What is the function of a power source in a circuit

Answer:the object is not accelerating

Explanation:

There object is not accelerating since there's no increase in velocity

Final answer:

Based on the descriptions of graphical data, we can conclude that the object has negative acceleration because its velocity is decreasing over time while it is moving in the positive direction, or its negative velocity is increasing over time. Also, since the object is moving in the negative direction, it experiences a negative displacement.

Explanation:

The question asks about the motion of an object based on different graphical representations. To determine the nature of this motion, we can analyze the provided diagrams. In this case, we have descriptions of how the velocity changes over time, which allows us to infer acceleration, and acceleration is defined as the change in velocity over time. According to the information, the object experiences a decrease in positive velocity, which indicates a negative acceleration, as acceleration is in the opposite direction to the velocity. Furthermore, it is mentioned that the object has a negative velocity which increases in magnitude, coherently resulting in negative acceleration as well.

Acceleration is a vector quantity, meaning it has both direction and magnitude. Since we are discussing a coordinate system where to the right is considered positive, any acceleration towards the left will be considered negative. The graphs that indicate an object having a constant negative velocity also imply that the object has negative displacement over the time period, because it's moving in the negative direction of the coordinate system.

The plants that are typically the first to live in soil are known as pioneer plants or pioneer species.

Pioneer plants or pioneer species are the plants that are often the first to live in soil. These plants are distinguished by their propensity to colonize bare or disturbed soil, such as on newly formed land or in the wake of a natural disaster.

The process of primary succession, which is the gradual formation of plant and animal communities in a region devoid of soil or organic matter, depends critically on pioneer plants.

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Answer:

The 500 watts motor

Explanation:

Power is the workdone per unit time, it can be expressed as;

P = VI

P = I^2 × R

Where;

P = power

V = potential difference

I = current

R = resistance

Making current the subject of formula;

I = P/V

I^2 = P/R

Since they are both connected to the same standard home outlet. The potential difference across them is thesame( V is constant). Therefore the higher the power the higher the current.

I ∝ P

So the electrical motors with higher power 500 watts draws greater current.

Answer:

Check the explanation

Explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

The equation modeling the exponential decay of the Beryllium-11 isotope is 50 = 800(1/2)^(t/14). This lets you find out the time that has passed since there were initially 800 atoms.

The situation described is an example of exponential decay, modeled by the formula N = N0(1/2)^(t/h). In this case, N0 is the original number of atoms (800), N is the remaining number of atoms (50), t is the time that has passed, and h is the half-life of the isotope (14 seconds for Beryllium-11).

So the equation modelling this scenario is 50 = 800(1/2)^(t/14). This equation will let you solve for the time t (in seconds) that has passed since the sample initially contained 800 atoms of Beryllium-11.

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Answer:

7350 J

Explanation:

Gravitational Potential Energy: This is defined as the energy possessed by a body due to it's position in the gravitational field. The S.I unit is Joules(J).

Applying,

E.p = mgh..................... Equation 1

Where E.p = Gravitational potential Energy, m = mass of the object, h = height of the object above the surface of the earth, g = acceleration due to gravity.

Given: m = 2.5 kg, h = 300 m

Constant: g = 9.8 m/s²

Substitute these values into equation 1

E.p = 2.5(300)(9.8)

E.p = 7350 J.

Answer:

1, 2, and 5

Explanation:

Answer:

1, 2 and 5

Explanation:

The mutual inductance of a Tesla coil system with two solenoids will double if the length and number of turns of the primary solenoid are both doubled, assuming all other factors remain constant.

When we are given a Tesla coil configuration with a solenoid of length l and cross-sectional area A, closely wound with N1 turns of wire, and another coil with N2 turns surrounding it at its center, we can calculate the mutual inductance based on the properties of the solenoids. If a new solenoid is introduced that has twice as many turns and is twice as long, the mutual inductance M of the system will be affected.

To understand how the mutual inductance changes, let's remember that for a closely wound solenoid, the mutual inductance can be calculated by a formula incorporating the number of turns, permeability of the core material, cross-sectional area, and the length of the solenoid. The mutual inductance is directly proportional to the product of the number of turns of each coil, the magnetic permeability of the core, and the area of the cross-section, and inversely proportional to the length of the solenoid. Therefore, if we double the length l and the number of turns N1 while keeping all other factors constant, the mutual inductance will also double.

