The thermal emission of the human body has maximum intensity at a wavelength of approximately 9.5 μm.What photon energy corresponds to this wavelength?

Answers

Answer 1

Answer:

Explanation:

2.1 x 10^2 - 20J


Related Questions

A car travels 150 kilometers west in 3 hours. What is its average velocity?
Your answer:
150 km/hr

50 km/hr

50 km/hr west

150 km/hr west

Answers

Answer:

C= 50km/hr west

Explanation:

150/3= 50

Because it asks for velocity, make sure to include the direction as well.

125 cm of gas are collected at 15 °C and
755 mmHg pressure. Calculate the volume of
the gas at s.t.p.​

Answers

The new volume will be ≈26mL
rounded to two significant figures.
Explanation:
This question involves the combined gas law. The equation to use is:
When working with gas laws, the temperature is always in Kelvins. To get Kelvins from a Celsius temperature, add 273.15 to the Celsius temperature.

The new springs will be identical to the original springs, except the force constant will be 5655.00 N/m smaller. When James removes the original springs, he discovers that the length of each spring expands from 8.55 cm (its length when installed) to 12.00 cm (its length with no load placed on it). If the mass of the car body is 1355.00 kg, by how much will the body be lowered with the new springs installed, compared to its original height

Answers

Answer:

Explanation:

For original spring , compression in spring due to a load of 1355 kg is

x = 12 - 8.55 = 3.45 cm = .0345 m

spring constant = W / x

= 1355 x 9.8 / .0345

= 384898.55 N /m

Spring constant of new spring

k = 384898.55 - 5655 = 379243.55 N /m

New compression for new spring

= W / k

= 1355 x 9.8 / 379243.55

= .035 m

= 3.50 cm

Difference of compression = 3.50 - 3.45

= .05 cm .

In later case , car will be more lowered by .05 cm .

It has been suggested that rotating cylinders several miles in length and several miles in diameter be placed in space and used as colonies. Inhabitants of the space colonies would live on the inside surface of the cylinder. Inertial effects would resemble gravity's influence and keep them 'plastered to the surface.' Suppose that you are an inhabitant of a space colony which is 1070 miles in length and 4.86 miles in diameter. How many revolutions per hour must the cylinder have in order for the occupants to experience a centripetal acceleration equal to the acceleration of gravity

Answers

Answer:

the required revolution per hour is 28.6849

Explanation:

Given the data in the question;

we know that the expression for the linear acceleration in terms of angular velocity is;

[tex]a_{c}[/tex] = rω²

ω² = [tex]a_{c}[/tex] / r

ω = √( [tex]a_{c}[/tex] / r )

where r is the radius of the cylinder

ω is the angular velocity

given that; the centripetal acceleration equal to the acceleration of gravity a [tex]a_{c}[/tex]  = g = 9.8 m/s²

so, given that, diameter = 4.86 miles = 4.86 × 1609 = 7819.74 m

Radius r = Diameter / 2 = 7819.74 m / 2 = 3909.87 m

so we substitute

ω = √( 9.8 m/s² / 3909.87 m )

ω = √0.002506477 s²  

ω = 0.0500647 ≈ 0.05 rad/s  

we know that; 1 rad/s = 9.5493 revolution per minute

ω = 0.05 × 9.5493 RPM

ω = 0.478082 RPM  

1 rpm = 60 rph  

so  

ω = 0.478082 × 60

ω = 28.6849  revolutions per hour  

Therefore, the required revolution per hour is 28.6849

The required revolution per hour is 28.6849

Calculation of revolution per hour:

The expression for the linear acceleration with respect to the angular velocity is

= rω²

So,

ω² =  / r

ω = √(  / r )

Here r represent the radius of the cylinder

ω represent the angular velocity

Now

diameter = 4.86 miles = 4.86 × 1609 = 7819.74 m

And,

Radius r = Diameter / 2 = 7819.74 m / 2 = 3909.87 m

So,

ω = √( 9.8 m/s² / 3909.87 m )

ω = √0.002506477 s²  

ω = 0.0500647 ≈ 0.05 rad/s  

Now

1 rad/s = 9.5493 revolution per minute

So,

ω = 0.05 × 9.5493 RPM

ω = 0.478082 RPM  

Now

1 rpm = 60 rph  

so  

ω = 0.478082 × 60

ω = 28.6849  revolutions per hour  

Learn more about the cylinder here: https://brainly.com/question/17262276

What is net force?
OA. a push or a pull
B. A measure of how fast an object is moving
OC. The amount of energy an object has
D. The combination of all forces acting on an object.

