4. According to Newton’s law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M, then the rate of change of T is proportional to the difference of temperature M − T. This gives the differential equation dT dt = k(M − T). (a) Solve the differential equation for T. (b) A thermometer reading 100◦F is placed in a medium having a constant temperature of 70◦F. After 6 min, the thermometer reads 80◦F. What is the reading after 20 min?

Answer:

T = D/S

Explanation:

Given the formula for calculating the average speed of an object as:

average speed = Distance/Time

Let average speed = S

Distance = D

Time = T

Substitute

S = D/T

Make T the subject of the formula:

From S = D/T

Cross multiply

ST = D

Divide both sides by S

ST/S = D/S

T = D/S

Hence the expression for he time T after rearrangement is T = D/S

Answer:

Explanation:

Given data

mass m= 1200kg

radius r=92m

coefficient of friction μ=0.65

We know that

F=mv2/r

F=μmg  

mv2/r = μsmg  

v^2/r = μsg  

vmax = √(rμg)

Substituting our data we have

vmax=√(92*0.65*9.81)

vmax=√586.638

vmax=24.22m/s

Explanation:

Given two capacitors 7.0 µF and 5.0 µF connected in series, let s calculate the effective capacitance.

[tex]\frac{1}{C_T} = \frac{1}{7.0} +\frac{1}{5.0}\\ \frac{1}{C_T} = \frac{5+7}{35} \\C_T = \frac{35}{12}\\ C_T = 2.9166\mu F[/tex]

Given

V = 5.0kV = 5000Volts

To get the total charge in the circuit, we will use the formula:

[tex]Q = C_TV\\Q = 2.9166\times 10^{-6} \times 5000\\Q = 0.014583 C\\Q = 1.4583 \times 10^{-2}C[/tex]

Since the same charge flows in a series connected capacitors, the charge on them in mC is 14.583mC

For the voltage across 7.0 µF:

[tex]V = \frac{Q}{C}\\V = \frac{0.014583}{0.000007} \\V = 2,083.28V[/tex]

Voltage across the 7.0 µF is 2,083.28V

The voltage across the  5.0 µF:

V = 5000 - 2,083.28

V = 2,916.72Volts

Voltage across the  5.0 µF is 2,916.72V

Answer:

The charge on the first capacitor is 14.59 mC

The voltage across the first capacitor is 2084 V

The charge on the second capacitor is 14.59 mC

The voltage across the second capacitor is 2918 V

Explanation:

Given;

first capacitor, C₁ = 7.0 µF

second capacitor, C₂ = 5.0 µF

potential difference, V = 5000 V

The equivalent capacitance is given by;

[tex]\frac{1}{C_{eq}}= \frac{1}{C_1} +\frac{1}{C_2}\\\\\frac{1}{C_{eq}}= \frac{C_1 + C_2}{C_1C_2}\\\\C_{eq} = \frac{C_1C_2}{C_1 +C_2}\\\\ C_{eq} = \frac{(7*10^{-6})(5*10^{-6})}{(7*10^{-6} \ +\ 5*10^{-6})}\\\\C_{eq} = 2.917*10^{-6} \ F[/tex]

The charge on the first capacitor is given by;

[tex]Q_1 = C_{eq} V\\\\Q_1 = 2.917*10^{-6} *5000\\\\Q_1 = 0.01459 \ C\\\\Q_1 = 14.59 \ mC[/tex]

The voltage across the first capacitor is given by;

[tex]V_1 = \frac{Q_1}{C_1} \\\\V_1 = \frac{0.01459}{7*10^{-6}}\\\\ V_1 = 2084.286 \ V[/tex]

V₁ = 2084 V

The charge on the second capacitor is given by;

[tex]Q_2 = C_{eq} V\\\\Q_2 = 2.917*10^{-6} *5000\\\\Q_2 = 0.01459 \ C\\\\Q_2 = 14.59 \ mC[/tex]

The voltage across the second capacitor is given by;

[tex]V_2 = \frac{Q_2}{C_2}\\\\ V_2 = \frac{0.01459}{5*10^{-6}}\\\\V_2 = 2918 \ V[/tex]

Answer:

hello your question is incomplete attached below is missing part of the question

answer:

1 )  Magnetic field due to long current carrying wire : [tex]B = \frac{U_{0} I}{2\pi d}[/tex]

