to the fixed point and the focus to the fixed point.
Thus, we can deduce that:
PS = PD, where P(x, y) is a moving point that lies on the parabola.
Now, we know that the latus rectum will be -4a, because the directrix is higher than the y-ordinate of the focus. Thus, we can say that the vertex will be the midpoint of the two points y = 7 and y = 8, because that is the only place where the definition of a parabola works.
Hence, we can say that the vertex lies at (4, 7.5).
Thus, our general form becomes:
(x - 4)² = 4a(y - 7.5)
To find a, we can say: 7 = 7.5 + a and 8 = 7.5 - a
a = -0.5, because a is the factor in which we move to find the directrix and focus.
Thus, our equation becomes: (x - 4)² = -2(y - 7.5)
1:10 or 100:1000 so the point is to just add one zero to each side and you'll get it right
Answer with Step-by-step explanation:
A continuous function is a function that is defined for all the values in it's domain without any sudden jumps in the values in the domain of the function. All the given situations are analysed below:
1) The temperature at la location as a function of time is continuous function since at any location the temperature is defined for all the time and the temperature cannot suddenly change from say 10 degrees Celsius to 100 degrees Celsius instantly without passing through intermediate values.
2) The temperature at a specific time as a function of the distance due west from New York city is a continuous function as temperature is defined for all the instants of time without any sudden changes as we move between places.
3) The altitude as an function of distance due west from New York is a discontinuous function as there may be sudden changes in the altitude due to changes in topography such as presence of cliff or valley.
4) The cost as a function of function of distance traveled is a discontinuous function since the cost of travel increases integrally in increments of distance and not in a continuous manner.
5) The current in a circuit as function of time is discontinuous function as the current jumps instantly from 0 to a non zero value when we switch on the circuit and same is true when we switch off the circuit it's value decreases instantly to 0.
Answer:
Range - {-4,0,12,20}
Step-by-step explanation:
Given that,
The function is :
g(x) = 4x –12
The domain of the function is {2, 3, 6, 8}.
g(2) = 4(2) –12 = -4
g(3) = 4(3) –12 = 0
g(6) = 4(6) –12 = 12
g(8) = 4(8) –12 = 20
Hence, the range of the function is {-4,0,12,20}.
