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loris [4]
3 years ago
8

How to do this here

Mathematics
1 answer:
Andru [333]3 years ago
8 0
Refer to the attached photo to see the problem worked out
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Which expression is equivalent to |x| > 9
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D)
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3 years ago
Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

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

brainly.com/question/14682292

#SPJ4

Complete Question

(Image Attached)

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WILL MARK BRAINLIEST!!!!<br> What is the equation of the line shown in this graph?
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Y=1 because no matter the x value y will be 1
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Y = (- 2x - 4)² + 1<br> what transformations were done?
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No x-intercept/Zero

Step-by-step explanation:

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What is the slope and y-intercept of this line?y -6x 2
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In the slope intercept method, it is very simple to find the y intercept and the slope. The slope is always accompanied with the x so in this problem, the slope is -6 meaning it has a negative correlation (it's pointing down on the graph) the y intercept is the other number on that side of the equals sign. It is 2 and is positive. 
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