Therefore the net magnetic field due the both wires ; B = B[tex]_{1}[/tex] + B[tex]_{2}[/tex] . when we adjust the current I[tex]_{1}[/tex] = I[tex]_{2}[/tex] then the Netfield (B ) = zero

2) The distance between the field lines are not equally spaced and this is because the separation between field lines increases with the increase in the distance between the wires

3) Increase in current through the wire will lead to increase in force and this can be explained via this equation

[tex]F = \frac{U_{0}I_{1}I_{2} }{2\pi d }[/tex]

Explanation:

1 )  Magnetic field due to long current carrying wire : [tex]B = \frac{U_{0} I}{2\pi d}[/tex]

Therefore the net magnetic field due the both wires ; B = B[tex]_{1}[/tex] + B[tex]_{2}[/tex] . when we adjust the current I[tex]_{1}[/tex] = I[tex]_{2}[/tex] then the Netfield (B ) = zero

2) The distance between the field lines are not equally spaced and this is because the separation between field lines increases with the increase in the distance between the wires

3) Increase in current through the wire will lead to increase in force and this can be explained via this equation

[tex]F = \frac{U_{0}I_{1}I_{2} }{2\pi d }[/tex]

Answer:

I believe the answer is Property taxes

Explanation:

Answer: I'm pretty sure property taxes

Explanation:

Answer:

The Navy Seal is accelerating downwards at the rate of 3.3 m/s²

Explanation:

Given;

mass of the Navy Seal, m = 80 kg

the upward resistive force on her, F = 520 N

Her net downward force is given by;

[tex]F_{net} = F_{down} - F_{up}\\\\F_{net} = (80*9.8) - 520\\\\F_{net} = 264 \ N[/tex]

Her downward acceleration at this time is given by;

F = ma

a = F / m

a = 264 / 80

a = 3.3 m/s²

Therefore, the Navy Seal is accelerating downwards at the rate of 3.3 m/s²

Answer: the work done by the force is 0

Explanation:

F (x², xy)

121 = 11²

so R = x² + y² = 11²

p = x². Q = xy

Δp/Δy = 0, ΔQ/Δx

using Green's theorem

woek = c_∫F.Δr = R_∫∫ ΔQ/Δx - Δp/Δy) ΔA

=  (x² + y² = 121)_∫∫ yΔA

now let x = rcosФ, y = rsinФ

ΔA = rΔrΔФ

so r from 0 to 11

and Ф from 0 to 2π

= 0_∫^2π   0_∫^11  rsinФ × rΔrΔФ

= 0_∫^2π SinФΔФ   0_∫^11  r²Δr

= [ -cosФ]^2π_0 [r³/3]₀¹¹ = ( -cos2π + cos0) (11³/3) = 0

therefore the work done by the force is 0

Explanation:

hope this helps, cheers!

The values for the average speed and average velocity are;

(a) [tex]Average \ speed = 1.37\overline{142857} \ m/s[/tex]

(b) [tex]The \ average \ velocity = 0.\overline{857142} \ m/s[/tex]

The reason the above values are correct is given as follows;

The given parameters are;

Distance of the nearest grocery store to the house, d = 60 m

Direction of the grocery store = East from the house

Walking speed, s = 1.2 m/s

Time of walking before the rain started, t₁ = 15.0 s

Time it takes to go back to the house, t₂ = 5.0 s

Speed at which the start walking again, s = 1.2 m/s

(a) The formula for average speed, [tex]s_{avg}[/tex], is given as follows;

[tex]s_{avg} = \dfrac{Total \ distance }{Sum \ of \ time \ taken}[/tex]

The distance walked before the rain, d₁ = 1.2 m/s × 15.0 s = 18 meters

Distance covered on returning to the house = d₂ = d₁ = 18 meters

The total distance covered, ∑Distance = d₁ + d₂ + 60

∴ ∑Distance = 18 m + 18 m + 60 m = 96 m

The time, t₃, it takes to get to the grocery store on the second attempt after getting the umbrella is given as follows;

[tex]t_3 = \dfrac{d}{v}[/tex]

[tex]t_3 = \dfrac{60 \ m}{1.2 \ m/s} = 50.0 \, s[/tex]

The total time, ∑Time = t₁ + t₂ + t₃

∴ ∑Time = 15.0 s + 5.0 s + 50.0 s = 70.0 s

[tex]Average \ speed = \dfrac{\sum Distance}{\sum Time}[/tex]

