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3 years ago

Compare the table and equation.

Mathematics

2 answers:

vfiekz [6]3 years ago

4 0

Answer:

The equation has the greatest slope

Step-by-step explanation:

General equation of a line is expressed as y = mx+c where:

m is the slope

c is the intercept

Slope or gradient of a line is expressed as

m = ∆y/∆x = y2-y1/x2-x1

According to the table, we can take any two value of y and its x equivalent to get the slope.

Using when x1 = 1, y1 = 3, and when x2 = 2, y2 = 6

Slope of the table m = 6-3/2-1

m = 3/1

m = 3

For the equation:

y = 4x

Comparing this to general equation of a line y = mx+c

m = 4

Comparing both value or the slope, it can be seen that the equation has the greatest slope which is 4

iren2701 [21]3 years ago

3 0

The slope formula is y2 - y1/x2 - x1.

First plug in x = 1, x = 2, and x = 3 in to the equation y = 4x to find the first 3 points(Like the first three are shown for the table.) which are (1, 4), (2, 8), and (3, 12).
The slope of the table would be 9 - 3/3 - 1, after subtracting you get 6/2. You would then divide 6 by 2, which gives you 3. 3 is the slope of the table.

The slope of the equation goes through the same process. 12 - 4/3 - 1, after subtracting it's 8/2, and after dividing you get 4. The slope of the equation is 4.

This means the equation has the greater slope.

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Find the generating function for the sequence 1,-2,4,-8, 16, ...

kirill [66]

Answer:

$a(x)=\dfrac{1}{1+2x}$

Step-by-step explanation:

The generating function a(x) produces a power series ...

$a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots$

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

$a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}$

This can be rearranged to ...

$a_n+2a_{n-1}=0$

We can formulate this in terms of a(x) as follows, then solve for a(x).

$\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}$

The generating function is ...

a(x) = 1/(1+2x)

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