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2 years ago

Translate the following statement into a mathematical equation:

Mathematics

1 answer:

steposvetlana [31]2 years ago

8 0

The answer is the first choice, 3(w-4)=5.

3 times = 3
a number minus four = (w-4)
is five = 5

I hope this helps.

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

2 years ago

Here's a graph of a linear function. Write the

Softa [21]

Answer:

y = 3/2x - 3

Step-by-step explanation:

Slope = 3/2

y-intercept = -3

y = mx + b

y = 3/2x - 3

6 0

2 years ago

A subway train travels at a rate of 50 miles per hour. Write and solve an equation to find the number of minutes it take for the

AVprozaik [17]

Answer:

12 minutes

Step-by-step explanation:

<u>50 miles</u> = <u>10 miles</u> << Equivalent

1 hour = x << fraction

You divide 50 by 5 to get 10,

so to get the number of minutes for 10 miles,

divide 60 by 5.

(1 hour = 60 minutes, 60/5 = 12)

7 0

2 years ago

In a clothing store, 65% of the customers buy a shirt, 30% of the customers

diamong [38]

Answer:

75%

Step-by-step explanation:

List out known probabilities

$\Pr(shirt) = 0.65 = \frac{65}{100} = \frac{13}{20}\\ \Pr(pants) = 0.40 = \frac{30}{100} = \frac{6}{20}\\\Pr(shirt \cap pants) = 0.20 = \frac{20}{100}=\frac{1}{5}$

recall equation

$\Pr(A \cup B)=\Pr(A)+\Pr(B)-\Pr(A \cap B)$

Plug in values

$\Pr(shirt \cup pants)=\frac{13}{20}+\frac{6}{20}-\frac{1}{5}\\\\therefore \Pr(shirt \cup pants) = \frac{15}{20} =\frac{3}{4} = 75\%$

4 0

2 years ago

71 cards 5 cards in each box 71 ÷5 with leftover How many boxes are needed for all the cards

Fofino [41]

Answer:

15 boxes

Step-by-step explanation:

Because 71 divided by 5 equals to 14.2, you know that you need at least 14 boxes. However, you cannot have 14.2 boxes, because that implies that you have a fifth of a box, which cannot happen. But because each box can only hold up to 5 cards max, you need to get a 15th box for the last card.

7 0

2 years ago

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