[tex]Average \ speed = \dfrac{96 \, m}{70 \, s} = \dfrac{48}{35} \ m/s= 1.37\overline{142857} \ m/s[/tex]

[tex]Average \ speed = 1.37\overline{142857} \ m/s[/tex]

(b) The average velocity, [tex]v_{avg}[/tex], is given as follows;

[tex]v_{avg}= \dfrac{Total \ displacement}{Total \ time}[/tex]

The total displacement = The total change in location = The change in location from the house to the grocery =  60 m

The total time is the same as for the average speed, ∑Time = 70 s

[tex]\therefore v_{avg}= \dfrac{60 \, m}{70 \, s} = \dfrac{6}{7} \ m/s = 0.\overline{857142} \ m/s[/tex]

[tex]The \ average \ velocity = 0.\overline{857142} \ m/s[/tex]

Learn more about average speed and average velocity here:

https://brainly.com/question/589950

https://brainly.com/question/20498289

https://brainly.com/question/12984400

Explanation:

According to newton's second law of motion.

[tex]\sum Fx = ma\\\\\sum Fx = 1061 - 915\\\\\sum Fx = 146N[/tex]

m is the mas of the sky diver = 93.4kg

a is the acceleration of the skydiver

From the formula above;

[tex]a = \frac{\sum Fx}{m}\\ \\a = \frac{146}{93.4}\\\\a = 1.563m/s^2[/tex]

Hence the acceleration of the sky diver is 1.563m/s²

Analysing the question:

Since the stone was dropped, there was no initial velocity applied on it and hence it's initial velocity of the stone is 0 m/s

We are given:

height of the tower (h) = 66 m

mass of the stone (m) = 0.5 kg

initial velocity of the stone (u) = 0 m/s

time taken by the stone to reach the ground (t) = t seconds

acceleration due to gravity = 10 m/s²

** Neglecting air resistance**

Finding the time taken by the stone to reach the ground:

from the second equation of motion

h = ut + 1/2at²

replacing the variables

66 = (0)(t) + 1/2 (10)(t)²

66 = 5t²

t² = 13.2

t = 3.6 seconds

I initially wanted to subtract the height of the student from the height of the tower since the time i calculated is the time taken by the stone to reach the ground and that means that the stone has already hit the student before 3.6 seconds

but since we were NOT given the height of a student, the person who posed this question wants the time taken by the stone to reach the ground and that is what we solved

Answer:

2

Explanation:

Answer:

significant

Explanation:

The digits in a measurement that are considered significant are all of those digits that represent marked calibrations on the measuring device plus one additional digit to represent the estimated digit (tenths of the smallest calibration).

Answer:

The wavelength is [tex]\lambda  =  1.2  * 10^8 nm[/tex]

Explanation:

From the question we are told that

   The frequency of operation of the microwave is  [tex]f =  2.50 GHz  =  2.50 *10^{9} \ Hz[/tex]

     Generally the wavelength is mathematically represented as

          [tex]\lambda  =  \frac{c}{f}[/tex]

Here c is the speed of light with value [tex]c =  3.0 *10^{8} \  m/s[/tex]

So  

         [tex]\lambda  =  \frac{3.0 *10^{8}}{  2.50 *10^{9}}[/tex]

=>       [tex]\lambda  =  0.12 \  m [/tex]

converting to nanometer

           [tex]\lambda  =  1.2  * 10^8 nm[/tex]

Answer:

a) The magnitude of the electric charge that a 60-kg human must have to overcome weight is 3.923 coulombs and its sign is negative.

b) The force of repulsion between two people is [tex]13.851\times 10^{6}[/tex] newtons. The use of the earth's electric field a feasible means of flight is not feasible since electric force of repulsion would destroy human body before taking advantage of any possible flight skill.

Explanation:

a) From Second Newton's Law, we form this equation of equilibrium:

[tex]\Sigma F = F_{E}-W = 0[/tex] (Eq. 1)

Where:

[tex]F_{E}[/tex] - Electrostatic force exerted on human, measured in Newton.

[tex]W[/tex] - Weight of the human, measured in Newton.

