Answer:
See explanation
Explanation:
Croton trees are indigenous to about ten countries in Sub-Saharan Africa. These croton forests consists of trees that are about 7–13 m tall, but sometimes grow as tall as 30 m.
These croton forests provide shade and play the very important role of acting as wind breaks thereby preventing wind erosion and other disasters caused by wind.
For this reason, croton forests should be maintained rather than cut down.
Answer:
4.5 times 10 Superscript negative 3
Explanation:
In scientific notation, the decimal is always after the first number so 14.5 times 10 Superscript 2 and 0.78 times 10 Superscript negative 6 is eliminated.
In scientific notation.=, the subscript is always 10 so 5.7 times 4 Superscript 8 is eliminated which leaves you with4.5 times 10 Superscript negative 3.
Hi there!
We can use implicit differentiation with respect to x:
![3xy = 4x + y^2](https://tex.z-dn.net/?f=3xy%20%3D%204x%20%2B%20y%5E2)
If a term with 'y' is differentiated, a 'dy/dx' must be included.
We can differentiate each term separately for the explanation.
<u>3xy</u>
We must use the power rule since 'x' and 'y' are both in this term.
Power rule:
![f(x) * g(x) = f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=f%28x%29%20%2A%20g%28x%29%20%3D%20f%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
![3xy \\\\f(x) = 3x\\g(x) = y \\\\f'(x)g(x) + g'(x)f(x) = 3y + 3x\frac{dy}{dx}](https://tex.z-dn.net/?f=3xy%20%5C%5C%5C%5Cf%28x%29%20%3D%203x%5C%5Cg%28x%29%20%3D%20y%20%5C%5C%5C%5Cf%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29%20%3D%203y%20%2B%203x%5Cfrac%7Bdy%7D%7Bdx%7D)
Now, we can do the others.
<u>4x</u>
This is a normal power rule derivative.
![f(x) = 4x\\f'(x) = 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%5C%5Cf%27%28x%29%20%3D%204)
<u>y²</u>
Since we are not differentiating with respect to y, we must include 'dy/dx'.
![f(x) = y^2\\f'(x) = 2y\frac{dy}{dx}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20y%5E2%5C%5Cf%27%28x%29%20%3D%202y%5Cfrac%7Bdy%7D%7Bdx%7D)
Combine the above:
![3y + 3x\frac{dy}{dx} = 4 + 2y\frac{dy}{dx}](https://tex.z-dn.net/?f=3y%20%2B%203x%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%204%20%2B%202y%5Cfrac%7Bdy%7D%7Bdx%7D)
Rearrange to solve for dy/dx.
Move dy/dx to one side:
![3x\frac{dy}{dx} - 2y\frac{dy}{dx} = 4 + 3y \\\\](https://tex.z-dn.net/?f=3x%5Cfrac%7Bdy%7D%7Bdx%7D%20-%202y%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%204%20%2B%203y%20%5C%5C%5C%5C)
Factor out dy/dx and divide:
![\frac{dy}{dx}(3x- 2y) = 4 + 3y \\\\\boxed{\frac{dy}{dx} = \frac{4+3y}{3x-2y}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%283x-%202y%29%20%3D%204%20%2B%203y%20%5C%5C%5C%5C%5Cboxed%7B%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B4%2B3y%7D%7B3x-2y%7D%7D)
none of them are a right angle since there isn't an angle on any of those measurements that are 90 degrees.