Answers

The answer is d my friend :)

Answer:

D

Explanation:

The net force is the combination of all forces acting on an object.

When rubbing a balloon against your head, you notice the balloon pulling your hair away from your head. What best explains why the balloon and your hair are attracted to each other?

They become oppositely charged, which causes them to be attracted to each other.

They become similarly charged, which causes them to be attracted to each other.

They stick together because of the friction between the two objects.

They are made of different materials, which is why they attract each other.

Answers

Answer:

They become oppositely charged, which causes them to be attracted to each other.

Answer: number A

Explanation:

If a positive charge and a negative charge interact, their forces act in the same direction, from the positive to the negative charge. As a result opposite charges attract each other: The electric field and resulting forces produced by two electrical charges of opposite polarity. Have a nice day <3

A 14.0-g wad of sticky clay is hurled horizontally at a 90-g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides 7.50 m before coming to rest. If the coefficient of friction between block and surface is 0.650, what was the speed of the clay immediately before impact

Answers

Answer:the speed of the clay immediately before impact =72.58m/s

Explanation:

Given that  

mass of the stick clay, M₁= 14.0 g = 0.014 kg

mass of the block ,M₂= 90 g = 0.09 kg

Therefore the total mass= (M₁+M₂) = 104g = 0.104 kg

Also, distance, s = 7.50 m

coefficient of friction μ= 0.650

Acceleration due to gravity ,g = 9.8 m/s²

 

Using the Work- Energy theorem,

change in kinetic energy =  work done

final kinetic energy(K₂) - initial  kinetic energy(K₁) =   force, F x coefficient of friction, μ x distance,s

The final kinetic energy is zero  because after the impact,  the block with the clay comes to a stop after 7.50m

kinetic energy =Work done

0.5 x m x v²=coefficient of friction,  μ x force(F)  x  distance,s(Since force = m g )

0.5 x m x v²= μ x m x g x s

0.5 x 0.104 x v² = 0.650 x 0.104x 9.8 x 7.5

v²= 0.650 x 0.104x 9.8 x 7.5 / 0.5 x 0.104

v²==95.55

V = 9.77 m/s

Using the  conservation of momentum formulae where

M₁ V₁ + M₂ V₂ = (M₁ + M₂ ) V

Since V₂  which is the velocity of block  is zero as the  block is initially at rest, We now have that

M₁ V₁ = (M₁ + M₂ ) V

0.014 kg x V₁ = 0.104 x 9.77

V₁=0.104 x 9.77 / 0.014

V=72.58m/s

Two very small +3.00-μC charges are at the ends of a meter stick. Find the electric potential (relative to infinity) at the center of the meter stick.

Answers

Answer:

The electric potential at the center of the meter stick is 54 KV.

Explanation:

Electric potential (V) is given as:

i.e V = [tex]\frac{kq}{r}[/tex]

Where: k is the Coulomb constant, q is the charge and r is the distance.

Given: q = 3.0 μC = 3.0 x [tex]10^{-6}[/tex] C, r = 0.5 m

So that,

V = [tex]\frac{9*10^{9}*3.0*10^{-6} }{0.5}[/tex]

   = [tex]\frac{2.7*10^{4} }{0.5}[/tex]

V = 54000

  = 54 000 volts

The electric potential at the center of the meter stick is 54 KV.

A hedgehog lives in a backyard in England. Every night, the house owner puts out a bowl of canned cat food and hard-boiled egg. The hungry hedgehog eats some of the food, then stops when it is no longer hungry. This pattern helps the hedgehog to maintain a steady energy level and weight.

What is the name for keeping a stable internal environment despite changes in the outside environment?

A. hormonal control
B. stimulus and response
C. balance
D. homeostasis

Answers

Answer: I think it C and B but I am really confident in C

Explanation:

Need help on another homework question

Rick places the blue lens of one pair of 3D glasses over the red lens of another pair. He then looks through both lenses at the same time. What color will he see?

