What is rule for (0,0), (1,4), (2,16), (3,36), (4, 64)

2 answers:

8 0

Here the set of input values is {0, 1, 2, 3, 4} and the set of output values is {0, 4, 16, 36, 64).

Because of the rapid growth in the set of output values (0 to 4, 4 to 16, 16 to 36, 36 to 64), we suspect that exponential growth is illustrated here.

Let's start with the basic equation for exponential growth: f(x) = ar^(n-1), where a is the value of the first term, n is the subscript of the term in question (e.g., n = 2 would indicate the second term), r is the common factor (if there is one).

The first y-value is 0; the second is 4, and the third is 16. Is 4 a common ratio here? Multiplying the first y value (0) by 4 results in 0. Is that the same as the second given y-value (4)? No. So 4 is not a common ratio, even though 4 times 4 = 16 (the third y-value).

If you are in an advanced algebra class, one approach to try next would be to "fit" the given points to a 2nd, 3rd, 4th or 5th order polynomial. For example, we could begin with given point (1,4) and attempt a 2nd order (quadratic) fit to (1,4) as a first step towards finding the "rule" in question.

The general form of a quadratic function is y=ax^2+bx+c. What happens if we let x=1 and y=4, to fit (1,4)? y = 4 = a(1)^2 + b(1) + c, which has 3 unknown coefficients. You must repeat this process until you have three equations in three unknowns {a, b, c}, and then you must solve for a, b and c. If you do this properly, you'll end up with a quadratic formula for the "rule" in question.

I'd suggest you double-check to ensure that you have copied the five given data points properly.

Lelu [443]3 years ago

5 0

x=+1

y=it adds 4,next is 8,so 4+8=12,and 12 is what you add next,after 12 is 16,12+16 is 28,so they add 28,and that gets you 64

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baherus [9]

11)

keeping in mind that, there are 3 feet in 1 yard, therefore, in 4 yards there are 4(3) feet or 12 feet.

now, 12 feet is twice as much as 6 feet. If the original grid, had each unit length to be 6 feet, that means each square was a 6x6 square. That means the new adjusted grid, will be twice as many feet per each unit, namely a 12 : 1. Check the first picture below.

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check the second picture below, that's the 30-60-90 rule.

now, if one angle in the triangle is 30°, and another is 60°, the last one must be a 90° angle, so the triangle is a 30-60-90 triangle, and thus the 30-60-90 rule applies, with the ratios as you see in the picture.

so, if any of the sides has a value of 6, that will be a constraint to the other sides, since the other sides must be at a ratio of 6.

because of those ratios constraints, you can only make one unique triangle, if one side is 6, the others cannot fluctuate in length, they must be at a ratio of 6.