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<h3>Answer: The average rate of change for both is -2</h3>
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Explanation:
The x interval [0,3] is the same as writing
It starts at x = 0 and ends at x = 3.
The graph shows that x = 0 leads to y = 3. So we have the point (0,3) on the parabola. We also have the point (3,-3) on the parabola.
Let's find the slope of the line through these endpoints.
The slope is -2. This is the average rate of change from x = 0 to x = 3.
This is because:
slope = rise/run = (change in y)/(change in x) = average rate of change.
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Now let's find the slope for the table.
Focus on the rows for x = 0 and x = 3. They lead to f(x) = 10 and f(x) = 4 respectively.
We have (0,10) and (3,4) as our two points this time.
We get the same slope as before, so we have the same rate of change.
Notice the change in y (-6) is the same as before. So we could pick any two y values we want as long as there's a gap of 6 between them, and the second y value is smaller than the first.
Answer:
6.708
Step-by-step explanation:
- Y varies directly as the square of x (Given)
......(1)
- Y varies inversely as the square root of z (Given)
......(2)
- Combining (1) & (2), we find:
(Where k is constant of proportionality).....(3)
- Now, when y = 2, x = 3 and z = 4, we find the value of k i.e. constant.
- Plugging the value of k in (3), we find:
....(4)
- Next, in equation (4), plug y = 5, x = n and z = 16 and obtain the value of n by solving it.