If we consider that human can be represented as a particle and make use of definitions of electric field and weight, the previous equation is expanded and electric charge is cleared afterwards:

[tex]q\cdot E-m\cdot g = 0[/tex]

[tex]q = \frac{m\cdot g}{E}[/tex] (Eq. 2)

[tex]E[/tex] - Electric field, measured in Newtons per Coloumb.

[tex]m[/tex] - Mass, measured in kilograms.

[tex]g[/tex] - Gravity acceleration, measured in meters per square second.

[tex]q[/tex] - Electric charge, measured in Coulomb.

As electric field of the Earth is directed in toward the center of the planet, that is, in the same direction of gravity, electric field must be a negative value. If we know that [tex]m = 60\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]E = -150\,\frac{N}{C}[/tex], the charge that a 60-kg human must have to overcome weight is:

[tex]q = \frac{(60\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{-150\,\frac{N}{C} }[/tex]

[tex]q = -3.923\,C[/tex]

The magnitude of the electric charge that a 60-kg human must have to overcome weight is 3.923 coulombs and its sign is negative.

b) The electric force of repulsion between two people with the same charge calculated in part (a) is determined by Coulomb's Law, whose definition we proceed to use:

[tex]F = \kappa \cdot \frac{q^{2}}{r^{2}}[/tex] (Eq. 3)

Where:

[tex]\kappa[/tex] - Electrostatic constant, measured in Newton-square meter per square Coulomb.

[tex]q[/tex] - Electric charge, measured in Coulomb.

[tex]r[/tex] - Distance between two people, measured in meters.

If we know that [tex]\kappa = 9\times 10^{9}\,\frac{N\cdot m^{2}}{C^{2}}[/tex], [tex]q = -3.923\,C[/tex] and [tex]r = 100\,m[/tex], then the force of repulsion between two people is:

[tex]F = \left(9\times 10^{9}\,\frac{N\cdot m^{2}}{C^{2}} \right)\cdot \left[\frac{(-3.923\,C)^{2}}{(100\,m)^{2}} \right][/tex]

[tex]F = 13.851\times 10^{6}\,N[/tex]

The force of repulsion between two people is [tex]13.851\times 10^{6}[/tex] newtons. The use of the earth's electric field a feasible means of flight is not feasible since electric force of repulsion would destroy human body before taking advantage of any possible flight skill.

Answer:

-9m/s²

Explanation:

Given parameters:

Initial velocity = 45m/s

Final velocity  = 0

duration  = 5s

Unknown:

acceleration = ?

Solution:

Acceleration is the rate of change of velocity with time;

        Acceleration  = [tex]\frac{v- u}{t}[/tex]

v is the final velocity

u is the initial velocity

t is the time taken

 Input the parameters and solve;

     Acceleration  = [tex]\frac{0 - 45}{5}[/tex]   = -9m/s²

The car accelerates at a rate of -9m/s² which is a deceleration

Answer:

A statement about you

Explanation:

Answer:

Personification is when you give an animal or object qualities or abilities that only a human can have. This creative literary tool adds interest and fun to poems or stories. Personification is what writers use to bring non-human things to life. It helps us better understand the writer's message.

Explanation:

Answer:True

Explanation:Matter is everything around you. Atoms and compounds are all made of very small parts of matter. Those atoms go on to build the things you see and touch every day. Matter is defined as anything that has mass and takes up space (it has volume).

Answer:

slower speeds = larger and faster steering wheel movements

faster speeds = small and slow steering wheel movements

Explanation:

When driving at slower speeds you need to use larger and faster steering wheel movements. This is because at slow speeds the car does not have enough momentum to make certain maneuvers with small steering wheel movements in a given amount of time, therefore making large and faster steering wheel movements gives the car enough time with the momentum it has to make the desired maneuver. At faster speeds only small and slow steering wheel movements are needed and while cause the car to quickly change to the desired direction due to the increased momentum of the car.

Object will start moving in the direction where comparatively high force  is directing to move

When the resultant force acting on a body is not equal to zero , the force acting on the body are known as unbalance forces . The body acted upon by unbalance forces changes its state of motion.

According to Newton if a body is experiencing net force =0 (which means that all horizontal and vertical forces are cancelling each other ), then the body will acquire an equilibrium state and will not move because forces are balancing each other and making net force on the body zero .

