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pochemuha
3 years ago
14

Worth 20 points

Mathematics
1 answer:
sladkih [1.3K]3 years ago
3 0
D(X+2)(2X+1) This is your answer. 

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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
Jlenok [28]
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).
5 0
3 years ago
If x^3 times x^b equals x^15, which could be a correct value for "b?"
crimeas [40]
B=5
Hope this helps!
Vote me brainliest!
4 0
3 years ago
(-4,19) and (8,-2) whats the slope intercept
Sever21 [200]

Answer:

slope = -7/4

Step-by-step explanation:

Plug the points into this formula: \frac{y2 - y1}{x2 - x1}

Plug in

\frac{-2 - 19}{8 - (-4)} \\\\\frac{-21}{12} = -7/4

The simplest form is -7/4

Hope this helps ya! Keep smiling!

6 0
3 years ago
Find the present to increase.round to the nearest percent. From 13 friends to 19 friends
vlada-n [284]

Answer:

20%

Step-by-step explanation:

4 0
3 years ago
What is the unknown digit 5.723<572?<5.725
vovangra [49]
The unknown digit is 5.724
4 0
3 years ago
Read 2 more answers
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