Answer:
real, rational, ineger, whole.
Step-by-step explanation:
Answer:
$6
Step-by-step explanation:
In order to find the amount of the tip that T.J. and Lindsey will leave for their waiter, you have to multiply the lunch cost for the percentage they want to leave as a tip for their waiter:
Lunch cost=$30
Percentage they want to leave as a tip= 20%
$30*20%=$6
According to this, the answer is that the amount of the tip is $6.
Let 'x' represent the total distance from point A to point B
During the first hour he gets 0.25 of the way there: 0.25x
During the second hour he covers an additional 0.2 of the distance: 0.2x
During the third hour, he covers 0.3 of the distance: 0.3x
The total distance the biker traveled is:
0.25x + 0.2x + 0.3x = (0.25 + 0.2 + 0.3)x = 0.75x
The biker has: x - 0.75x = (1 - 0.75)x = 0.25x of the total distance left to go.
Answer:
D. undefined
General Formulas and Concepts:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
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)
Trig Derivative: ![\displaystyle \frac{d}{dx}[sinu] = u'cosu](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bsinu%5D%20%3D%20u%27cosu)
Derivatives of Parametrics: ![\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B%5Cfrac%7Bdy%7D%7Bdt%7D%7D%7B%5Cfrac%7Bdx%7D%7Bdt%7D%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
![\displaystyle \frac{dx}{dt} = 5](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%205)
![\displaystyle \frac{dy}{dt} = sin(t^2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20sin%28t%5E2%29)
<u>Step 2: Differentiate</u>
- [x Derivative] Basic Power Rule:
![\displaystyle \frac{d^2x}{dt^2} = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2x%7D%7Bdt%5E2%7D%20%3D%200)
- [y Derivative] Trig Derivative [Chain Rule]:
![\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot \frac{d}{dt}[t^2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%20cos%28t%5E2%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D)
- [y Derivative] Basic Power Rule:
![\displaystyle \frac{d^2y}{dt^2} = cos(t^2) \cdot 2t^{2 - 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%20cos%28t%5E2%29%20%5Ccdot%202t%5E%7B2%20-%201%7D)
- [y Derivative] Simplify:
![\displaystyle \frac{d^2y}{dt^2} = 2tcos(t^2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%202tcos%28t%5E2%29)
- [Derivative] Rewrite:
![\displaystyle \frac{d^2y}{dx^2} = \frac{2tcos(t^2)}{0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%20%3D%20%5Cfrac%7B2tcos%28t%5E2%29%7D%7B0%7D)
Anything divided by 0 is undefined.
Topic: AP Calculus BC (Calculus I/II)
Unit: Differentiation with Parametrics
Book: College Calculus 10e