I add up all of the terms that is given and got that Darrel wins.
Answer:
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Step-by-step explanation:
Given in the question a piece of cardboard having dimensions 32 by 40
Suppose we cut square of length x
When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths
<h3>Step 1</h3>
Formula for the volume of box
v = height * length * width
v = x (32-2x) (40-2x)
v = 4x³ - 144x² + 1280x
<h3>Step 2</h3>
Find derivative and equal it to 0
dv/dx = 4(3)x² - (2)144x + 1280
0 = 12x² - 288x + 1280
x1 = 18.110
x2 =5.88
<h3>Step 3</h3>
Select x and plug value of x to find dimension
(32-2x) > 0
2x < 32
x < 16
so domain say that x should be less than 16 which means x = 5.88 ≈ 6 cm
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Answer:
Yes, \sqrt{2}(\sqrt{3.5} + 2\sqrt{5} )
Step-by-step explanation:
By roots property, the roots can be re-write as multiplications or division, like this:
![\sqrt[n]{a} . \sqrt[n]{b} =\sqrt[n]{ab}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20.%20%5Csqrt%5Bn%5D%7Bb%7D%20%3D%5Csqrt%5Bn%5D%7Bab%7D)
Here, we can re-write both roots:
and 
Now we have:
And we can take out the common expression:
⇒ Answer