Answer:

The answer is "[tex]1.94 \ m^2[/tex]".

Explanation:

Formula:

[tex]F= \frac{1}{2} \times C_D \times density \times area \times velocity^2\\\\Power (P) = F \times velocity \\\\P = \frac{C_D}{2} \times density \times area \times velocity^3\\[/tex]

Given value:

[tex]\ P = 10.25 \ W \\\\\ density = 1.2 \ kg/m^3 \\\\\ velocity= 2.5 \\\\[/tex]

[tex]10.25 = \frac{C_D A}{2} \times 1.2 \times 2.5^3\\\\C_D A= \frac{10.25 \times 2 }{1.2 \times 2.5^3}\\\\C_D A = 1.94 m^2\\[/tex]

Answer:b-The person and the earth

Explanation:

The best system will be the person and earth as a system

It is so because whatever the energy required by the person is derived from earth resource and thus by depleting the earth resource person is getting is required form of energy .

for example person want thermal energy , for this he need coal which is earth resource and thus all the energy is derived from earth and is being converted into some other form of energy.

Answer:

As the Ballon pulls up, the distance between the Ballon and the center of the earth increases, the gravitational pull reduces and the gravity potential energy increases.

Answer:

L = 182.4 m      

Explanation:

Given:-

- The number of turns of the coil, N = 50

- The shape of the coil = square

- The angle between the coil and magnetic field, θ = 30°

- The change in magnetic field, ΔB = ( 700 - 250 ) μT

- The time duration in which magnetic field changes, Δt = 0.3 s

- The induced emf, E = 60.0 mV

Solution:-

- The problem at hand is an application of Faraday's law. The law states that the induced emf ( E ) is proportional to the negative rate of change of magnetic flux ( ΔФ / Δt ) and number of turns of the coil ( N ).

- The Faraday's law is mathematically expressed as:

                    E =  - N* ( ΔФ / Δt )

Where,

- The flux ( Ф ) through a current carrying with an cross-sectional area ( A ) at a normal angle ( θ ) to the direction of magnetic field ( B ) is given by the following relationship.

                    Ф = B*A*cos ( θ )

- We need the rate of change of magnetic flux ( ΔФ / Δt ) for the Faraday's law. I.e the induced emf ( E ) is proportional to rate of change in magnetic field ( ΔB / Δt ), rate of change of angle between the coil and magnetic field ( Δθ / Δt ) or rate of change of cross-sectional area of the coil under the influence of magnetic field.

- To determine the exact relationship. We will derive the multi-variable function of flux ( Ф ) with respect to time "t":

                     Ф ( B , A , θ ) = B*A*cos ( θ )

- The first derivative would be ( Use chain and product rules )

    ( ΔФ / Δt ) = ΔB / Δt*A*cos ( θ ) + B*ΔA/Δt*cos ( θ ) - B*A*sin ( θ )*Δθ/Δt

- For the given problem the only dependent parameter that is changing is magnetic field ( B ) with respect to time "t". Hence, ( ΔA/Δt = Δθ/Δt = 0 ):

                        ΔФ / Δt  = (ΔB/Δt)*A*cos ( θ )

- Substitute the rate of change of magnetic flux  ( ΔФ / Δt ) into the expression for Faraday's Law initially stated:

                        E =  - N*(ΔB/Δt)*A*cos ( θ )

- Plug in the values and evaluate the Area of the square coil:

                       A =  - E / ( N*(ΔB/Δt)*cos ( θ ) )

                       A = - 0.06 / ( 50*[ (250-700)*10^-6/0.3 ] *cos ( 30° ) )

                       A = - 0.06 / -0.07216

                       A = 0.8314 m^2

- The square coil has equal sides ( x ). The area of a square A is given by:

                      A = x^2

                      x = √0.8314

                      x = 0.912 m

- The perimeter length of a single coil in terms of side length "x" is given as:

                      P = 4x

Whereas for a coil of N turns the total length ( L ) would be:

                      L = N*P

                      L = 4Nx

                      L = 4 * 50 * 0.912

                      L = 182.4 m                 ... Answer

The slope of the line is calculated by dividing the change in distance over the change in time.