But unbalance force can tend the body to move in that direction in which a comparatively high force is acting due to which cancellation will not occur ( equilibrium state will not occur )

hence correct option A)Object moves

learn more about unbalance forces

https://brainly.com/question/13259103?referrer=searchResults

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Answer:

it depends on the wind and any other conditions but if you have a controlled environment it should take 1 second to get 40 meters but it could go higher in which it could take about 5 seconds to go 200 meters

Explanation:

hope it helped

:)

Answer:

liquids

Explanation

Answer:

A. 1.4 m/s to the left

Explanation:

To solve this problem we must use the principle of conservation of momentum. Let's define the velocity signs according to the direction, if the velocity is to the right, a positive sign will be introduced into the equation, if the velocity is to the left, a negative sign will be introduced into the equation. Two moments will be analyzed in this equation. The moment before the collision and the moment after the collision. The moment before the collision is taken to the left of the equation and the moment after the collision to the right, so we have:

[tex]M_{before} = M_{after}[/tex]

where:

M = momentum [kg*m/s]

M = m*v

where:

m = mass [kg]

v = velocity [m/s]

[tex](m_{1} *v_{1} )-(m_{2} *v_{2})=(m_{1} *v_{3} )+(m_{2} *v_{4})[/tex]

where:

m1 = mass of the basketball = 0.5 [kg]

v1 = velocity of the basketball before the collision = 5 [m/s]

m2 = mass of the tennis ball = 0.05 [kg]

v2 = velocity of the tennis ball before the collision = - 30 [m/s]

v3 =  velocity of the basketball after the collision [m/s]

v4 = velocity of the tennis ball after the collision = 34 [m/s]

Now replacing and solving:

(0.5*5) - (0.05*30) = (0.5*v3) + (0.05*34)

1 - (0.05*34) = 0.5*v3

- 0.7 = 0.5*v

v = - 1.4 [m/s]

The negative sign means that the movement is towards left

Answer:

A. 1.4 m/s to the left

Explanation:

Answer:

The speed is     v = 25 - 9.8 t

the velocity is   v = (25 - 9.8 t) j^

the position is   y = 25 t - 4.9 t²

Explanation:

This is a vertical throwing exercise.

The first thing we must do is set a coordinate system, in this case we will make the upward direction positive.

Let's write the kinematics equations

        v = v₀ - g t

        v² = v₀² - g (y-y₀)

        y = y₀ + v₀ t - ½ g t²

in our case the initial velocity is

         v₀ = 25 m / s

and we zero the system at the launch point

        y₀ = 0

the equations remain

      v = 25 - 9.8 t

        v² = 25² - 9.8 y

        y = 0 + 25 t - ½ 9.8 t²

The speed is     v = 25 - 9.8 t

the velocity is   v = (25 - 9.8 t) j^

the position is   y = 25 t - 4.9 t²

Answer:

34k+B plus 9 :)

Explanation:

Answer:

A) T1 = 269.63 K

T2 = 192.59 K

B) W = -320 KJ

Explanation:

We are given;

Initial volume: V1 = 7 m³

Final Volume; V2 = 5 m³

Constant Pressure; P = 160 KPa

Mass; m = 2 kg

To find the initial and final temperatures, we will use the ideal gas formula;

T = PV/mR

Where R is gas constant of helium = R = 2.0769 kPa.m/kg

Thus;

Initial temperature; T1 = (160 × 7)/(2 × 2.0769) = 269.63 K

Final temperature; T2 = (160 × 5)/(2 × 2.0769) = 192.59 K

B) world one is given by the formula;

W = P(V2 - V1)

W = 160(5 - 7)

W = -320 KJ

Answer:

The spring constant is 3.44x10⁶ kg/s².

Explanation:

We cand find the spring constant by conservation of energy:

[tex] E_{i} = E_{f} [/tex]

[tex] mgh = \frac{1}{2}kx^{2} [/tex]   (1)

Where:

m is the mass =  41700 kg

g is the gravity = 9.81 m/s²

h is the height = 2.65 m

x is the distance of spring compression = 79.4 cm

k is the spring constant =?

Solving equation (1) for k:

[tex]k = \frac{2mgh}{x^{2}} = \frac{2*41700 kg*9.81 m/s^{2}*2.65 m}{(0.794 m)^{2}} = 3.44 \cdot 10^{6} kg/s^{2}[/tex]              

Therefore, the spring constant is 3.44x10⁶ kg/s².

I hope it helps you!