Answer:
Choice C. ![(f-g)(x)=-x^2+17x+7](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D-x%5E2%2B17x%2B7)
Step-by-step explanation:
Recall that
is defined by
![(f-g)(x)=f(x)-g(x)](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Df%28x%29-g%28x%29)
Therefore we compute
![(f-g)(x)=f(x)-g(x)=10x+7-x^2+7x=-x^2+17x+7](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Df%28x%29-g%28x%29%3D10x%2B7-x%5E2%2B7x%3D-x%5E2%2B17x%2B7)
Answer:point c
Step-by-step explanation:
because point c is three lines down from -1. making -1 and 3/8
Answer:
Isosceles triangle
Step-by-step explanation:
Given
Two congruent angles and two congruent sides
Base on the given description, the concept being described is an isosceles triangle, as it has two congruent sides and two congruent angles.
If each angle measures 45 degrees each, then the third angle is 90 degrees.
This is shown below.
--- angles in a triangle
![\theta + 90= 180](https://tex.z-dn.net/?f=%5Ctheta%20%2B%2090%3D%20%20180)
Subtract 90 from both sides
![\theta = 90](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2090)
Answer:
See explanation.
General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Factoring
<u>Algebra II</u>
<u>Pre-Calculus</u>
<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 [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)
Parametric Differentiation: ![\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>
<em>Identify</em>
![\displaystyle x = 2t - \frac{1}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%202t%20-%20%5Cfrac%7B1%7D%7Bt%7D)
![\displaystyle y = t + \frac{4}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20t%20%2B%20%5Cfrac%7B4%7D%7Bt%7D)
<u>Step 2: Find Derivative</u>
- [<em>x</em>] Differentiate [Basic Power Rule and Quotient Rule]:
![\displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%202%20%2B%20%5Cfrac%7B1%7D%7Bt%5E2%7D)
- [<em>y</em>] Differentiate [Basic Power Rule and Quotient Rule]:
![\displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%201%20-%20%5Cfrac%7B4%7D%7Bt%5E2%7D)
- Substitute in variables [Parametric Derivative]:
![\displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%20-%20%5Cfrac%7B4%7D%7Bt%5E2%7D%7D%7B2%20%2B%20%5Cfrac%7B1%7D%7Bt%5E2%7D%7D)
- [Parametric Derivative] Simplify:
![\displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7Bt%5E2%20-%204%7D%7B2t%5E2%20%2B%201%7D)
- [Parametric Derivative] Polynomial Long Division:
![\displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B7%7D%7B2%282t%5E2%20-%201%29%7D)
- [Parametric Derivative] Factor:
![\displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%201%20-%20%5Cfrac%7B9%7D%7B2t%5E2%20%2B%201%7D%20%5Cbigg%29)
Here we see that if we increase our values for <em>t</em>, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence
.
Topic: AP Calculus BC (Calculus I + II)
Unit: Parametrics
Book: College Calculus 10e
Answer:
no solutions
Step-by-step explanation:
Subtract the two equations
3x+y=18
-(3x+y=16)
--------------------
0 + 0 = -2
0 does not equal negative 2
This is never true so there are no solutions