The volume of a cylinder is calculated from the product of its base area and the height. The base area is equal to the area of a circle which is expressed as A = πr^2 where r is one half the diameter and the radius of the circular base. So, the volume of a cylinder is equal to:
Volume of cylinder = π(r^2)h
r = D/2 = 3.5 in / 2 = 1.75 in
h = 12 in
Volume of cylinder = π((1.75 in)^2)( 12 in )
Volume of cylinder = 147π/4 in^3 or 115.45353 in^3
Therefore, the volume of the cylinder given its specifications would be equal to 115.45 cubic inches.
Answer:
Point N(4, 1)
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>
</u>
<u>Algebra I</u>
- Coordinates (x, y)
- Functions
- Function Notation
- Terms/Coefficients
- Anything to the 0th power is 1
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u /><u />
<u />
<u>Step 2: Differentiate</u>
- [Function] Rewrite [Exponential Rule - Root Rewrite]:
- Chain Rule:
- Basic Power Rule:
- Simplify:
- Multiply:
- [Derivative] Rewrite [Exponential Rule - Rewrite]:
- [Derivative] Rewrite [Exponential Rule - Root Rewrite]:
<u>Step 3: Solve</u>
<em>Find coordinates</em>
<em />
<em>x-coordinate</em>
- Substitute in <em>y'</em> [Derivative]:
- [Multiplication Property of Equality] Multiply 2 on both sides:
- [Multiplication Property of Equality] Multiply √(x - 3) on both sides:
- [Equality Property] Square both sides:
- [Addition Property of Equality] Add 3 on both sides:
<em>y-coordinate</em>
- Substitute in <em>x</em> [Function]:
- [√Radical] Subtract:
- [√Radical] Evaluate:
∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
This is the formula for percentage increase and decrease
If you are going by looks the number line is just a horizontal line that usually had little dashes on it that show where the number is. A coordinate plane has two lines. One line goes up and down and another goes left and right. points can be places anywhere on or not on the lines of a coordinate plane
Answer:
160
Step-by-step explanation:
Using Exterior angle theorem
30+130=160