Answer:
16
Step-by-step explanation:
The existence of the constant rate of change is given the ratio of y to x is the same. Then:






In consequence, the constant rate of change is 16.
Answer:
The magnitude is 
The direction is
i.e toward the x-axis
Step-by-step explanation:
From the question we are told that
The function is 
The point considered is 
Generally the maximum rate of change of f at the given point and the direction is mathematically represented as
![\Delta f(x,y) = [\frac{\delta (9sin(xy))}{\delta x} i + \frac{\delta (9sin(xy))}{\delta y} i ]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%20%5B%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20x%7D%20i%20%20%2B%20%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20y%7D%20i%20%20%20%5D)
![\Delta f(x,y) = [9y cos (x,y) i + 9xcos (x,y) j]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%5B9y%20cos%20%28x%2Cy%29%20i%20%2B%20%209xcos%20%28x%2Cy%29%20j%5D)
At 
![\Delta f (0,8) = [9(8) cos(0* 8)i + 9(8) sin(0* 8)j ]](https://tex.z-dn.net/?f=%5CDelta%20%20f%20%280%2C8%29%20%3D%20%20%5B9%288%29%20cos%280%2A%208%29i%20%20%2B%209%288%29%20sin%280%2A%208%29j%20%20%5D)

Answer: d. 512
Step-by-step explanation:
You need to remember that:
![(\sqrt[3]{x})^3=x](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7Bx%7D%29%5E3%3Dx)
Then, given the equation:
![\sqrt[3]{n}=8](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%3D8)
You can find the value of "n" that make the equation true, by solving for "n".
So, to solve for "n", you need to raise both side of the equation to power 3. Therefore, you get:
![\sqrt[3]{n}=8](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%3D8)
![(\sqrt[3]{n})^3=(8)^3](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7Bn%7D%29%5E3%3D%288%29%5E3)

Then, the value of "n" that makes the equation
true is: 512 (You can observe that this matches with the option d).