Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Calculus</u>
Implicit Differentiation
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule:
Chain Rule:
Quotient Rule:
Step-by-step explanation:
<u>Step 1: Define</u>
-y - 2x³ = y²
Rate of change of tangent line at point (-1, -2)
<u>Step 2: Differentiate Pt. 1</u>
<em>Find 1st Derivative</em>
- Implicit Differentiation [Basic Power Rule]:
- [Algebra] Isolate <em>y'</em> terms:
- [Algebra] Factor <em>y'</em>:
- [Algebra] Isolate <em>y'</em>:
- [Algebra] Rewrite:
<u>Step 3: Differentiate Pt. 2</u>
<em>Find 2nd Derivative</em>
- Differentiate [Quotient Rule/Basic Power Rule]:
- [Derivative] Simplify:
- [Derivative] Back-Substitute <em>y'</em>:
- [Derivative] Simplify:
<u>Step 4: Find Slope at Given Point</u>
- [Algebra] Substitute in <em>x</em> and <em>y</em>:
- [Pre-Algebra] Exponents:
- [Pre-Algebra] Multiply:
- [Pre-Algebra] Add:
- [Pre-Algebra] Exponents:
- [Pre-Algebra] Divide:
- [Pre-Algebra] Add:
- [Pre-Algebra] Simplify:
Measure 2 sides, then multiply them, and divide by 2.
<h2><u>Solution</u> :-</h2>
Height of Eric = 6 + 1/6 feet
= 37/6 feet
Height of his brother = 5 + 3/4 feet
= 23/4 feet
Difference between their height :
= 37/6 - 23/4
= (74 - 69)/12
= 5/12
<u>Hence</u>,
Eric is 5/12 feet taller than his brother.
Ok so basically it will be 4 x 3 = 12 which leaves $24 ok then you divide 24 by 2 and you get 12 so the amount of brushes that can be purchased is 12.