The first step to solving this expression is to factor out the perfect cube
![\sqrt[3]{m^{2} n^{3} X n^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bm%5E%7B2%7D%20%20n%5E%7B3%7D%20X%20n%5E%7B2%7D%20%20%20%7D%20)
The root of a product is equal to the product of the roots of each factor. This will make the expression look like the following:
![\sqrt[3]{ n^{3} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%20n%5E%7B3%7D%20%7D%20)
![\sqrt[3]{ m^{2} n^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%20m%5E%7B2%7D%20n%5E%7B2%7D%20%20%7D%20)
Finally,, reduce the index of the radical and exponent with 3
n
This means that the correct answer to your question is n
![\sqrt[3]{ m^{2} n^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%20m%5E%7B2%7D%20n%5E%7B2%7D%20%7D%20)
.
Let me know if you have any further questions
:)
Answer:
$200
Step-by-step explanation:
First, find the unit rate:
12/3= 4
Then multiply:
4*50= 200
Hope this helps!
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
To learn more about Maximization visit
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Complete Question
(Image Attached)
Answer:
<h3>k = 10</h3>
Step-by-step explanation:
Given the equation;
We are to find the value of k.
Cross multiply;
Divide both sides by 10
Hence the value of k is 10
48 ten units and 1 five unit.
