Answer:
![\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%7D)
Step-by-step explanation:
Our expression is: ![\frac{1}{3} \sqrt[3]{81}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Csqrt%5B3%5D%7B81%7D)
.
Let's focus on the cube root of 81 first. What's the prime factorisation of 81? It's simply: 3 * 3 * 3 * 3, or 
. Put this in for 81:
![\sqrt[3]{81} =\sqrt[3]{3^3*3}=\sqrt[3]{3^3} *\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81%7D%20%3D%5Csqrt%5B3%5D%7B3%5E3%2A3%7D%3D%5Csqrt%5B3%5D%7B3%5E3%7D%20%2A%5Csqrt%5B3%5D%7B3%7D)
We know that the cube root of 3 cubed will cancel out to become 3, but the cube root of 3 cannot be further simplified, so we keep that. Our outcome is then:
![\sqrt[3]{3^3} *\sqrt[3]{3}=3\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%5E3%7D%20%2A%5Csqrt%5B3%5D%7B3%7D%3D3%5Csqrt%5B3%5D%7B3%7D)
Now, let's multiply this by 1/3, as shown in the original problem:
![\frac{1}{3}* 3\sqrt[3]{3}=\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%2A%203%5Csqrt%5B3%5D%7B3%7D%3D%5Csqrt%5B3%5D%7B3%7D)
Thus, the answer is .
<em>~ an aesthetics lover</em>
Answer:
Step-by-step explanation:
The given rational function is
Let
Interchange x and y
Cross multiply
Expand
Solve for y;
or
Therefore
Step-by-step explanation:
fcgfsykmcsunvdsihjiutt
A rational number is any number that can be expressed as a ratio of two integers (hence the name "rational"). For example, 1.5 is rational since it can be written as 3/2, 6/4, 9/6 or another fraction or two integers. Pi (π) is irrational since it cannot be written as a fraction.
Answer:
15 feet
Step-by-step explanation:
if the dog run is a rectangles then the formula for the perimeter is 2h+2l
if we plug in the numbers we know we get this:
2h+2(5)=40
2h+10=40
2h=30
h=15
