Answer: 6:15
Step-by-step explanation:
Use the chain rule to compute the second derivative:
![f(x)=\ln(\sin(2x))](https://tex.z-dn.net/?f=f%28x%29%3D%5Cln%28%5Csin%282x%29%29)
The first derivative is
![f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%5Cln%28%5Csin%282x%29%29%29%27%3D%5Cdfrac%7B%28%5Csin%282x%29%29%27%7D%7B%5Csin%282x%29%7D%3D%5Cdfrac%7B%5Ccos%282x%29%282x%29%27%7D%7B%5Csin%282x%29%7D%3D%5Cdfrac%7B2%5Ccos%282x%29%7D%7B%5Csin%282x%29%7D)
![f'(x)=2\cot(2x)](https://tex.z-dn.net/?f=f%27%28x%29%3D2%5Ccot%282x%29)
Then the second derivative is
![f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'](https://tex.z-dn.net/?f=f%27%27%28x%29%3D%282%5Ccot%282x%29%29%27%3D-2%5Ccsc%5E2%282x%29%282x%29%27)
![f''(x)=-4\csc^2(2x)](https://tex.z-dn.net/?f=f%27%27%28x%29%3D-4%5Ccsc%5E2%282x%29)
Then plug in π/4 for <em>x</em> :
![f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4](https://tex.z-dn.net/?f=f%27%27%5Cleft%28%5Cdfrac%5Cpi4%5Cright%29%3D-4%5Ccsc%5E2%5Cleft%28%5Cdfrac%7B2%5Cpi%7D4%5Cright%29%3D-4)
Answer:
In 1 min a gazelle runs 3,900 ft.
As a fraction, 1/65
In order to find the solution to this problem you could use a table.
Since we are using seconds we have to convert the 1 min = 60 seconds.
<u>Sec</u><u> | 12 | 60</u>
<u>Fts</u><u> | 780 | x </u>
12 goes into 60 5 times, so we have to multiply 780 by 5 which gives us 3900.
x=3900
Answer: 37 + 19 = 56
Step-by-step explanation: easy all you need to do is take away nineteen from 56 then you get m
Answer:
![\displaystyle m=3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D3)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Slope Formula:
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
Point (6, 8)
Point (5, 5)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope<em> m</em>
- Substitute in points [SF]:
![\displaystyle m=\frac{5-8}{5-6}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B5-8%7D%7B5-6%7D)
- [Fraction] Subtract:
![\displaystyle m=\frac{-3}{-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-3%7D%7B-1%7D)
- [Fraction] Divide:
![\displaystyle m=3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D3)