Answer:
50 laps
Step-by-step explanation:
20+1.25x+15+2.5x+40+1.5x+25+1.75x=450
7x+100=450
7x+200-200=450-100
7x=350
7x/7=350/7
x=50
Answer:
Slope = -3/7
Step-by-step explanation:
The formula for slope is y2-y1/x2-x1.
Substitute for the points.
5-2/3-10 = -3/7
Answer:
try and move the line to touch more dots.
Step-by-step explanation:
then salve for y intersept
Answer:
False.
General Formulas and Concepts:
<u>Algebra I</u>
Terms/Coefficients
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [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)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
![\displaystyle \frac{d}{dx}[x^3e^x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E3e%5Ex%5D)
<u>Step 2: Differentiate</u>
- Derivative Rule [Product Rule]:
![\displaystyle \frac{d}{dx}[x^3e^x] = \frac{d}{dx}[x^3]e^x + x^3 \frac{d}{dx}[e^x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E3e%5Ex%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E3%5De%5Ex%20%2B%20x%5E3%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5D)
- Derivative Rule [Basic Power Rule]:
![\displaystyle \frac{d}{dx}[x^3e^x] = 3x^2e^x + x^3 \frac{d}{dx}[e^x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E3e%5Ex%5D%20%3D%203x%5E2e%5Ex%20%2B%20x%5E3%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5D)
- Exponential Differentiation:
![\displaystyle \frac{d}{dx}[x^3e^x] = 3x^2e^x + x^3e^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E3e%5Ex%5D%20%3D%203x%5E2e%5Ex%20%2B%20x%5E3e%5Ex)
- Factor:
![\displaystyle \frac{d}{dx}[x^3e^x] = (x^3 + 3x^2)e^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E3e%5Ex%5D%20%3D%20%28x%5E3%20%2B%203x%5E2%29e%5Ex)
∴
but
.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Slope = (4 +1) / (-3 - 2) = 5/-5 = -1
Answer
- 1