The answer is 3√5. You use the distance formula: √((x2-x1)^2+(y2-y1)^2)
Each liter of water weighs 1 kg, so the weight of the water in a cubic meter is 1,000 kg.
m∠AOC = m∠AOB + m∠BOC
We have m∠AOC = 19°, m∠AOB = 4x - 15 and m∠BOC = 2x + 10. Substitute:
19 = (4x - 15) + (2x + 10)
19 = (4x + 2x) + (-15 + 10)
19 = 6x - 5 <em>add 5 to both sides</em>
24 = 6x <em>divide both sides by 6</em>
4 = x
m∠BOC = 2x + 10 → m∠BOC = 2(4) + 10 = 8 + 10 = 18
m∠AOB = 4x - 15 → m∠AOB = 4(4) - 15 = 16 - 15 = 1
<h3>Answer: c. m∠BOC = 18°, m∠AOB = 1°</h3>
Here is the solution...
1) ![\sqrt[3]{135} \\](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%5C%5C)
Solution
We can rewrite ![\sqrt[3]{135} = \sqrt[3]{27} *\sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D%20%5Csqrt%5B3%5D%7B27%7D%20%2A%5Csqrt%5B3%5D%7B5%7D)
Here, ![\sqrt[3]{27} = 3](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%20%3D%203)
Now substitute the value, we get
![\sqrt[3]{135} = 3 \sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D%203%20%5Csqrt%5B3%5D%7B5%7D)
The answer is ![3\sqrt[3]{5}](https://tex.z-dn.net/?f=3%5Csqrt%5B3%5D%7B5%7D)
2) ![-5\sqrt[3]{40} Solution[tex]-5\sqrt[3]{40} = -5\sqrt[3]{8} *\sqrt[3]{5}](https://tex.z-dn.net/?f=-5%5Csqrt%5B3%5D%7B40%7D%20%3C%2Fp%3E%3Cp%3E%3Cstrong%3ESolution%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%5Btex%5D-5%5Csqrt%5B3%5D%7B40%7D%20%3D%20-5%5Csqrt%5B3%5D%7B8%7D%20%2A%5Csqrt%5B3%5D%7B5%7D)
Here ![\sqrt[3]{8} = \sqrt[3]{2^{3} } = 2\\](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%20%5Csqrt%5B3%5D%7B2%5E%7B3%7D%20%7D%20%3D%202%5C%5C)
Therefore, we get ![-5*2\sqrt[3]{5} = -10 \sqrt[3]{5}](https://tex.z-dn.net/?f=-5%2A2%5Csqrt%5B3%5D%7B5%7D%20%3D%20-10%20%5Csqrt%5B3%5D%7B5%7D)
The answer is-10 \sqrt[3]{5}[/tex]
2) ![2\sqrt[3]{5} * 4\sqrt[3]{8}](https://tex.z-dn.net/?f=2%5Csqrt%5B3%5D%7B5%7D%20%2A%204%5Csqrt%5B3%5D%7B8%7D)
Solution
![\sqrt[3]{8} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%202)
Now plug in the above in the given expression, we get
{2*4*2 = 16]
The answer is ![16\sqrt[3]{5}](https://tex.z-dn.net/?f=16%5Csqrt%5B3%5D%7B5%7D)