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
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Complete Question
(Image Attached)
Answer:
You distribute the 2xy and get
2xy(3xy + 5y - xy^2) = 6(x^2)(y^2) + 10xy^2 - 2(x^2)(y^3)
C. Got you man.
Lemme know if I’m right
Answer:
3x - y + 
Step-by-step explanation:
Hooboy okay here we go.
1.) Rewrite the equation in the classic division method
3x³ + 2x²y - xy² 
2.) Divide using normal division rules, but it's super hard now 'cause there are letters involved. Basically, what can you multiply 3x³ by to get 9x⁴? 3x. So 3x is your first number. Then multiply everything else by 3x, and subtract
3x
3x³ + 2x²y - xy²
-(9x⁴ + 6x³y - 3x²y²)
= 0 - 3x³y - 2x²y² - 5x²y + xy³
Now lets do that again, see what happens. 3x³ times -y should get -3x³y
3x - y
3x³ + 2x²y - xy²
- (9x⁴ + 6x³y - 3x²y²)
= 0 - 3x³y - 2x²y² - 5x²y + xy³
- ( - 3x³y - 2x²y² + xy³)
= 0 + 0 - 5x²y + 0
So! From this information, we can know that the answer is 3x-y with a remainder of - 5x²y. How it's written is shown above, in "Answer"
Answer:
<h2>
18000 seconds!</h2>
Step-by-step explanation:
<h2>
<u>5 hours is 18000 seconds!</u></h2>
