How to simplify 7 1\2

Find the circumference of the circle to the nearest hundredth. Use 3.14 for π. Radius 21 cm.

Ierofanga [76]

Answer:

$131.95$ $cm$

Step-by-step explanation:

$C=2 \pi r$

$C=2 \pi \times 21$

$C=42\pi$

$C \approx 131.946891451$

3 0

3 years ago

Guys pls help me i have to write about angle on an A4 size paper

barxatty [35]

Answer:

90 degrees

Step-by-step explanation:

A corner of a A4 size paper forms the angle of 90°. Every corner of a A4 size paper forms the angle of 90°.

5 0

2 years ago

The third-degree Taylor polynomial about x = 0 of In(1 - x) is

gizmo_the_mogwai [7]

Answer:

$\displaystyle P_3(x) = -x - \frac{x^2}{2} - \frac{x^3}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation

Calculus

Derivatives

Derivative Notation

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

MacLaurin/Taylor Polynomials

Approximating Transcendental and Elementary functions
MacLaurin Polynomial: $\displaystyle P_n(x) = \frac{f(0)}{0!} + \frac{f'(0)}{1!}x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + ... + \frac{f^{(n)}(0)}{n!}x^n$
Taylor Polynomial: $\displaystyle P_n(x) = \frac{f(c)}{0!} + \frac{f'(c)}{1!}(x - c) + \frac{f''(c)}{2!}(x - c)^2 + \frac{f'''(c)}{3!}(x - c)^3 + ... + \frac{f^{(n)}(c)}{n!}(x - c)^n$

Step-by-step explanation:

*Note: I will not be showing the work for derivatives as it is relatively straightforward. If you request for me to show that portion, please leave a comment so I can add it. I will also not show work for elementary calculations.

Step 1: Define

Identify

f(x) = ln(1 - x)

Center: x = 0

n = 3

Step 2: Differentiate

[Function] 1st Derivative: $\displaystyle f'(x) = \frac{1}{x - 1}$
[Function] 2nd Derivative: $\displaystyle f''(x) = \frac{-1}{(x - 1)^2}$
[Function] 3rd Derivative: $\displaystyle f'''(x) = \frac{2}{(x - 1)^3}$

Step 3: Evaluate Functions

Substitute in center x [Function]: $\displaystyle f(0) = ln(1 - 0)$
Simplify: $\displaystyle f(0) = 0$
Substitute in center x [1st Derivative]: $\displaystyle f'(0) = \frac{1}{0 - 1}$
Simplify: $\displaystyle f'(0) = -1$
Substitute in center x [2nd Derivative]: $\displaystyle f''(0) = \frac{-1}{(0 - 1)^2}$
Simplify: $\displaystyle f''(0) = -1$
Substitute in center x [3rd Derivative]: $\displaystyle f'''(0) = \frac{2}{(0 - 1)^3}$
Simplify: $\displaystyle f'''(0) = -2$

Step 4: Write Taylor Polynomial

Substitute in derivative function values [MacLaurin Polynomial]: $\displaystyle P_3(x) = \frac{0}{0!} + \frac{-1}{1!}x + \frac{-1}{2!}x^2 + \frac{-2}{3!}x^3$
Simplify: $\displaystyle P_3(x) = -x - \frac{x^2}{2} - \frac{x^3}{3}$

Topic: AP Calculus BC (Calculus I/II)

Unit: Taylor Polynomials and Approximations

Book: College Calculus 10e

5 0

3 years ago

Use the expression 5.2v - (30 ÷ 6) + 12 to answer 9-10.

s2008m [1.1K]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

5.2v - (30 ÷ 6) + 12

9) We need to determine which part of the expression represents a quotient?

We know that when we divide one rational expression by another, the result would be termed as 'quotient'.

Here, it is clear that:

(30 ÷ 6) represents the expression part for a quotient.

When we divide 30 by 6, we get the result 5 which would be the quotient of the expression 30 ÷ 6.

10. Which part of the expression represents a product of two factors?

We know that when a multiply two number, we get the product. The multiplying numbers are the factors of the product.

For example, 4 × 9 = 36 therefore, 4 and 9 are the factors of 36.

In our case, 5.2v represents a product of two factors 5.2 and v. In other words, 5.2 and v are the factors of the product of 5.2v.

4 0

3 years ago

Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year.

Drupady [299]

Answer:

Range = 13

Variance = 10.22

Standard deviation = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

Step-by-step explanation:

We are given the number of hurricanes that occurred in each year in a certain region.

8 9 8 7 9 15 5 6 8 4 12 7 8 2

Range:

The range of the data set is found by

Range = Maximum value - minimum value

The maximum value in the data set is 15

The minimum value in the data set is 2

Range = 15 - 2

Range = 13

Variance:

To find the variance, first compute the mean of the data set.

Mean = Sum/n

Mean = (8+9+8+7+9+15+5+6+8+4+12+7+8+2)/14

Mean = 108/14

Mean = 7.714

The variance is given by

σ² = (x - mean)²/(n - 1)

σ² = (8 - 7.714)² + (9 - 7.714)²+ (8 - 7.714)² + (7 - 7.714)² + (9 - 7.714)² + (15 - 7.714)² + (5 - 7.714)² + (6 - 7.714)² + (8 - 7.714)² + (4 - 7.714)² + (12 - 7.714)² + (7 - 7.714)² + (8 - 7.714)² + (2 - 7.714)²/(14 - 1)

σ² = 10.22

Standard deviation:

The standard deviation of the data set is given by

σ² = √σ

σ² = √10.22

σ² = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

7 0

3 years ago