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Leya [2.2K]
3 years ago
8

Find the constant of proportionality for the table of values.

Mathematics
1 answer:
Citrus2011 [14]3 years ago
7 0

Answer:

k = 1.5

Step-by-step explanation:

Pairs: (2, 3), (3, 4.5), (4, 6), (5, 7.5)

If there is a proportionality between two numbers or, as in this case, two variables, then:

y = kx

Where:

k = proportionality constant

The constant can therefore be found by rearranging:

k = y/x

Now, simply substitute any given pair of x- and y- values;

I will use (2, 3) as these are the smallest numbers so easier to use but any of the pairs can be used:

k = 3/2

k = 1.5

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8 0
3 years ago
A1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16. a1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16.
ICE Princess25 [194]
a_1=12-12=(1\times12-0)-(12+0)
a_2=23-13=(2\times12-1)-(12+1)
a_3=34-14=(3\times12-2)-(12+2)
a_4=45-15=(4\times12-3)-(12+3)
a_5=56-16=(5\times12-4)-(12+4)

Clearly, the general for the n-th term is

a_n=(12n-(n-1))-(12+n-1)=10n-10

(Aside: given the simple pattern, it's curious why the terms would be given the way they are. It's easier to divine 10n-10 from a_1=0,a_2=10,a_3=20,\ldots, but that's just my opinion.)

The sequence does not converge. As n\to\infty, so does a_n\to\infty.
8 0
3 years ago
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