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3 years ago

7

what is the volume, in cubic centimeters, of a cylinder with a height of 12 cm and a base radius of 6 cm, to the nearest tenths

place?

1 answer:

mars1129 [50]3 years ago

6 0

Answer:

Step-by-step explanation:

V = πr²h = π·6²·12 = 432π ≅ 1,357.2 cm³

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You have a 25 cm piece of ribbon. How many cuts do you need to make obtain the greatest number of pieces, where each piece is di

max2010maxim [7]

Answer:

24

Step-by-step explanation

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7 0

3 years ago

Read 2 more answers

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

3 years ago

What is the value of ''a'' in the following equation:

marshall27 [118]

The value of "a" is 10.1

5 0

3 years ago

Can anyone solve the last question?

sesenic [268]

As stated in (i), the equation of the line is: ln y = -0.015x + .26
(By the way, I checked your answers for parts (i) and (ii) and they are both correct)

(iii)
Plug in (1.1) for y and solve:
ln (1.1) = -0.015x + .26
0.095 = -0.015x + .26
-0.165 = - 0.015x
10.979 = x

Answer: x = 10.979

7 0

3 years ago

A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the

Ne4ueva [31]

The number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040

<h3>What is the rule of product in combinatorics?</h3>

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in $p \times q$ ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

We're specified that:

The password needs to be 4 characters long
It must have 3 letters and 1 of 10 special characters.
Repetition is allowed.

So, each of 3 characters get 26 ways of being 1 letter. (assuming no difference is there between upper case letter and lower case letter).

And that 1 remaining character get 10 ways of being a special character.

So, by product rule, this choice (without ordering) can be done in:

$26 \times 26 \times 26 \times 10 = 175760$ ways.

Now, the password may look like one of those:

L, L, L, S
L, L, S, L
L, S, L, L
S, L, L, L

where S shows presence of special character and L shows presence of letter.

Those 175760 ways are available for each of those four ways.

Thus, resultant number of ways this can be done is:

$175760 \times 4 = 703040$

Thus, the number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040

Learn more about rule of product here:

brainly.com/question/2763785

5 0

2 years ago