3) The snow is falling and the stores run out of snow shovels. This relationship can best be described as causal.
A causal relationship is a relationship between two events wherein the occurrence of the first events gives rise to the second event. The first event causes the second event to happen.
The falling snow is the first event, had it not happened, it would not have resulted to the second event which is the stores running out of snow shovels.
Answer: 96 cubes could fit
Step-by-step explanation:
4x4x3=48
48x2=96
Answer:
All of the values that can go into a relation or function (input) are called the domain. ... The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.
He already practiced 40%, he needs to do the rest, the remaining 60%.
now, we know that 40% is 12 minutes, what is the 60% anyway?
he needs to practice an extra "x" minutes.
Answer:
Radius of Convergence: 2
Interval of Convergence: [-2, 2]
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Exponential Rule [Multiplying]:
- Exponential Rule [Dividing]:
<u>Calculus</u>
Series Convergence Tests
- P-Series:
- Direct Comparison Test (DCT)
- Alternating Series Test (AST)
- Ratio Test:
Radius of Convergence (ROC)
Interval of Convergence (IOC)
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Find ROC</u>
<em>Apply Ratio Test</em>
- [Series] Set up [Ratio Test]:
- [Ratio Test] Rewrite exponentials [Exponential Rule - Multiplying]:
- [Ratio Test] Simplify:
- [Ratio Test] Multiply:
- [Ratio Test] Evaluate limit:
- [Ratio Test] Isolate <em>x</em>:
<em>Our ROC is 2.</em>
<u>Step 3: Find IOC</u>
<em>Test endpoints</em>
- [ROC] Find interval bound:
<em>x = -2</em>
- Substitute in <em>x</em> [Series]:
- [Series] Rewrite [Exponential Rules - Multiplying]:
- [Series] Simplify:
<em>Test convergence of modified series: Alternating Series Test</em>
- [AST] Condition 1 [Limit Test]:
- [AST] Condition 2 [aₙ vs bₙ comparison]:
<em>At x = -2, the series is convergent.</em>
∴ Current IOC is -2 ≤ x < 2 or [-2, 2); 2 undetermined
<em>x = 2</em>
- Substitute in <em>x</em> [Series]:
- [Series] Simplify:
<em>Test convergence of modified series: Direct Comparison Test</em>
- [DCT] Condition 1 [Define comparing series]:
- [DCT] Condition 1 [Test convergence of comparing series]:
- [DCT] Condition 2 [aₙ vs bₙ comparison]:
<em>At x = 2, the series is convergent. </em>
∴ IOC for is -2 ≤ x ≤ 2 or [-2, 2]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations - Power Series (BC Only)
Book: College Calculus 10e