Answer:
2π/7
Step-by-step explanation:
A cosine wave is:
y = A cos(2π/T x + B) + C
where A is the amplitude,
T is the period,
B is the horizontal shift,
and C is the vertical shift.
In this case:
7 = 2π/T
T = 2π/7
Answer:
The answer is c = 2 + 3d .
Step-by-step explanation:
It is given that a cab ride cost $2 which is a fixed amount and charges additional $3 per mile. So you have to make an equation of c in terms of d :
Let c be the cost,
Let d be the distance,
c = 2 + 3d
9514 1404 393
Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
_____
<em>Additional comments</em>
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
__
At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
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: ![\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Quotient Rule: ![\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
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:
