Answer:
112.5 deg
Step-by-step explanation:
First we find the area of the entire circle.
A = pi * r^2
A = pi * (4 m)^2
A = 16pi m^2
The entire circle has area = 16pi m^2.
The sector has area 5pi m^2.
Now we find the fraction the area of the sector is of the entire circle.
fraction = (5pi m^2)/(16pi m^2) = 5/16 = 0.3125
The full circle has a central angle of 360 deg, the entire circle.
The measure of the central angle of the arc of the sector is the same fraction of the entire circle.
measure of sector angle = 0.3125 * 360 deg = 112.5 deg
Answer:
x^2+x+1
Step-by-step explanation:
(3x^2+4x−1)+(−2x^2−3x+2)
Combine like terms
3x^2-2x^2+4x-3x-1+2
x^2+x+1
Answer:
Width = 2x²
Length = 7x² + 3
Step-by-step explanation:
∵ The area of a rectangle is 
∵ Its width is the greatest common monomial factor of
and 6x²
- Let us find the greatest common factor of 14 , 6 and
, x²
∵ The factors of 14 are 1, 2, 7, 14
∵ The factors of 6 are 1, 2, 3, 6
∵ The common factors of 14 and 6 are 1, 2
∵ The greatest one is 2
∴ The greatest common factor of 14 and 6 is 2
- The greatest common factor of monomials is the variable with
the smallest power
∴ The greatest common factor of
and x² is x²
∴ The greatest common monomial factor of
and 6x² is 2x²
∴ The width of the rectangle is 2x²
To find the length divide the area by the width
∵ The area = 
∵ The width = 2x²
∴ The length = (
) ÷ (2x²)
∵
÷ 2x² = 7x²
∵ 6x² ÷ 2x² = 3
∴ (
) ÷ (2x²) = 7x² + 3
∴ The length of the rectangle is 7x² + 3
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]: ![\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)
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:
![\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%28x%20-%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%20-%203%5D)
- 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
The area of the classroom is 768 square feet