For f(x)=3x+1 and g(x)= x2-6, find (f/g)(x)

Mathematics

1 answer:

Sliva [168]3 years ago

3 0

Answer:

(3x+1)/(x^2-6)

Step-by-step explanation:

f/g(x)=f(x)/g(x)=(3x+1)/(x^2-6)

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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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3 years ago

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Write parametric equations of the line 2x-y=3

dangina [55]

In this item we are given with the equation, 2x - y = 3. The equation contains two variables, x and y. We assume in this item that the value of x is independent of the value of y; however, y values depends on the given values of x. In parametric form, the equation would take the form,

f(x) = y = ax + b

where a is the numerical coefficient of x and b is constant. Transforming the given equation to this form,

f(x) = y = 2x - 3

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3 years ago

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Suppose that a normal distribution has a mean of 20 and a standard deviation of 4. What is the z-score of 13?

Papessa [141]

Answer:

-1.75.

Step-by-step explanation:

The z-score = (n - m) / d where n is the value (13) m = mean and d = standard deviation.

= (13 - 20) / 4

= -1.75 (answer)

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