Question 1
Answer
0.46 : rational(/ ); irrational(x);
Solving Steps
Question 2
Answer
1100 : rational(/): irrational(x);
Solving Steps
Categorize the number :
Question 3
Answer
-16 : rational(V); irrational(x);
Solving Steps
Categorize the number:
-16 : rational(/); irrational(x);
Question 4
Answer
V21: rational (×); irrational(r);
Solving Steps
Categorize the number
V21 : rational(×): irrational():
Select the second and fourth options.
Answer:
explain further or send a picture of what you mean and then I can help you
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
Answer:
40
Step-by-step explanation:
(2x+1/(2x))^5 *(2x -1/(2x))^5
= ((2x)^2 -1/(2x)^2)^5 (a+b)*(a-b) =a2-b2
= (4x^2-1/4(x)^2)^5
now
x =4x^2. ,a = 1/4(x)^2 ,n =5
we have
general term = Cr *x^r *a^(n-r)
= Cr * (4x^2)^r * (1/4(x)^2)^(n-r)
= Cr *4^r * X^2r * 1/( 4^(n-r) *x^(2n-2r)
= Cr * 4^r/4^(n-r) * x^(2r)/x^(2n-2r)
= Cr * 4(2r-n) *x(4r-2n)
now for x^2
4r-2n = 2
4r -10=2
4r =12
r = 3
now for coeff
C(5,3) * 4^(2*3-5)
5!/(3!*(5-3)!) * 4
5*4/(2*1)*4
40