A. blue
B. black
C. red
D. white

Answers

Black
Explanation : I've tried

Answer:

a

Explanation:

Potential energy is energy due to motion.
True or False?

Answers

Answer:

true

Explanation:

Answer:

true

Explanation:

please give brainlest need 1

A crate rests on a flatbed truck which is initially traveling at 17.9 m/s on a level road. The driver applies the brakes and the truck is brought to a halt in a distance of 46.1 m. If the deceleration of the truck is constant, what is the minimum coefficient of friction between the crate and the truck that is required to keep the crate from sliding

Answers

Answer:

The minimum coefficient of friction required is 0.35.  

Explanation:

The minimum coefficient of friction required to keep the crate from sliding can be found as follows:

[tex] -F_{f} + F = 0 [/tex]      

[tex] -F_{f} + ma = 0 [/tex]      

[tex] \mu mg = ma [/tex]

[tex] \mu = \frac{a}{g} [/tex]

Where:

μ: is the coefficient of friction

m: is the mass of the crate

g: is the gravity

a: is the acceleration of the truck

The acceleration of the truck can be found by using the following equation:

[tex] v_{f}^{2} = v_{0}^{2} + 2ad [/tex]

[tex] a = \frac{v_{f}^{2} - v_{0}^{2}}{2d} [/tex]

Where:  

d: is the distance traveled = 46.1 m

[tex] v_{f}[/tex]: is the final speed of the truck = 0 (it stops)      

[tex]v_{0}[/tex]: is the initial speed of the truck = 17.9 m/s

[tex] a = \frac{-(17.9 m/s)^{2}}{2*46.1 m} = -3.48 m/s^{2} [/tex]        

If we take the reference system on the crate, the force will be positive since the crate will feel the movement in the positive direction.  

[tex] \mu = \frac{a}{g} [/tex]  

[tex] \mu = \frac{3.48 m/s^{2}}{9.81 m/s^{2}} [/tex]

[tex] \mu = 0.35 [/tex]

Therefore, the minimum coefficient of friction required is 0.35.  

I hope it helps you!

Velocity time graph and how to draw it

Answers

Answer:

Velocity time graph

Explanation:

Draw on graph paper two straight lines originating at the same point and perpendicular to each other. This is the x-y axis. The x-axis is the horizontal line and the y-axis is the vertical line.

Mark appropriate equally-spaced time intervals on the x-axis so that you can easily graph the time values from the table.

Mark appropriate velocity increments on the y-axis so that you can easily graph the velocity values from the table. If you have negative velocity values, extend the y-axis downward.

Find the first time value from the table and locate it on the x-axis. Look at the corresponding velocity value and find it on the y-axis.

Put a dot where a straight line vertically drawn up through the x-axis value and a straight line horizontally drawn through the y-axis value intersect.

Plot in similar fashion for all other velocity-time pairs in your table.

Draw a straight line with a pencil, connecting each dot you have put down on the graph paper, going from left to right

Two people each do 100 joules of work by pushing a crate to the right. During this process, 50 joules of heat is generated from the
friction between the floor and the crate. How much energy is gained by the crate during this process?

Answers

Because of friction, net work on the crate is less. ∆KE = Net work = net force x distance = (100 N – 70 N)(10 m) = 300 J.

A parallel-plate capacitor is connected to a battery until it is fully charged. Then, the capacitor is disconnected from the battery and connected to two uncharged parallel plates that make up a capacitor. The potential between the plates of the initial capacitor will

Answers

Answer:

The potential between the plates will decrease.

Explanation:

An insulator is usually placed between the parallel plates and is also called a dielectric because it makes the amount of charge a capacitor can accommodate to increase at a particular potential difference.

Furthermore, the dielectric effect will make the electric field of the charged capacitor which is not connected to a source of supply to decrease.

Now, when the battery is removed, the charge Q remains constant and Capacity C will increase.

Formula for the potential difference is here;

V = Q/C

Since the numerator Q is constant and the denominator C increases, it means the potential difference V will decrease

m
A 3.0 kg model train going right at 2.8 bumps into another 2.0 kg model train car moving in the same
S
m
direction at 1.6 . The heavier train car has a final speed of 2.2 to the right.
S
S
What is the final speed of the lighter 2.0 kg train car?

