Implicit Differentiation
Step-by-step explanation:
Given:

Recall:
![x^{\frac{2}{3}} -y^{\frac{2}{3}} = 6 \\ \frac{\text{d}}{\text{d}x}(x^{\frac{2}{3}} -y^{\frac{2}{3}}) = \frac{\text{d}}{\text{d}x}(6) \\ \frac{\text{d}}{\text{d}x}(x^{\frac{2}{3}}) -\frac{\text{d}}{\text{d}x}(y^{\frac{2}{3}}) = 0 \\ \frac{2}{3}x^{\frac{2}{3} -1} -\frac{2}{3}y^{\frac{2}{3} -1}\cdot \frac{\text{d}y}{\text{d}x} = 0 \\ \frac{2}{3}x^{-\frac{1}{3}} - \frac{2}{3}y^{-\frac{1}{3}} \cdot \frac{\text{d}y}{\text{d}x} = 0 \\ \frac{2}{3\sqrt[3]{x}} -\frac{2}{3\sqrt[3]{y}}\cdot \frac{\text{d}y}{\text{d}x} = 0 \\ -\frac{2}{3\sqrt[3]{y}}\cdot \frac{\text{d}y}{\text{d}x} = -\frac{2}{3\sqrt[3]{x}} \\ -2 \cdot \frac{\text{d}y}{\text{d}x} = -\frac{6\sqrt[3]{y}}{3\sqrt[3]{x}} \\ \frac{\text{d}y}{\text{d}x} = -\frac{6\sqrt[3]{y}}{-6\sqrt[3]{x}} \\ \frac{\text{d}y}{\text{d}x} = \frac{\sqrt[3]{y}}{\sqrt[3]{x}}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%20-y%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%20%3D%206%20%5C%5C%20%5Cfrac%7B%5Ctext%7Bd%7D%7D%7B%5Ctext%7Bd%7Dx%7D%28x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%20-y%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%20%3D%20%5Cfrac%7B%5Ctext%7Bd%7D%7D%7B%5Ctext%7Bd%7Dx%7D%286%29%20%5C%5C%20%5Cfrac%7B%5Ctext%7Bd%7D%7D%7B%5Ctext%7Bd%7Dx%7D%28x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%20-%5Cfrac%7B%5Ctext%7Bd%7D%7D%7B%5Ctext%7Bd%7Dx%7D%28y%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%20%3D%200%20%5C%5C%20%5Cfrac%7B2%7D%7B3%7Dx%5E%7B%5Cfrac%7B2%7D%7B3%7D%20-1%7D%20-%5Cfrac%7B2%7D%7B3%7Dy%5E%7B%5Cfrac%7B2%7D%7B3%7D%20-1%7D%5Ccdot%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%200%20%5C%5C%20%5Cfrac%7B2%7D%7B3%7Dx%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%20-%20%5Cfrac%7B2%7D%7B3%7Dy%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%20%5Ccdot%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%200%20%5C%5C%20%5Cfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7Bx%7D%7D%20-%5Cfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7By%7D%7D%5Ccdot%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%200%20%5C%5C%20-%5Cfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7By%7D%7D%5Ccdot%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%20-%5Cfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7Bx%7D%7D%20%5C%5C%20-2%20%5Ccdot%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%20-%5Cfrac%7B6%5Csqrt%5B3%5D%7By%7D%7D%7B3%5Csqrt%5B3%5D%7Bx%7D%7D%20%5C%5C%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%20-%5Cfrac%7B6%5Csqrt%5B3%5D%7By%7D%7D%7B-6%5Csqrt%5B3%5D%7Bx%7D%7D%20%5C%5C%20%5Cfrac%7B%5Ctext%7Bd%7Dy%7D%7B%5Ctext%7Bd%7Dx%7D%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7By%7D%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D)
Answer:
The diameter of an atom is 25000 times the diameter of a pearl.
Step-by-step explanation:
Given that,
The diameter of a pearl is 
The diameter of an atom is 
Taking the ratio,

So, the diameter of an atom is 25000 times the diameter of a pearl.
Answer:
multiply t from both sides by t, then divide both sides by s.
it should be txy/s = r
4x=y
2x^2 -y =0 so than we substitute the y value from the first equation inside second equation in place of y we get
2x^2 -4x =0 than we solve it for x we get
2x^2 -4x =0
2x(x-2) =0
2x =0
x_1 = 0
x - 2 =0
x_2 = 2
so for x_1 = 0 result y_1 = 4*0 = 0 so the solution set will be (0,0)
and in case of x_2 = 2 result y_2 = 4*2 = 8 so the sol. set will be (2,8)
hope this will help you
Answer:
-120
Step-by-step explanation: