Answer:
Step-by-step explanation:
1 are = 100 m²
Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are
16 are × 100 m²/are = 1600 m²
each side is √1600 = 40 m
Answer:
he will owe $1,047 in total and $97.37 in interest
Answer:
![sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}](https://tex.z-dn.net/?f=sin%282%5Calpha%20%29%3D2%28%5Cfrac%7B5%7D%7B12%7D%29%28%5Cfrac%7B12%7D%7B13%7D%29%3D%5Cfrac%7B10%7D%7B13%7D%5C%5Ccot%282%5Calpha%20%29%20%3D%20%5Cfrac%7B16511%7D%7B18720%7D)
Step-by-step explanation:
![\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\](https://tex.z-dn.net/?f=%5Ctext%7Bif%20%7D%20cos%28%5Calpha%29%3D%5Cfrac%7B12%7D%7B13%7D%5C%5C%5Ctext%7BThat%20must%20mean%20we%20have%20a%20triangle%20with%20base%2012%2C%20and%20hypotenuse%2013.%7D%5C%5C%5Ctext%7BUsing%20Pythagoras%2C%20we%20can%20determine%20the%20base%20of%20the%20triangle%20must%20be%205.%7D%5C%5Ca%5E2%2Bb%5E2%3Dc%5E2%20%5Ctext%7B%2C%20where%20c%20is%20the%20hypotenuse%20and%20a%2C%20b%20are%20the%20two%20other%20sides.%7D%5C%5Cc%5E2-b%5E2%3Da%5E2%5C%5C%5Csqrt%7Bc%5E2-b%5E2%7D%3Da%5C%5C%5Csqrt%7B13%5E2-12%5E2%7D%3D%5Csqrt%7B169-144%7D%3D%5Csqrt%7B25%7D%3D5%5C%5C%5Ctext%7BTherefore%2C%20%7Dsin%28%5Calpha%29%20%3D%20%5Cfrac%7B5%7D%7B12%7D%5C%5Csin%282%5Calpha%29%3D2sin%28%5Calpha%20%29cos%28%5Calpha%29%5C%5C%5Ctext%7B%28From%20double%20angle%20formulae%20identities%29%7D%5C%5C)
![sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}](https://tex.z-dn.net/?f=sin%282%5Calpha%20%29%3D2%28%5Cfrac%7B5%7D%7B12%7D%29%28%5Cfrac%7B12%7D%7B13%7D%29%3D%5Cfrac%7B10%7D%7B13%7D%5C%5Ccos%282%5Calpha%20%29%3Dcos%5E2%28%5Calpha%29-sin%5E2%28%5Calpha%29%5C%5Ccos%282%5Calpha%20%29%3D%28%5Cfrac%7B12%7D%7B13%7D%29%5E2-%28%5Cfrac%7B5%7D%7B12%7D%29%5E2%3D%5Cfrac%7B16511%7D%7B24336%7D%5C%5Ccot%282%5Calpha%29%3D%5Cfrac%7Bcos%282%5Calpha%29%7D%7Bsin%282%5Calpha%29%7D%3D%5Cfrac%7B%5Cfrac%7B16511%7D%7B24336%7D%7D%7B%5Cfrac%7B10%7D%7B13%7D%7D%3D%5Cfrac%7B16511%7D%7B18720%7D)
Answer:
The equation of the line is: ![y = 0.6x + 0.6](https://tex.z-dn.net/?f=y%20%3D%200.6x%20%2B%200.6)
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which m is the slope and b is the y-intercept.
Two points:
We have these following two points in this exercise:
x = -6, y = -3, so (-6,-3)
x = 4, y = 3, so (4,3)
Finding the slope:
Given two points, the slope is given by the change in y divided by the change in x.
Change in y: 3 - (-3) = 3 + 3 = 6
Change in x: 4 - (-6) = 4 + 6 = 10
So
![m = \frac{6}{10} = 0.6](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B6%7D%7B10%7D%20%3D%200.6)
Then
![y = 0.6x + b](https://tex.z-dn.net/?f=y%20%3D%200.6x%20%2B%20b)
Finding b:
We replace one of the points in the equation to find b. I will use (4,3).
![y = 0.6x + b](https://tex.z-dn.net/?f=y%20%3D%200.6x%20%2B%20b)
![3 = 0.6*4 + b](https://tex.z-dn.net/?f=3%20%3D%200.6%2A4%20%2B%20b)
![2.4 + b = 3](https://tex.z-dn.net/?f=2.4%20%2B%20b%20%3D%203)
![b = 0.6](https://tex.z-dn.net/?f=b%20%3D%200.6)
The equation of the line is: ![y = 0.6x + 0.6](https://tex.z-dn.net/?f=y%20%3D%200.6x%20%2B%200.6)