Answers

Answer:

it’s 2.5 m/s

Explanation:

i’m too lazy but trust

This question can be solved by using the law of conservation of momentum.

The final speed of the lighter 2 kg train is " 2.5 ".

When two moving objects collide with each other, the law of conservation of momentum can be applied to them as follows:

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/tex]

where,

m₁ = mass of heavier train = 3 kg

m₂ = mass of lighter train = 2 kg

u₁ = initial speed of heavier train = 2.8

u₂ = initial speed of lighter train = 1.6

v₁ = final speed of heavier train = 2.2

v₂ = final speed of lighter train = ?

Therefore,

(3 kg)(2.8) + (2 kg)(1.6) = (3 kg)(2.2) + (2 kg)(v₂)

[tex]v_2 = \frac{5 kg}{2 kg}[/tex]

v₂ = 2.5

Learn more about the law of conservation of momentum here:

https://brainly.com/question/1113396?referrer=searchResults

The attached picture illustrates the law of conservation of momentum.

two faer coin and unbayers
dice are thrown together list the
Sample space
determine the probabilities that
A head and even number
A prime number and atleast a tail​

Answers

Say A be the event of getting head and B be the event of getting six.

So probability of getting head or six =

P = P(A) + P(B) - P(A intersection B)

P = (1/2) + (1/6) - (1/12)

P = 7/12

Also you can do by the following method :-

Total possible outcomes-

[ {H,1},{H,2},{H,3},{H,4},{H,5},{H,6},{T,1},{T,2},{T,3},{T,4},{T,5},{T,6} ] = 12 outcomes

Favourable = [ {H,1},{H,2},{H,3},{H,4},{H,5},{H,6},{T,6}] = 7 outcomes

So P = 7/12

A point charge, Q1 = -4.2 μC, is located at the origin. A rod of length L = 0.35 m is located along the x-axis with the near side a distance d = 0.45 m from the origin. A charge Q2 = 10.4 μC is uniformly spread over the length of the rod.Part (a) Consider a thin slice of the rod, of thickness dx, located a distance x away from the origin. What is the direction of the force on the charge located at the origin due to the charge on this thin slice of the rod? Part (b) Write an expression for the magnitude of the force on the point charge, |dF|, due to the thin slice of the rod. Give your answer in terms of the variables Q1, Q2, L, x, dx, and the Coulomb constant, k. Part (c) Integrate the force from each slice over the length of the rod, and write an expression for the magnitude of the electric force on the charge at the origin. Part (d) Calculate the magnitude of the force |F|, in newtons, that the rod exerts on the point charge at the origin.

Answers

Answer:

a) attractiva, b) dF = [tex]k \frac{Q_1 \ dQ_2}{dx}[/tex], c)  F = [tex]k Q_1 \frac{Q_2}{d \ (d+L)}[/tex], d) F = -1.09 N

Explanation:

a) q1 is negative and the charge of the bar is positive therefore the force is attractive

b) For this exercise we use Coulomb's law, where we assume a card dQ₂ at a distance x

           dF = [tex]k \frac{Q_1 \ dQ_2}{dx}[/tex]

where k is a constant, Q₁ the charge at the origin, x the distance

c) To find the total force we must integrate from the beginning of the bar at x = d to the end point of the bar x = d + L

         ∫ dF = [tex]k \ Q_1 \int\limits^{d+L}_d {\frac{1}{x^2} } \, dQ_2[/tex]

as they indicate that the load on the bar is uniformly distributed, we use the concept of linear density

          λ = dQ₂ / dx

          DQ₂ = λ dx

we substitute

         F = [tex]k \ Q_1 \lambda \int\limits^{d+L}_d \, \frac{dx}{x^2}[/tex]

         F = k Q1 λ ([tex]-\frac{1}{x}[/tex])  

we evaluate the integral

        F = k Q₁ λ [tex](- \frac{1}{d+L} + \frac{1}{d} )[/tex]

