Step-by-step explanation:
Volume of figure=length×width×height
=(1/2)×(1/2)×6
=0.5×3
=1.5m³
PLEASE GIVE BRAINLIEST
Given parameters:
Total length of curtains bought = 20m
She used 8m for the living room
She used 7m for the dining room
unknown:
Quantity used for the kitchen = ?
Solution:
Quantity used for the kitchen = Total length - (living room + dining room)
Input the parameters given solve;
Quantity used for the kitchen = 20 - (8 + 7) = 5m
The length of curtain used for the kitchen is 5m
Answer:
a) lower limit = 4.295 minutes
b) upper limit = 6.365 minutes
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 5.33 minutes
Standard deviation r = 1.33 minutes
Number of samples n = 11
Confidence interval = 99%
z(at 99% confidence) = 2.58
Substituting the values we have;
5.33+/-2.58(1.33/√11)
5.33+/-2.58(0.401010088288)
5.33+/-1.0346060277
5.33+/-1.035
= ( 4.295, 6.365) minutes
Therefore at 99% confidence interval (lower, upper limit) = ( 4.295, 6.365) minutes
a) lower limit = 4.295 minutes
b) upper limit = 6.365 minutes
Answer:
<u>$4,680</u>
Step-by-step explanation:
<u>Rate</u> : 10 dollars a week
- Per year : 10 x 52 = $520
- 9 x 520 = $4,680
You will have saved up <u>$4,680</u> in 9 years.
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
<u>Calculus</u>
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)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
MacLaurin/Taylor Polynomials
- Approximating Transcendental and Elementary functions
- MacLaurin Polynomial:

- Taylor Polynomial:

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.
<u />
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = ln(1 - x)
Center: x = 0
<em>n</em> = 3
<u>Step 2: Differentiate</u>
- [Function] 1st Derivative:

- [Function] 2nd Derivative:

- [Function] 3rd Derivative:

<u>Step 3: Evaluate Functions</u>
- Substitute in center <em>x</em> [Function]:

- Simplify:

- Substitute in center <em>x</em> [1st Derivative]:

- Simplify:

- Substitute in center <em>x</em> [2nd Derivative]:

- Simplify:

- Substitute in center <em>x</em> [3rd Derivative]:

- Simplify:

<u>Step 4: Write Taylor Polynomial</u>
- Substitute in derivative function values [MacLaurin Polynomial]:

- Simplify:

Topic: AP Calculus BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations
Book: College Calculus 10e