Which equation shows exponential GROWTH?
A) y=.5^x
B) y=.25^x
C) y= 25^x
D) y= .2^x
1 answer:
c) y = 25^x
explanation
because y increase as x increases
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If it is perpendicular then the slope of it will be:
![-3 \times x = -1\\\\x = \frac{1}{3}](https://tex.z-dn.net/?f=-3%20%5Ctimes%20x%20%3D%20-1%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
y = 1/3 x + b
-1 = (1/3)(3) + b
-1 = 1 + b
b = -2
The equation is:
Answer:
C- no because the graph is not a straight line
Answer:
1. Function
2. Function
3. Function
4. Not a Function
5. Not a Function
Step-by-step explanation:
Hope it helps:)
im sorry i need the points
Note that
![\frac{17 \pi }{12} = \frac{3 \pi }{12} + \frac{14 \pi }{12} = \frac{ \pi }{4} + \frac{7 \pi }{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B17%20%5Cpi%20%7D%7B12%7D%20%3D%20%5Cfrac%7B3%20%5Cpi%20%7D%7B12%7D%20%2B%20%5Cfrac%7B14%20%5Cpi%20%7D%7B12%7D%20%3D%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%20%2B%20%5Cfrac%7B7%20%5Cpi%20%7D%7B6%7D%20)
Note that
![x= \frac{ \pi }{4}:\,\, sin(x) =cos(x)= \frac{1}{ \sqrt{2} },\,tan(x)=1\\x= \frac{7 \pi }{6} :\,\,sin(x)=- \frac{1}{2} ,\,\,cos(x)=- \frac{ \sqrt{3} }{2} ,\,\,tan(x)= \frac{1}{ \sqrt{3} }](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%3A%5C%2C%5C%2C%20sin%28x%29%20%3Dcos%28x%29%3D%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B2%7D%20%7D%2C%5C%2Ctan%28x%29%3D1%5C%5Cx%3D%20%5Cfrac%7B7%20%5Cpi%20%7D%7B6%7D%20%3A%5C%2C%5C%2Csin%28x%29%3D-%20%5Cfrac%7B1%7D%7B2%7D%20%2C%5C%2C%5C%2Ccos%28x%29%3D-%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B2%7D%20%2C%5C%2C%5C%2Ctan%28x%29%3D%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
Use the identity
![tan(x+y)= \frac{tan(x)+tan(y)}{1-tan(x)tan(y)}](https://tex.z-dn.net/?f=tan%28x%2By%29%3D%20%5Cfrac%7Btan%28x%29%2Btan%28y%29%7D%7B1-tan%28x%29tan%28y%29%7D%20)
Therefore
![tan( \frac{17 \pi }{12} )= \frac{1+ \frac{1}{ \sqrt{3} } }{1- \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3}+1 }{ \sqrt{3}-1} = \frac{( \sqrt{3}+1 )^{2}}{( \sqrt{3}-1 )( \sqrt{3}+1 )} = \frac{3+1+2 \sqrt{3}}{3-1} =2+ \sqrt{3}](https://tex.z-dn.net/?f=tan%28%20%5Cfrac%7B17%20%5Cpi%20%7D%7B12%7D%20%29%3D%20%5Cfrac%7B1%2B%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%7D%7B1-%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%7D%20%3D%20%5Cfrac%7B%20%5Csqrt%7B3%7D%2B1%20%7D%7B%20%5Csqrt%7B3%7D-1%7D%20%3D%20%20%5Cfrac%7B%28%20%5Csqrt%7B3%7D%2B1%20%29%5E%7B2%7D%7D%7B%28%20%5Csqrt%7B3%7D-1%20%29%28%20%5Csqrt%7B3%7D%2B1%20%29%7D%20%20%3D%20%5Cfrac%7B3%2B1%2B2%20%5Csqrt%7B3%7D%7D%7B3-1%7D%20%3D2%2B%20%5Csqrt%7B3%7D)
Answer: 2 + √3