A would equal 4 because you would first convert the mixed numbers into improper fractions, then move the constant to the right, and finally add the factions
a-2(1/2)=1(1/2)
a-(5/2)=(3/2)
a=(3/2)+(5/2)
a=4
Answer:
7 strips
Step-by-step explanation:
One way we can solve this is through guess and check. Let's start with 4 strips. If Joe's grandma makes 4 strips, she will have 0.75*4 = 3.00 yards of fabric. That's a really low amount of fabric. Let's double that to 8, where Joe's grandma would need 0.75*8 = 6.00 yards of fabric. That's really close! Let's remove one strip. 0.75*7 = 5.25 yards of fabric. Perfect! Joe's grandma can cut exactly 7 strips
Answer:
![\displaystyle \frac{d}{dx}[(4x + 1)^2] = 8(4x + 1)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%284x%20%2B%201%29%5E2%5D%20%3D%208%284x%20%2B%201%29)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Derivative Property [Addition/Subtraction]: ![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
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>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Basic Power Rule [Derivative Rule - Chain Rule]:
![\displaystyle y' = 2(4x + 1) \cdot \frac{d}{dx}[4x + 1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%202%284x%20%2B%201%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5B4x%20%2B%201%5D)
- Basic Power Rule [Addition/Subtraction, Multiplied Constant]:

- Simplify:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer:
Point B is (7,3)
Step-by-step explanation:
point A to point B is 7 units apart and 1 unit down.
then from point M you do the same thing based on the slope, you move 7 units right from point M and lastly move 1 unit down which the coordinate point for B should be (7,3).