Your answer would be <em />answer choice C. The initial number of transactions is a dependent variable, because the number of transactions made are dependent on the number of hours that have passed.
Hope this helps,
<em>♥A.W.E.<u>S.W.A.N.</u>♥</em>
Answer:
![A = 4](https://tex.z-dn.net/?f=A%20%3D%204)
Step-by-step explanation:
The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:
![y = \frac{2}{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%7D%7Bx%7D)
![y'=-2\cdot x^{-2}](https://tex.z-dn.net/?f=y%27%3D-2%5Ccdot%20x%5E%7B-2%7D)
The numerical value of the slope is:
![y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}](https://tex.z-dn.net/?f=y%27%20%3D%20-2%20%5Ccdot%20%289%29%5E%7B-2%7D%5C%5Cy%27%20%3D%20-%5Cfrac%7B2%7D%7B81%7D)
The component of the y-axis is:
![y = \frac{2}{9}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B2%7D%7B9%7D)
Now, the tangent line has the following mathematical model:
![y = m \cdot x + b](https://tex.z-dn.net/?f=y%20%3D%20m%20%5Ccdot%20x%20%2B%20b)
The value of the intercept is found by isolating it within the equation and replacing all known variables:
![b = y - m \cdot x](https://tex.z-dn.net/?f=b%20%3D%20y%20-%20m%20%5Ccdot%20x)
![b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B2%7D%7B9%7D-%28-%5Cfrac%7B2%7D%7B81%7D%20%29%5Ccdot%20%289%29%5C%5Cb%20%3D%20%5Cfrac%7B4%7D%7B9%7D)
Thus, the tangent line is:
![y = -\frac{2}{81}\cdot x + \frac{4}{9}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B2%7D%7B81%7D%5Ccdot%20x%20%2B%20%5Cfrac%7B4%7D%7B9%7D)
The vertical distance between a point of the tangent line and the origin is given by the intercept.
![d_{y} = \frac{4}{9}](https://tex.z-dn.net/?f=d_%7By%7D%20%3D%20%5Cfrac%7B4%7D%7B9%7D)
In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:
![-\frac{2}{81}\cdot x + \frac{4}{9}=0](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B81%7D%5Ccdot%20x%20%2B%20%5Cfrac%7B4%7D%7B9%7D%3D0)
![-\frac{2}{9}\cdot x + 4 = 0](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B9%7D%5Ccdot%20x%20%2B%204%20%3D%200)
![x = 18](https://tex.z-dn.net/?f=x%20%3D%2018)
![d_{x} = 18](https://tex.z-dn.net/?f=d_%7Bx%7D%20%3D%2018)
The area of the triangle is computed by this formula:
![A = \frac{1}{2}\cdot d_{x}\cdot d_{y}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20d_%7Bx%7D%5Ccdot%20d_%7By%7D)
![A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%2818%29%5Ccdot%20%28%5Cfrac%7B4%7D%7B9%7D%20%29)
![A = 4](https://tex.z-dn.net/?f=A%20%3D%204)
Answer:
10
Step-by-step explanation:
The volume of a cube is equal to its (side length)^3
so s^3 = 1000
![s=\sqrt[3]{1000} =10](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B3%5D%7B1000%7D%20%3D10)
Step-by-step explanation:
So the Ap will be x,x+10,x+20,x+30
Sum of the angles of a quadrilateral is 360
x+x+10+x+20+x+30=360
4x+60=360
4x=300
x=75
So the angles are 75,85,95,105