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Serjik [45]
4 years ago
10

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

(C) independent 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
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