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vredina [299]
3 years ago
15

A lidless box is to be made using 2m^2 of cardboard find the dimensions of the box that requires the least amount of cardboard

Mathematics
1 answer:
Jlenok [28]3 years ago
5 0
1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3 . Find the dimensions of the box that requires the least amount of cardboard. Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From these, we obtain x 2y = 8 = xy2 . This forces x = y = 2, which forces z = 1. Calculating second derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus, moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).
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Hep hep math math math asap
Hoochie [10]

Answer:

V ≈ 5575.28  

Step-by-step explanation:

First, you will get the radius and in order to get the radius you have to divide 22/2 which will give you 11 then you will plug 11 into the formula which is V= 4/3 pi r^3 then it will come out as this V=4/3 pi 11^3 and if you plug that into the calculator it will give you an answer of 5575.28.

6 0
2 years ago
EASY POINTS Find the domain of the graphed function.
Vladimir [108]

Using it's concept, it is found that the domain of the graphed function is given as follows:

D. -4 \leq x \leq 2

<h3>What is the domain of a function?</h3>

It is the set that contains all possible input values for the function. In a graph, it is given by the values of x.

In this graph, x assumes values between -4 and 2, inclusive due to the closed circle, hence the domain is given by:

D. -4 \leq x \leq 2

More can be learned about the domain of a function at brainly.com/question/10891721

#SPJ1

4 0
2 years ago
If m angle GEF is thirteen less than five times m angle DEG and m angle DEF = 149º, find m angle GEF. ​
Nina [5.8K]

Answer:

122*

122 degrees

Step-by-step explanation:

m∠GEF is 13 less than 5 times m∠DEG and m∠DEF = 149*

Solution:

As per given data,

m∠GEF = 5m∠DEG - 13* … (i)

m∠DEF = 149* -> m∠GEF + m∠DEG = 149* .. (ii)

Substituting value of m∠GEF in (ii)

We get,

(5m ∠DEG - 13*) + m∠DEG = 149*

6m ∠DEG - 13* = 149*

6m ∠DEG = 149* + 13* = 162*

m∠DEG = * = 27*

Substituting value of m∠DEG in (i)

We get,

m∠GEF = 5(27*) - 13*

m∠GEF = 135* - 13* = 122*

7 0
3 years ago
Which order does it go?
gladu [14]
Subtract 4 from each side
Divide both sides by 5
Take square root of both sides
Add 3 to both sides
4 0
3 years ago
What is the quotient of 8887/4
Savatey [412]

Answer:

2221.75

Step-by-step explanation:

8887 ÷ 4 = 2221.75

4 0
2 years ago
Read 2 more answers
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