ACDE is reflected over the y-axis.

A baker has 10 cups of sugar to make cookies. Each batch calls for 113 cups of sugar. How many batches of cookies can he make? E

Lilit [14]

So I guess this would look like this originally 113/10, then as a mixed number 11 3/10

8 0

3 years ago

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The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a r

olga55 [171]

Dividing the volume by the base area, you find the height to be ...
$\frac{x^{4}+4x^{3}+3x^{2}+8x+4}{x^{3}+3x^{2}+8}=x+1-\frac{4}{x^{3}+3x^{2}+8}$

The height of the prism is $x+1-\frac{4}{x^{3}+3x^{2}+8}$

3 0

3 years ago

Read 2 more answers

2. Each of the following lines has a slope that can be determined by examining the graph. Use another point

Natali [406]

The slope, y-intercept and the equation of the following graph are as follows:

1(a)

slope : 1

y-intercept: 2

Equation: y = x + 2

(b)

slope : - 1 / 3

y-intercept: - 1

Equation: y = - 1 / 3x - 1

2.

(a)

slope : 3 / 4

y-intercept: 5 / 4

Equation: y = 3 / 4 x + 5 / 4

(b)

slope : - 3 / 2

y-intercept: 1 / 2

Equation: y = - 3 / 2 x + 1 / 2

<h3 />

<h3>Slope intercept equation</h3>

y = mx + b

where

m = slope

b = y-intercept

Therefore lets find the slope, y-intercept and equation of the following graph.

1.

(a)

(0, 2)(1, 3)

m = 3 - 2 / 1 - 0 = 1

b = 2

y = x + 2

(b)

(0, -1)(-3, 0)

m = 0 + 1 / -3 - 0 = - 1 / 3

b = -1

y = - 1 / 3x - 1

2.

(a)

(1, 2)(-3, -1)

m = -1 - 2 / -3 - 1 = 3 / 4

2 = 3 / 4 (1) + b

b = 2 - 3 / 4 = 5 / 4

y = 3 / 4 x + 5 / 4

3.

(b)

(-3, 5)(1, -1)

m = - 1 - 5 / 1 + 3 = - 6 / 4 = - 3 / 2

-1 = - 3 /2 (1) + b

b = -1 + 3 / 2 = 1 /2

y = - 3 / 2 x + 1 / 2

learn more on y-intercept here: brainly.com/question/2833377?referrer=searchResults

6 0

3 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

2 units/ 3 units if you triple the recipe would the rate change

Sergeeva-Olga [200]

No if you tripled the recipe the rate wouldn't change. The only difference would be that you're values would be tripled.

7 0

3 years ago