1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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).
You might be interested in
Question 4: Diego has 25 ounces of water left from a full bottle. He
Nataliya [291]

Answer:

31.25

Step-by-step explanation:

25 is 80% of the original. Divide 25 by 8 to get 10%. This is 3.125. Multiply this by 10 to get 100%, and therefore the full amount.

6 0
3 years ago
Read 2 more answers
Help me please !!<br> I need this ASAP please helpppp
Kobotan [32]

Answer:

C

Step-by-step explanation:

y=(2x-3)/5

5y=2x-3

(5y+3)/2=x

(5x+3)/2=y

f^{-1}(x)=(5x+3)/2

8 0
3 years ago
Select the equation of the line that passes through the point (5, 7) and is perpendicular to the line x = 4.
Dmitry_Shevchenko [17]
Yes, I think the answer is y = 7. The line x = 4 runs vertical (because all of the points in that line have an x-value of 4) so any line that is perpendicular to it has to be horizontal. Any line that is horizontal is in the form y = (some number). In order for the new line to run through the point (5,7) it would have to have the same y-value as that point, which is 7. So the new line is y = 7. Hope this helps :) (P.S. try graphing them both if you need a visual.)
8 0
3 years ago
Read 2 more answers
The equation y=2x+3 represents the cost y (in dollars) of mailing a package that weighs x pounds. a. Graph the equation. b. Usin
FinnZ [79.3K]

Answer:

B. Slightly more than $5

Step-by-step explanation:

y = 2x + 3

Firstly we check variables to make sure we understand.

y = dollars

x = pounds

On the scale, it says 1.126 lb. Which means 1.126 pounds.

And so, x = 1.126

y = 2x + 3

y = 2(1.126) + 3

y = 2.252 + 3

y = 2.252

The graph for part a and park b. It is underneath. I wrote 1.1, because it is rounded down from 1.126 lb, which is part b. The one with one line and no dots is part a.

4 0
2 years ago
Suppose in this semester, our Exam 1 average was about 86 with an SD of about 10. Suppose the correlation between our Exam 1 and
Oduvanchick [21]

Answer:

the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

Step-by-step explanation:

Given the data in the question;  

mean X" = 86

SD σx = 10

Y" = 76

SD σy = 8.2

r = 0.6

Here, Exam 2 is dependent and Exam 1 is independent.

The Regression equation is

y - Y" = r × σy/σx  ( x - x" )

we substitute

y - 76 = 0.6 × 8.2/10  ( x - 86 )

y  - 76 = 0.492( x - 86 )

y  - 76 = 0.492x - 42.312

y = 0.492x - 42.312 + 76

y = 0.492x + 33.688

Hence, the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

4 0
3 years ago
Other questions:
  • A second number is 6 less than a first number. A third number is twice the first number. If the sum of three number is 306, find
    11·1 answer
  • A bag contains 6 blocks:2green,1black,1white,and 2orange.if the event is drawing a black block,find the number of favorable outc
    7·1 answer
  • What is the constant of proportionality in the equation y = 2/3x?
    7·1 answer
  • Need help for this question
    11·1 answer
  • @mehek14
    5·2 answers
  • The area of the base of the box is square units if the height of the box is 10 units then what is the volume of the box
    5·2 answers
  • Can somebody help me, please?
    8·1 answer
  • Factor the algebraic expression <br> 16a + 10
    10·2 answers
  • If c/7.75 = 1/24. What does c equal?
    14·1 answer
  • Find the area of the regular polygon. Give the answer to the nearest tenth.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!