        F = k Q₁ λ  [tex]( \frac{L}{d \ (d+L)})[/tex]

we change the linear density by its value

      λ = Q2 / L

       F = [tex]k Q_1 \frac{Q_2}{d \ (d+L)}[/tex]

d) we calculate the magnitude of F

       F =9 10⁹ (-4.2 10⁻⁶)   [tex]\frac{10.4 10x^{-6} }{0.45 ( 0.45 +0.35)}[/tex]

       F = -1.09 N

the sign indicates that the force is attractive

Answer:

a)Toward the rod

b)|dF| = k|Q1|Q2(dx/L)/x^2

c)|F| = k|Q1|Q2/(d(d+L))

d)Plug in for answer c and solve

Explanation:

A)

Q1 is negative and Q2 is positive so it is an attractive force to  where the rod is located.

B)

The formula for Force due to electric charges is F=kQ1Q2/r^2

In this case, Q2 is distrusted through the length of the rod as opposed to a single point charge. As such Q2 is actually Q2*dx/L as dx is a small portion of the full length, L.

The radius between Q1 and Q2 depends on the section of the rod taken so r will be the variable x distance from Q1.

The force is only from a small portion of the rod so more accurately, we are finding |dF| as opposed to the full force, F, caused by the whole rod.

The final formula is |dF| = k|Q1|Q2(dx/L)/x^2

C)

Integrating with respect to the only changing variable, x, which spans the length of the rod, from radius = d to d+L we get this:

F = integral from d to d+L of k|Q1|Q2(dx/L)/x^2

factor out constants

F = kQ1Q2/L * integral d to d+L(1/x^2)dx

F = kQ1Q2/L * (-1/x)| from d to d+L

F = kQ1Q2/L * (-1/d+L - -1/d)

F = kQ1Q2/L * (-d/(d(d+L)) + (d+L)/(d(d+L))

F = kQ1Q2/L * (L)/(d(d+L))

F = kQ1Q2/(d(d+L))

D)

Plug in the given values into c and you have your answer.

The force of gravity on a person or object on the surface of a planet is called
A. gravity
ОВ.
B. free fall
OC
c. terminal velocity
D. weight

Answers

Answer:

D. Weight

Explanation:

Hope that helps:)

D. Weight is the correct answer.
HOPE IT HELPS U!!!!!!

For PN junctions, determine if each statement below is True or False:

a. There can be large net current from p-side to n-side under forward bias.
b. There can be large net current from n-side to p-side under reverse bias if reverse bias is sufficiently high.
c. Electron diffusion current flows from n-side to p-side.
d. Electric field magnitude is higher under reverse bias
e. Electrons in the transition region drift from p-side to n-side.

Answers

Answer:

a) True

b) True

c) false

d) True

e) True

Explanation:

a) True

In forward bias, the resistance of the p–n junction reduces and hence the electric charges can flow easily.

b) True

In reverse bias condition, the electric current is due to the minority charge carriers (negative).

c) False

direction of diffusion current is in the direction of movement of positive charge i,e towards n side

d) True

Because the breakdown of charge carriers occur due to which the current increases rapidly

e) True

a passenger on cruise between San Juan, Puerto Rico and Miami, Florida accidentally drops a souvenir metal cube over the side of the boat, into the water. Each side of the metal cube measures 1 meter. The cube promptly sinks to the deepest part of the Puero Rico Trench. Once at the bottom, what pressure does the cube experience? Neglect Atmospheric Pressure. Use wikipedia to see depth of Trench!

Answers

Answer:

P = 84.1 MPa

Explanation:

The pressure at the bottom of column of of salt water of height h, is given by the following expression:

       [tex]P = \rho * g * h (1)[/tex]

       where ρ = density of salt water (in Kg/m³),

       g = acceleration due to  gravity  (in m/s²)

       h = height of the column of water.

Replacing by their values in (1):

      [tex]P = \rho * g * h = 1023.6kg/m3*9.8m/s2*8380m = 84.1 MPa (2)[/tex]

Neglecting the atmospheric pressure, the pressure on the cube at the bottom of Puerto Rico Trench is given by (2):P = 84.1 MPa.

An ideal gas in a 50.0 L tank has a
pressure of 2.45 atm at 22.5°C.
How many moles of gas are in
the tank?

