Answer:
The base is 0.1
The base is less than 1 so the function is decreasing
The x intercept is (3,0)
Step-by-step explanation:
The base of a logarithm refers to the number that must be raised to the power of the number on the right hand side of the logarithmic equation in order to yield the number on the left hand side of the logarithmic equation. It is always written as a subscript below the log symbol. In this case, the base is 0.1.
When the base of a logarithm is less than 1, it means that the function is decreasing as is the case in this question.
Looking at the graph, the x axis is cut at the point (3,0). This is the x-intercept of the graph.
Answer:
The answer should be rectangle only.
Answer:
65.56°
Step-by-step explanation:
We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them
That is let p and q be any two vectors and A be the angle between them
So, p·q=|p|*|q|*cosA
⇒![cosA=\frac{u.v}{|u||v|}](https://tex.z-dn.net/?f=cosA%3D%5Cfrac%7Bu.v%7D%7B%7Cu%7C%7Cv%7C%7D)
Given u=-8i-3j and v=-8i+8j
![|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544](https://tex.z-dn.net/?f=%7Cu%7C%3D%5Csqrt%7B%28-8%29%5E%7B2%7D%2B%20%28-3%29%5E%7B2%7D%7D%20%3D8.544)
![|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137](https://tex.z-dn.net/?f=%7Cv%7C%3D%5Csqrt%7B%28-8%29%5E%7B2%7D%2B%20%288%29%5E%7B2%7D%7D%20%3D11.3137)
let A be angle before u and v
therefore, ![cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}](https://tex.z-dn.net/?f=cosA%3D%5Cfrac%7Bu.v%7D%7B%7Cu%7C%7Cv%7C%7D%3D%5Cfrac%7B%28-8%29%2A%28-8%29%2B%28-3%29%2A%288%29%7D%7B8.544%2A11.3137%7D%20%3D%5Cfrac%7B40%7D%7B96.664%7D)
⇒![A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56](https://tex.z-dn.net/?f=A%3Darccos%28%5Cfrac%7B40%7D%7B96.664%7D%20%29%3Darccos%280.4138%20%29%3D65.56)
Therefore angle between u and v is 65.56°
THE first option is correct