Answer:
38
Step-by-step explanation:
Notice that the first triangle is an isosceles triangle, meaning that the base angles are equivalent. Since one angle is 62, we know that the other is 62 as well, which makes 124. This means that angle 2 is 56 degrees. Since 2 and 3 are on the same 'line', they both add up to 180. If 2 is 56, then angle 3 is 124. So the three angles inside the triangle are 124, 18, and x. So, 124+18=142. 180-142= 38
Answer:
2 pieces
Step-by-step explanation:
3/4 ÷ 3/8
3/4 x 8/3 = 12/6 = 2
:)
Answer:

Step-by-step explanation:
we know that
The quadratic equation in standard form is equal to

we have
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This is a quadratic equation in vertex form
Convert to standard form
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Apply distributive property
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Combine like terms
----> quadratic equation in standard form
I'm sure the measurement was made in grams because:
1. most cell phones weigh between about 100 and 150 grams
2. there's no cell phone that weighs 113 kg, 113 pounds, 113 ounces etc.
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