Find what n equals 8(2n-2) = 4 - 4n (explanation please)
2 answers:
Answer:
Step-by-step explanation:
In order to find the value of n that satisfies this equation, we can perform a series of algebraic steps on it to solve for n.
- <em>Distribute in the 8 on the left side:</em>
- <em />
<em> </em>
- <em>Add 4n to both sides</em>
- <em>Add 16 to both sides</em>
- <em>Divide both sides by 20</em>
Therefore, n=1 is the value of n that satisfies this equation.
Hope this helped!
You might be interested in
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
#SPJ4
Complete Question
(Image Attached)
