Answer:
The simplest radical form of the cubic root is ![3x^2y^4\sqrt[3]{2x}](https://tex.z-dn.net/?f=3x%5E2y%5E4%5Csqrt%5B3%5D%7B2x%7D)
Step-by-step explanation:
Cube root of 54x^8y^12
That is:
![\sqrt[3]{54x^8y^12}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E8y%5E12%7D)
Can be simplified as:
![\sqrt[3]{54x^8y^12} = \sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E8y%5E12%7D%20%3D%20%5Csqrt%5B3%5D%7B54%7D%5Csqrt%5B3%5D%7Bx%5E8%7D%5Csqrt%5B3%5D%7By%5E12%7D)
We find each separate simplification, and multiply them:
Cubic root of 54:

So
![\sqrt[3]{54} = \sqrt[3]{2*3^3} = 3\sqrt[3]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54%7D%20%3D%20%5Csqrt%5B3%5D%7B2%2A3%5E3%7D%20%3D%203%5Csqrt%5B3%5D%7B2%7D)
Cubic root of x^8
![\sqrt[3]{x^8} = \sqrt[3]{x^6*x^2} = x^2\sqrt[3]{x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E8%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E6%2Ax%5E2%7D%20%3D%20x%5E2%5Csqrt%5B3%5D%7Bx%5E2%7D)
Cubic root of y^12
![\sqrt[3]{y^{12}} = y^4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7By%5E%7B12%7D%7D%20%3D%20y%5E4)
Multiplying all these terms:
![\sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12} = 3\sqrt[3]{2}(x^2\sqrt[3]{x^2})(y^4) = 3x^2y^4\sqrt[3]{2x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54%7D%5Csqrt%5B3%5D%7Bx%5E8%7D%5Csqrt%5B3%5D%7By%5E12%7D%20%3D%203%5Csqrt%5B3%5D%7B2%7D%28x%5E2%5Csqrt%5B3%5D%7Bx%5E2%7D%29%28y%5E4%29%20%3D%203x%5E2y%5E4%5Csqrt%5B3%5D%7B2x%7D)
The simplest radical form of the cubic root is ![3x^2y^4\sqrt[3]{2x}](https://tex.z-dn.net/?f=3x%5E2y%5E4%5Csqrt%5B3%5D%7B2x%7D)
30 mins = 180°
15 mins = 90°
10 mins = 60°
1 min = 6°
hope this helps you
For this case we find the slopes of each of the lines:
The g line passes through the following points:

So, the slope is:

Line h passes through the following points:

So, the slope is:

By definition, if two lines are parallel then their slopes are equal. If the lines are perpendicular then the product of their slopes is -1.
It is observed that lines g and h are not parallel. We verify if they are perpendicular:

Thus, the lines are perpendicular.
Answer:
The lines are perpendicular.