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2 years ago

A sphere has a radius of 2 inches. What is the approximate volume of half of the sphere?

Mathematics

1 answer:

Schach [20]2 years ago

4 0

Answer:

1 inch

Step-by-step explanation:

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James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They deposited $500 into the a

zhuklara [117]

Answer:

$275

Step-by-step explanation:

This is what I got:

You first convert 2.75% into 0.0275

You then multiply 500 x 0.0275 = 13.75

Finally you multiply 13.75 x 20 = 275

so the answer should be 275

5 0

4 years ago

What is a equivalent expression for 4(x-2)

sweet-ann [11.9K]

Ig HD kbcoudy kvyshgsy bc b hygyxfj

3 0

3 years ago

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

2x(X-5)+6=24 X=numar necunoscut

finlep [7]

Answer:

2x² + 6 = 34x

Step-by-step explanation:

2x² - 10x + 6 = 24x

Collect like terms

2x² + 6 = 24x + 10x

2x² + 6 = 34x

5 0

4 years ago

Please help me find the nth term of this sequence 0, 3, 8, 15, 24

Setler [38]

Answer:

Step-by-step explanation:

0, 3, 8, 15, 24, 35, 48, 63, 80 which is the nth term

first step you have to find how many steps the sequence was going with.

examples= from 0 to 3 the steps were 3

=from 3 to 8 the steps were 5

= from 8 to 15 the steps were 7

you will recognize that the steps the sequence is going with is odd numbers.

so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.

7 0

3 years ago

Read 2 more answers