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Anarel [89]
3 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]3 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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viva [34]

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In summer hot days, body evaporates water in the form of sweat, in order to remain itself cool. Rise of temperature up to 100°F is normal. It is recommended to hydrate body to maintain temperature in summer days.

3 0
3 years ago
The length of vector A is 93.8 meters and the length of Ay is 38.4 meters, then the length of A, must be
vaieri [72.5K]

Answer:

85.556metres

Explanation:

Using pythagorean theorem

C²=A²+B²

we have c as the hypotenuse vector A thus:

93.8²=A²+38.4²

93.8²-38.4²=A²

8794.44-1474.56=A²

7319.88=A²

A=85.556

3 0
3 years ago
You can enter compound units that are combinations of other units that are multiplied together. to enter the ⋅ explicitly, type
alexdok [17]

Answer:

30 N \cdot m

Explanation:

The torque applied by a force can be calculated as

\tau = F d sin \theta

where

F is the magnitude of the force

d is the length of the arm

\theta is the angle between the direction of the force and the arm

In this problem, we have

F = 15 N

d = 2.0 m

\theta=90^{\circ}

Substituting into the equation, we find

\tau = (15)(2.0) sin 90^{\circ}=30 N \cdot m

7 0
3 years ago
A nonconducting container filled with 25 kg of water at 23°C is fitted with a stirrer, which is made to turn by gravity acting o
Paul [167]

Explanation:

Given that,

Weight of water = 25 kg

Temperature = 23°C

Weight of mass = 32 kg

Distance = 5 m

(a). We need to calculate the amount of work done on the water

Using formula of work done

W=mgh

W=32\times9.8\times5

W=1568\ J

The amount of work done on the water is 1568 J.

(b). We need to calculate the internal-energy change of the water

Using formula of internal energy

The change in internal energy of the water equal to the amount of the  work done on the water.

\Delta U=W

\Delta U=1568\ J

The  change in internal energy is 1568 J.

(c). We need to calculate the final temperature of the water

Using formula of the change internal energy

\Delta U=mc_{p}\Delta T

\Delta U=mc_{p}(T_{2}-T_{1})

T_{2}=T_{1}+\dfrac{\Delta U}{mc_{p}}

T_{2}=23+\dfrac{1568}{25\times4.18\times10^{3}}

T_{2}=23.01^{\circ}\ C

The final temperature of the water is 23.01°C.

(d). The amount of heat removed from the water to return it to it initial temperature is the change in internal energy.

The amount of heat is 1568 J.

Hence, This is the required solution.

6 0
3 years ago
What is the tangential velocity of a record player which makes 11 revolutions in 20 seconds? Please help
Deffense [45]

Answer:

oh umm it think its TV=11x*20s

Explanation:

4 0
3 years ago
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