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Anarel [89]
4 years ago
12

You are planning to make an open rectangular box from an 8-inch by 15-inch piece of cardboard by cutting congruent squares from

the corners and folding up the sides. what is the largest volume you can make from a box this way in cubic inches?
Physics
1 answer:
Phoenix [80]4 years ago
4 0

Let us say that x is the cut that we will make on the sides to make a box, therefore the new dimensions are:

l = 15 – 2x

w = 8 – 2x

It is 2x since we cut on two sides.

 

We know that volume is:

V = l w x

V = (15 – 2x) (8 – 2x) x

V = 120x – 30x^2 – 16x^2 + 4x^3

V = 120x – 46x^2 + 4x^3

 

Taking the 1st derivative:

dV/dx = 120 – 92x + 12x^2

 

Set dV/dx = 0 to get maxima:

120 – 92x + 12x^2 = 0

 

Divide by 12:

x^2 – (92/12)x + 10 = 0

(x – (92/24))^2 = -10 + (92/24)^2

x - 92/24 = ±2.17

x = 1.66, 6

We cannot have x = 6 because that will make our w negative, so:

x = 1.66 inches

 

So the largest volume is:

V = 120x – 46x^2 + 4x^3

V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3

V = 90.74 cubic inches

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Ben hit a 0.25kg nail into a wood with a 5.2kg hammer. If the hammer moves witht the speed of 52 m/s and two fifth of its kineti
Art [367]

Answer:

Explanation:

Mass of nails is 0.25kg

Mass of hammer 5.2kg

Speed of hammer is =52m/s

Then, Ben kinetic energy is given as

K.E= ½mv²

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Internal energy (I.E) = 2/5 × K.E

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7 0
3 years ago
What total mass must be converted into energy
Eduardwww [97]

This question apparently wants you to get comfortable
with  E = m c² .  But I must say, this question is a lame
way to do it.

c = 3 x 10⁸ m/s
                                                    E = m c²

                           1.03 x 10⁻¹³ joule  =  (m) (3 x 10⁸ m/s)²

Divide each side by (3 x 10⁸ m/s)²:

                         Mass = (1.03 x 10⁻¹³ joule) / (9 x 10¹⁶ m²/s²)

                                   =  (1.03 / 9) x (10⁻¹³ ⁻ ¹⁶) (kg)

                                   =        1.144 x 10⁻³⁰  kg .    (choice-1)

This is roughly the mass of (1 and 1/4) electrons, so it seems
that it could never happen in nature.  The question is just an
exercise in arithmetic, and not a particularly interesting one.
______________________________________

Something like this could have been much more impressive:
 
The Braidwood Nuclear Power Generating Station in northeastern
Ilinois USA serves Chicago and northern Illinois with electricity.
<span>The station has two pressurized water reactors, which can generate
a net total of 2,242 megawatts at full capacity, making it the largest
nuclear plant in the state.
If the Braidwood plant were able to completely convert mass
to energy, how much mass would it need to convert in order
to provide the total electrical energy that it generates in a year,
operating at full capacity ?

Energy = (2,242 x 10⁶ joule/sec) x (86,400 sec/day) x (365 da/yr)

             =  (2,242 x 10⁶ x 86,400 x 365) joules

             =          7.0704 x 10¹⁶ joules .

How much converted mass is that ?

                                           E  =  m c²

Divide each side by  c² :    Mass  =  E / c² .
c = 3 x 10⁸ m/s

              Mass = (7.0704 x 10¹⁶ joules) / (9 x 10¹⁶ m²/s²)

                        =        0.786 kilogram ! ! !

THAT should impress us !  If I've done the arithmetic correctly,
then roughly  (1 pound  11.7 ounces) of mass, if completely
converted to energy, would provide all the energy generated
by the largest nuclear power plant in Illinois, operating at max
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</span>
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Answer:

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Explanation:

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