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White raven [17]
3 years ago
14

A square piece of tin has 12 inches on a side. An open box is formed by cutting out equal square pieces at the corners and bendi

ng upward the projecting portion which remain. Find the maximum volume that can be obtained.
Physics
1 answer:
Citrus2011 [14]3 years ago
6 0

Answer:

Explanation:

Given a square Piece whose side is 12 inches

Now square pieces are cut from each corner to make it a open box

Suppose x is the length of square piece at each corner

then

base square has a length of 12-2x

Dimension of new box is (12-2x)\times (12-2x)\times x

Volume V=(12-2x)\times (12-2x)\times x

V=\left ( 12-2x\right )^2\cdot x

For maximum volume differentiate with respect to x we get

\Rightarrow\frac{\mathrm{d} V}{\mathrm{d} x}=2\times \left ( 12-2x\right )\times \left ( -2\right )\cdot x+\left ( 12-2x\right )^2=0

we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid

V=\left ( 12-2\cdot 4\right )^2\cdot 4

V=4^3

V=64\ in.^3

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3 0
2 years ago
What is it called cavity left behind in the rock after an organism's hard part has dissolved.
Lapatulllka [165]

Mold

Explanation:

A mold is a cavity that is left behind in the rock after an organism hard part has been dissolved. These are important fossils that useful in relative dating.

  • Some hard parts of organism are preserved in form of molds in soft sediments.
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5 0
3 years ago
Which of the following best expresses the definition of mass?
sergey [27]
The quantity of matter in a body regardless of its volume or of any forces acting on it.
4 0
3 years ago
A person is lifting a heavy box using a lever. What is the purpose of the lever in this situation?
ruslelena [56]

Answer:

to reduce the <em>force</em> needed to lift the box and <em>change</em> the direction of the force

Explanation:

1. "A lever consists of a rigid bar that is able to pivot at one point. This point of rotation is known as the fulcrum. A force is applied at some point away from the fulcrum (typically called the effort)."

By this definition, we know that force is needed to lift an object using a lever.

2.<u> "When the input and output forces are on opposite sides of the fulcrum, </u><u>the lever changes the direction of the applied force.</u> This occurs only with first-class levers. When both the input and output forces are on the same side of the fulcrum, the direction of the applied force does not change"

For example, on a sew saw, if a force is applied on one end, you on the other side/end would go up, meaning <u>a change in direction</u>.

3. Lastly, we know <u><em>a lever is typically used to reduce work</em></u>, in other words, the force needed to move something.

Basically, if we were to put a lever into an equation:

reduced force + change in direction = lever

(<em>the expection</em>) <u>unless load and force are on the same side</u>, there will be <u>no change in direction. </u>

For example, if you and your friend sit on the same side of a sew saw, the sew saw would not go up or down, meaning no change in direction.

So if not stated otherwise you can assume the load and force are on opposite sides. The purpose of a lever in that situation would be to reduce the force needed to lift the box and change the direction of the force.

*While reading my explanation, it may be helpful to look up a diagram containing a lever, with a load, fulcrum, and applied force.

6 0
2 years ago
How much heat is absorbed by a 71g iron skillet when its temperature rises from 11oC to 29oC?
diamong [38]
The right formula to use for this calculation is the heat capacity formula, 
Heat absorbed, Q = MCT, Where 
M = Mass of the substance = 71
C = Specific heat capacity for iron = 0.450 J/gc
T = Change in temperature = 29 - 11 = 18
Q = 71 * 0.450 *18 = 575.10
The amount of heat absorbed by the iron skillet is 575 J.
5 0
3 years ago
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