Answers

Answer:

5.05225 moles

Explanation:

The computation of the number of moles of gas in the tank is shown below:

Given that

Volume = V = 50 L = 50.0 × 10^-3m^3

Pressure = P = 2.45 atm = 2.45 × 101325

Temperature = T = 22.5°C  = (22.5 + 273)k = 295.5 K

As we know thta the value of gas constant R is 8.314 J/mol.K

Now

PV = nRT

n = PV ÷ RT

= ((2.45 × 101325) (50.0 × 10^-3)) ÷ ((8.314) (295.5))

= 5.05225 moles

A loaded wagon of mass 10,000 kg moving with a speed of 15 m/s strikes a stationary wagon of the same mass making a perfect inelastic collision. What will be the speed of coupled wagons after collision?

Answers

Answer:

7.5 m/s

Explanation:

Unfortunately, I don't have an explanation but I guessed the correct answer.

An aluminum wire having a cross-sectional area equal to 2.20 10-6 m2 carries a current of 4.50 A. The density of aluminum is 2.70 g/cm3. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire.

Answers

Answer:

The drift speed of the electrons in the wire is 2.12x10⁻⁴ m/s.

Explanation:

We can find the drift speed by using the following equation:

[tex] v = \frac{I}{nqA} [/tex]

Where:

I: is the current = 4.50 A

n: is the number of electrons

q: is the modulus of the electron's charge = 1.6x10⁻¹⁹ C

A: is the cross-sectional area = 2.20x10⁻⁶ m²

We need to find the number of electrons:

[tex] n = \frac{6.022\cdot 10^{23} atoms}{1 mol}*\frac{1 mol}{26.982 g}*\frac{2.70 g}{1 cm^{3}}*\frac{(100 cm)^{3}}{1 m^{3}} = 6.03 \cdot 10^{28} atom/m^{3} [/tex]                  

Now, we can find the drift speed:

[tex]v = \frac{I}{nqA} = \frac{4.50 A}{6.03 \cdot 10^{28} atom/m^{3}*1.6 \cdot 10^{-19} C*2.20 \cdot 10^{-6} m^{2}} = 2.12 \cdot 10^{-4} m/s[/tex]              

Therefore, the drift speed of the electrons in the wire is 2.12x10⁻⁴ m/s.

I hope it helps you!      


Bill is walking to the store and he walks the first 500m in 60s. He then runs 1000m in 90s. After stopping for 45s, he was the remaining 450m to the store in 50s. What is the average velocity for Bills entire
trip?

Answers

Answer:

letra A segundo o couculo a divisão e completa

Why are carbon atoms able to form many organic compounds?

A. Carbon atoms have strong attraction to other elements.

B. Carbon atoms attract electrons from other atoms.

C. Carbon atoms can form many types of bonds with other carbon.

D. All of the above​

Answers

Answer:

yo imma so I dunno find out yourself

Explanation:

dhdhdhdnndsisijjsksskskekekekkekssisisieieieiiwiwiwieiwieidjdjddi?

Which list of reaction types are all redox reactions?
A.
Synthesis, decomposition, single-replacement, combustion
B.
Synthesis, double-replacement, combustion, decomposition
C.
Acid-base, single-replacement, double-replacement, synthesis
D.
Decomposition, double-replacement, acid-base, synthesis

Answers

A. Synthesis, decomposition, single-replacement, combustion

List of reaction types are redox reactions:

Synthesis, decomposition, single-replacement, combustion.What are redox reaction ?

"Redox reactions are oxidation-reduction chemical reactions in which the reactants undergo a change in their oxidation states." The term 'redox' is a short form of reduction-oxidation. All the redox reactions can be broken down into two different processes – a reduction process and an oxidation process.

Know more about redox reaction here

https://brainly.com/question/13293425

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A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lbs of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank the mixture at 2 gpm. Find the amount of salt in the tank at the end of 30 minutes.
A. 171.24 lbs
B. 124.11 lbs
C. 143.25 lbs
D. 105.12 lbs

Answers

Answer:

A. 171.24 Ibs

Explanation:

To find the amount of salt in the tank,

Let Q = Amount of salt in the mixture

And let 100 + (3-2)t = 100 + t be the volume of mixture at anytime t.

