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Snezhnost [94]
3 years ago
5

Tara cut a square cake vertically to make 2 rectangle slices. each rectangle had a perimeter of 63 inches . how long is each sid

e of the original square cake ?
​
Mathematics
1 answer:
AlekseyPX3 years ago
7 0

Answer:

126

Step-by-step explanation:

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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)

3 0
1 year ago
Which expressions are equivalent. Picture Provided. NO LINKS! NEED ANSWER ASAP
DIA [1.3K]

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).

3 0
3 years ago
Sorry guys the highness of the % is 93 points so here you go thx for helping!!:}
agasfer [191]

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:

3 0
3 years ago
Why is the moon so ugly
statuscvo [17]

Answer:

it's not open your heart AND eyes

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Roseanne makes 1 1/2 L of lemonade. She pours 1/4 of liter of lemonade into a thermos to take to the park. Her brother drinks 2/
Elis [28]

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.

4 0
3 years ago
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