I need help on this question please!!!
1 answer:
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Answer:
Step-by-step explanation:
<u>Recursive sequence </u>
In a recursive sequence formula, each term is computed as a function of one or more previous terms. In the formula
n is the number of the term we want to calculate. If n=8, then the formula becomes
We can see is the previous term. It means we need
to be able to compute
. But we also need
to compute
and so on until some known data is reached. The question provides five terms,
Well, it is 
. That is, the equation is 
. The run could be found when y=0, so 
or 
or 
or 
. 375 inches. 30 feet means 360 inches, as far as I remember (in my country only metric systems are being used :) ) so it doesn't really work -- the ramp is just a bit too long.
<h3>Answer:</h3>
Yes. The pattern is predicted by the formula ...
f(x) = -0.465x +11.68 +0.015·mod(x, 2)
<h3>Step-by-step explanation:</h3><em>Initial investigation</em>
The predictions from a line of best fit alternate being too low and too high. That is to say, every other point fits perfectly on a line, and the alternate points fit perfectly on a parallel line.
<em>Line through alternate points</em>
If we use x=1, 2, 3, ... for the number of the member of the sequence, then we have ....
(x, f(x)) = (2, 10.75), (4, 9.82), (6, 8.89)
These points describe a line that can be found using the two-point form of the equation for a line:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
y = (9.82 -10.75)/(4 -2)·(x -2) +10.75 . . . . . using the values from the first two even-numbered points
y = (-0.93/2)·(x -2) +10.75 . . . . . . . . . . simplify a bit
y = -0.465x +11.68 . . . . . . . . . . . . . . . . simplify to slope-intercept form
<em>Correction for other points</em>
We know that this predicts a value too low when x is odd. We can find the amout the prediction is low and add a conditional term to make up the difference.
For x = 1,
y = -0.465·1 +11.68 = 11.215
The actual value is 11.23, or 11.23 -11.215 = 0.015 higher than the equation predicts. We can use the modulo function to give a value that is 1 for odd numbers and 0 for even numbers. For odd values of x, we can add this difference to make the formula predict every number in the sequence.
f(x) = -0.465x +11.68 +0.015·mod(x, 2) . . . . equation for the given points
_____
The table attached shows the given points (y1) and the values predicted using the above formula (f(x1)). (The x1 and y1 used in the attachment are the names of the lists of x-values and y-values. They are not related to the x1 and y1 used above in the 2-point form of the equation for a line.)