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26 Μαΐ 2020 · After cutting out the squares from the corners, the width of the open-top box will be 5-2x, and the length will be 7-2x. We’re being asked to maximize the volume of a box, so we’ll use the formula for the volume of a box, and substitute in the length, width, and height of the open-top box.
If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. The quantity we want to optimize is the volume of the box. Let V be the volume of the box. We want to find the maximum value of V.
21 Δεκ 2020 · The remaining flaps are folded to form an open-top box. Step 1: We are trying to maximize the volume of a box. Therefore, the problem is to maximize \(V\). Step 2: The volume of a box is \(V=L⋅W⋅H\), where \(L,W,\)and \(H\) are the length, width, and height, respectively.
21 Μαρ 2023 · $$Volume= xy \left(\frac{A-xy}{2(x+y)}\right)$$ Then I need to find $\frac{d}{dx} xy \left(\frac{A-xy}{2(x+y)}\right)$ and $\frac{d}{dy} xy \left(\frac{A-xy}{2(x+y)}\right)$ Here are the derivatives $$\frac{d}{dx} xy \left(\frac{A-xy}{2(x+y)}\right)=\frac{y^2(a-x^2-2xy)}{2(x^2+y^2+2xy)}$$ $$\frac{d}{dy} xy \left(\frac{A-xy}{2(x+y)}\right ...
A box with a square base and an open top is to be made. You have $1200\operatorname{cm}^2$ of material to make it. What is the maximum volume the box could have? Here's what I did: $$1200 = x^2+4xz;$$ where $x$ is length of base and $z$ is height of box. Also, let the volume of box be $V$, then
30 Ιουλ 2024 · To find the volume of a box, simply multiply length, width, and height — and you're good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters. For dimensions that are relatively small whole numbers, calculating volume by hand is easy.
20 Σεπ 2024 · An open-top box is to be made from a 35 inches by 50 inches piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. Part A. If inches is the amount to be removed from each corner, write a formula for the volume of the box.
