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
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Answer:
B) 3^-5 <em>(1 / 243)</em> and D) 2^5 x 6^-5 <em>(</em><em>1</em><em> </em><em>/</em><em> </em><em>2</em><em>4</em><em>3</em><em>)</em>
Step-by-step explanation:
3 to the negative 5th power as a fraction is
1 / 243.
2 to the power of 5 multiplied by 6 to the power of negative 5 also equals 1 / 243.
Both expressions are equivalent to 2^5 / 6^5 because they equal the same thing (1 / 243).
Answer:
Thanks! But why report when the people can't see this question or even get the points since its from a while ago
step-by-step explanation:
Answer:
it's not open your heart AND eyes
Step-by-step explanation:
Answer:
1/2 L
Step-by-step explanation:
She makes 1 1/2 L of lemonade i.e. 3/2 L of lemonade.
She pours 1/4 of liter of lemonade into a thermos to take to the park. The amount of lemonade left is:
3/2 - 1/4 = 1 1/4 L = 5/4 L
Her brother drinks 2/5 of the remaining lemonade. The amount of lemonade that her brother drinks is:
2/5 * 5/4 = 1/2 L
Her brother drinks 1/2 L.
