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Kobotan [32]
3 years ago
7

A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

(Let x, y, and z be the dimensions of the cardboard box.)
Mathematics
1 answer:
Reika [66]3 years ago
6 0

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 cm^{3}

The function that represents the area of the cardboard without a lid is given by

f (x,y,z) = xy + 2xz + 2yz ------  (1)

Volume of the cardboard with sides x, y & z is

xyz = 16384

z =  \frac{16384}{xy}

Put this value of z in equation (1) we get

f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )

f (x,y,z) = xy + \frac{32768}{y}  + 2y(\frac{32768}{x} )

Differentiate above equation with respect to x & y we get

f_{x}  = y - \frac{32768}{x^{2} }

f_{y}  = x - \frac{32768}{y^{2} }

Take f_{x}  = 0 \ and  \ f_{y} = 0

y - \frac{32768}{x^{2} } = 0

y = 32768 \ x^{-2}  ------ (2)

x - \frac{32768}{y^{2} } = 0

x = 32768 \ y^{-2}  ------- (3)

By solving equation (2) & (3) we get

x^{3} = 32768

x = 31 cm

From equation 2

y = 32768 \ x^{-2}

y = 32768 (31^{-2})

y = 34 cm

z =  \frac{16384}{xy}

z =  \frac{16384}{(34)(31)}

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

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Shtirlitz [24]

Divide 15 by 20 and then take that and multiply it by 16 and you'll get 12

when you have a problem like this and you need the smaller triangle measurements then the value from the smaller triangle will be on the top and if you need the larger triangle values then the larger value will be on top to find the ratios and multiply it by the other value from the denominator triangle

8 0
3 years ago
A college student completed some courses worth 3 credits and some
-BARSIC- [3]

Answer:

  • A. 13

Step-by-step explanation:

<u><em>Note:</em></u><em> It seems typo in the question. 5% should read 59.</em>

Let 3 credit courses = x, 4 credit courses = y

<u>As per  given we have following equations:</u>

  • x + y = 18
  • 3x + 4y = 59

<u>Solve the system by elimination. Multiply the first equation by 4 and subtract the second one:</u>

  • 4(x + y) - (3x + 4y) = 4(18) - 59
  • 4x + 4y - 3x - 4y = 72 - 59
  • x = 13

The answer is 13

Correct choice is A

4 0
3 years ago
Read 2 more answers
HELP! will mark BRAINILEST !
Sedbober [7]
I like A as the best one

420 = 100*price - (fixed costs)
220 = 60*price - (fixed costs)

If we subtract one from the other one, we get 200 = 40*price, price = 5
that said, fixed costs are 500 - 420 = 80

Now if we move -220 to the right in Answer A, we'll get:

y = 5x -300 + 220 = 5x - 80

So it looks like A describes the model best
6 0
3 years ago
Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros.
kifflom [539]
The given statement is:
An integer is divisible by 100 if and only if its last two digits are zeros

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have last two digits zeros. 

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, the option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true
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telo118 [61]

Answer:

0.0024

Step-by-step explanation:

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