Rate of gain - Rate of loss = dQ / dt

Concentration of salt = Q / (100+t)

For the linear differential equation,

dQ / dt = 3(2) - 2 [Q/ (100 + t)]

dQ /dt + Q [2 / (100 + t)] = 6

The general solution of the linear differential equation is:

Q (i.f) = ∫ A(t) (i.f) dt + C

Therefore,

i.f = e ^ ∫ P(t) dt

And P(t) = 2 / (100 + t)

i.f = e ^ ∫ 2 / (100 + t)

  = e ^ 2㏑ (100 + t)

     = e ^ ㏑ (100 + t) ^2 = (100 + t) ^2

Q(100 + t) ^ 2 = ∫6 (100 + t) ^2 dt + C

 Q(100 + t) ^2 = 2(100 + t) ^ 3 + C

  When t = 0, Q = 50

Therefore,

50( 100) ^2 = 2(100) ^3 + C

 C = -1.5 * 10 ^6

therefore, when t = 30,

Q (100 + 30) ^2 = 2(100 + 30) ^3 - 1.5 * 10 ^6

 Q (400) ^2 = 2(130) ^3 - 1.5 * 10 ^6

    Q = 171.24 Ibs

The amount of salt in the tank at the end of 30 minutes is 171.24 lbs.

The given parameters:

Initial volume of the tank, i = 100 gallonsRate of gain of salt = 3 gpmRate of loss of salt = 2 gpm

The linear differential equation of the salt solution is calculated as follows;

[tex]\frac{dx}{dt} = Gain - loss[/tex]

where;

x is the salt concentration

The salt concentration at time t, is calculated as follows;

[tex]\frac{dx}{dt} = 2(3) - 2(\frac{X}{100 + t} )\\\\\frac{dx}{dt} = 6 - 2(\frac{X}{100 + t} )\\\\\frac{dx}{dt} +2(\frac{X}{100 + t} ) =6[/tex]

Apply the general solution of linear differential equation as follows;

[tex]X(f) = \int\limits {At} \, dt \ + C\\\\f = e^{\int\limits {At} \, dt}\\\\ f = e^{\int\limits {\frac{2}{100 + t} } \, dt}\\\\f = e^{2 ln(100 + t)}\\\\f = (100 + t)^2[/tex]

[tex]X(100 + t)^2 = \int\limits {6(100 + t)^2} \, dt \ + \ C\\\\ X(100 + t)^2 = 2(100 + t)^3 + C[/tex]

When t = 0 and X = 50

[tex]50(100 + 0)^2 = 2(100+ 0)^3 + C\\\\C = -1.5 \times 10^6[/tex]

When t = 30 min, the concentration is calculated as;

[tex]X (100 + 30)^2 = 2(100 + 30)^3- 1.5 \times 10^6\\\\X(130)^2 = 2(130)^3 - 1.5\times 10^6\\\\X(130)^2 = 2894000\\\\X = \frac{2894000}{130^2} \\\\X = 171.24 \ lbs[/tex]

Learn more about solution of Linear differential equation here: https://brainly.com/question/5508539

. You have two carts, one which is empty and has mass m. The second cart is of the same mass but loaded with twice the mass of the empty cart i.e. it has mass 3m. You push each of them (one at a time) with the same constant force, over the same distance, starting from rest. After you have pushed them through this distance, you remove the force. How will the kinetic energy of the loaded and empty carts compare to each other

Answers

Answer:

Their kinetic energies would be the same

Explanation:

This is because, since the force, F acting on them moves the same distance, d, the work done by the force is W = Fd.

Now, from work-kinetic energy principles,

W = ΔK where ΔK = change in kinetic energy of the carts.

Since the work-done is the same for both carts, their change in kinetic energies would also be the same.

Since they start from rest, ΔK = K' - K =  K' - 0 = K'

So, the kinetic energies of the carts would be the same

A car hits a tree with a force of 45 N, the mass of the tree is 65g. What is the resulting acceleration?
a. 0.69 m/s2
b. 692 m/s2
c. 2,925 m/s2
d. 2.93 m/s2

Answers

Answer:

i think 692m/s2 is the correct answer

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