Answer:
Point A(9, 3)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Coordinates (x, y)
- Functions
- Function Notation
- Terms/Coefficients
- Anything to the 0th power is 1
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<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)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em />
<em />
<em />
<em />
<em />
<u>Step 2: Differentiate</u>
- [Function] Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle y = x^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
- Basic Power Rule:
![\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%20-%201%7D)
- Simplify:
![\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
- [Derivative] Rewrite [Exponential Rule - Rewrite]:
![\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D)
- [Derivative] Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle y' = \frac{1}{2\sqrt{x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D)
<u>Step 3: Solve</u>
<em>Find coordinates of A.</em>
<em />
<em>x-coordinate</em>
- Substitute in <em>y'</em> [Derivative]:
![\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D)
- [Multiplication Property of Equality] Multiply 2 on both sides:
![\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%7D)
- [Multiplication Property of Equality] Cross-multiply:
![\displaystyle \sqrt{x} = 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7Bx%7D%20%3D%203)
- [Equality Property] Square both sides:
![\displaystyle x = 9](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%209)
<em>y-coordinate</em>
- Substitute in <em>x</em> [Function]:
![\displaystyle y = \sqrt{9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Csqrt%7B9%7D)
- [√Radical] Evaluate:
![\displaystyle y = 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%203)
∴ Coordinates of A is (9, 3).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
BC = 25 units
Step-by-step explanation:
The triangle is isosceles, so sides AB and AC equal each other.
4x+1=2x+23.
If you subtract 1 from both sides and 2x from both sides you end up with 2x=22.
Divide by 2 and you get x=11.
BC = 3x-8.
Substitute and you get 3(11)-8=33-8= 25 units
Answer:
Practice, Practice & More Practice. It is impossible to study maths properly by just reading and listening. ...
Review Errors. ...
Master the Key Concepts. ...
Understand your Doubts. ...
Create a Distraction Free Study Environment. ...
Create a Mathematical Dictionary. ...
Apply Maths to Real World Problems.
Step-by-step explanation:
Hope this helps sorry if incorrect
Answer:
D.
Step-by-step explanation:
The original antenna revolves at a rate of 30 per 2 minutes, or 15 per minute.
Twice as fast = 15 X 2 = 30 per minute
Only the data in Table D fits.
660 / 22 = 30
720 / 24 = 30