If I'm not wrong, it should be 27cm^3. Hope this helps!!
9514 1404 393
Answer:
Step-by-step explanation:
The bottom dot and the top dot are on a line with two other dots, the one at (0, 1) and the one at (1, 4). That line has a rise/run = 3/1. The point (0, 1) is its y-intercept, so its equation can be ...
y = 3x +1
The left dot and the lower right dot are on a line with three other dots. One of those (1, 4) is shared with the previous line. This line has a rise/run = 1/1. The point (0, 3) is its y-intercept, so its equation can be ...
y = x + 3
These two equations capture all of the coins.
Answer:
Correct answer: q = 4
Step-by-step explanation:
Given:
3, 12, 48, 192, .....
First term b₁ = 3
Second term b₂ = 12
Third term b₃ = 48
Fourth term b₄ = 192
Common ratio or quotient is:
q = b₂ / b₁ = b₃ / b₂ = 12 / 3 = 48 / 12 = 4
q = 4
God is with you!!!
Answer:
(3,2)
Step-by-step explanation:
Y=-2x+8 equation 1
y=x-1 equation 2
x-1=-2x+8 substi y of second equation into y of first equation.
3x=9
x=3
solve for y by putting the x value into either equation
y=x-1
y=3-1
y=2
Answer:
![\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B3cos%282x%29%20-2%283x%20%2B%201%29%5Bsin%282x%29%20%2B%20cos%282x%29%5D%7D%7Be%5E%7B2x%7D%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Factoring
- Exponential Rule [Dividing]:

- Exponential Rule [Powering]:

<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule: ![\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%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)
Quotient Rule: ![\displaystyle \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=%5Cdisplaystyle%20%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)
Trig Derivative: ![\displaystyle \frac{d}{dx}[cos(u)] = -u'sin(u)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%28u%29%5D%20%3D%20-u%27sin%28u%29)
eˣ Derivative: ![\displaystyle \frac{d}{dx}[e^u] = u'e^u](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Eu%5D%20%3D%20u%27e%5Eu)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Differentiate</u>
- [Derivative] Quotient Rule:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - \frac{d}{dx}[e^{2x}](3x + 1)cos(2x)}{(e^{2x})^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%283x%20%2B%201%29cos%282x%29%7D%7B%28e%5E%7B2x%7D%29%5E2%7D)
- [Derivative] [Fraction - Numerator] eˣ derivative:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{(e^{2x})^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7B%28e%5E%7B2x%7D%29%5E2%7D)
- [Derivative] [Fraction - Denominator] Exponential Rule - Powering:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] Product Rule:
![\displaystyle y' = \frac{[\frac{d}{dx}[3x + 1]cos(2x) + \frac{d}{dx}[cos(2x)](3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Cfrac%7Bd%7D%7Bdx%7D%5B3x%20%2B%201%5Dcos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] Basic Power Rule:
]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%281%20%5Ccdot%203x%5E%7B1%20-%201%7D%29cos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] (Parenthesis) Simplify:
]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B3cos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] Trig derivative:
![\displaystyle y' = \frac{[3cos(2x) -2sin(2x)(3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B3cos%282x%29%20-2sin%282x%29%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] Factor:
![\displaystyle y' = \frac{e^{2x}[(3cos(2x) -2sin(2x)(3x + 1)) - 2(3x + 1)cos(2x)]}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Be%5E%7B2x%7D%5B%283cos%282x%29%20-2sin%282x%29%283x%20%2B%201%29%29%20-%202%283x%20%2B%201%29cos%282x%29%5D%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction] Simplify [Exponential Rule - Dividing]:

- [Derivative] [Fraction - Numerator] Factor:
![\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B3cos%282x%29%20-2%283x%20%2B%201%29%5Bsin%282x%29%20%2B%20cos%282x%29%5D%7D%7Be%5E%7B2x%7D%7D)
Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e