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4 years ago

1. Label the following as transformations on the independent variable or the

Mathematics

1 answer:

Ad libitum [116K]4 years ago

7 0

Answer:

(A) dependent variable

(B) Dependent variable

(D) independent variable

Step-by-step explanation:

F(x) is equivalent to y, so the first two equations are saying y+3 and y-3

The last two equations are saying y=x+3 and y=x-3

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

What inequality symbol below makes the statement above true? 3.5_3/5

mylen [45]

Answer:

3.5>3/5

Step-by-step explanation:

8 0

3 years ago

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.

Maslowich

Answer: 2

Step-by-step explanation:

By the law of sines,

$\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \frac{\sin B}{14}=\frac{\sin 30^{\circ}}{8} \\ \\ \frac{\sin B}{14}=\frac{1}{16} \\ \\ \sin B=\frac{14}{16} \\ \\ B=\sin^{-1} \left(\frac{14}{16} \right), 180^{\circ}-\sin^{-1} \left(\frac{14}{16} \right) \\ \\ B \approx 61.04^{\circ}, 118.96^{\circ}$

Since either of these values for B will form a triangle (as A+B will be less than 180 degrees), 2 triangles can be formed with these measurements.

5 0

2 years ago

In a bag, there are 6 blue, 1 purple, 3 yellow, and 5 orange marbles. If a single choice is made from the

Dmitry [639]

Answer:

it would be a 3/15 or 1/5 chance

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Question 1) In a random sample of 10 on-line statistics students, information was collected about their minutes studied and thei

AVprozaik [17]

First, arrange the data in a table for easy reference:

x y
20 50
30 45
45 55
60 70
80 80
90 90
45 80
120 100
90 95
70 85

Then, use the calculator to find the relationship of the two variables, x (minutes studied) and y (test scores)

The equation is

y = 0.56686x + 38.15

3 0

3 years ago