Answer:

The wavelength of the laser, λ = 5.625 * 10⁻⁷ m

Explanation:

Separation of the narrow slits, d = 7.5 * 10⁻⁵ m

The distance between the screen and the two slits, d = 4m

The distance between the bright spot and the center of the pattern, Y = 1.5 cm

Y = 1.5 * 10⁻² m

To calculate the wavelength, λ, of the laser we will use the relationship:

[tex]Y = \frac{\lambda L}{2d} \\1.5 * 10^{-2} = \frac{\lambda * 4}{2*7.5*10^{-5} }\\\lambda = \frac{1.5 * 10^{-2} * 15 * 10^{-5} }{4}[/tex]

λ = 5.625 * 10⁻⁷ m

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The minimum mass of [tex]M_1 = 90\ kg[/tex] correct option is  E

Explanation:

 Free body diagram of the set up  in the question is shown on the third uploaded image

  The mass of board is  [tex]M = 60kg[/tex]

   The length of the board is [tex]L = 6 \ m[/tex]

    The length extending over the edge is [tex]L_e = 4 \ m[/tex]

    The second mass is  [tex]M_2 = 30kg[/tex]

Now to obtain [tex]M_1[/tex] we take moment about the edge of the platform

               [tex]M_1 g L_1 = Mg \frac{L}{2} + M_2 g L_2[/tex]

              [tex]M_1 L_1 = M \frac{L}{2} + M_2 L_2[/tex]

  Substituting value  

               [tex]M_1 (2) = (60)(1) + (30)(4)[/tex]

               [tex]M_1 = 90 \ kg[/tex]

The minimum value of M1 needed to keep the board from falling off the platform is 90 kg.

From the information given, we are to find:

Given that:

Consider the center of gravity in the board that lies at the length of the board midpoint.

Then, the distance (D) of the gravity center from the platform end = 3 - 2

= 1 m

∴

Considering the moment about the platform end, the mass (M1) placed on the left side edge of the board can be computed as:

[tex]\mathbf{M_1gL_1 = MgD + M_2gL_2} \\ \\ \mathbf{M_1L_1 = MD + M_2gL_2} \\ \\ \mathbf{M_1(2) = 60 \ kg \times 1 + 30 \ kg \times (4)} \\ \\ \mathbf{ M_1 =\dfrac{60 \ kg + 120 kg }{2} } \\ \\ \mathbf{ M_1 =\dfrac{180 \ kg}{2} } \\ \\ \mathbf{ M_1 =90 \ kg }[/tex]

Therefore, we can conclude that the minimum value M1 needed to keep the board from falling off the platform is 90 kg.

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For the first question

Answers:

b.) All these technologies use radio waves, including high-frequency microwaves

d.) Microwave ovens emit in the same frequency band as some wireless Internet devices.

e.) The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above.

f.) All these technologies emit waves with a wavelength in the range of 0.10 to 10.0 m.

For second question

Answer:

B. The earth absorbs visible light and emits radiation with a longer wavelength

C. The earth absorbs visible light and emits radiation with a lower frequency.

Both options are correct

Explanation:

In the EM spectrum, wavelenght reduces with increasing energy and frequency increases with increasing energy. The order of increasing energy is radio wave, microwave, infrared rays, visible rays, ultraviolet rays, xrays, gamma rays.

If the earth absorbs visible rays of higher energy, and radiates infrared rays of lower energy, then this means that the radiated radiation will have a longer wavenght, and a lower frequency.

1) The statements that correctly describe the various applications given in the question are;

B. All these technologies use radio waves, including high-frequency microwaves

D. Microwave ovens emit in the same frequency band as some wireless Internet devices.

E. The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies.

F. All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.

2) The correct statements on the EM spectrum in the question are;

B. The earth absorbs visible light and emits radiation with a longer wavelength.

C. The earth absorbs visible light and emits radiation with a lower frequency.

1) We are told about different waves being used by different technologies such as;

- Radio and TV emitting radio waves

- microwave oven using microwaves to cook food

- Dentists checking teeth with x-rays

All these waves are electromagnetic waves.

Looking at the options, options B, D, E and F are true because;

2) The correct options are Options B and C because;

In the EM radiation spectrum, when the energy increases, the wavelength usually reduces and the frequency usually increases. The order of  radio waves according to increase in energy is;

radio waves < infrared radiation < visible rays < ultraviolet rays <  xrays < gamma rays.

Now, if we say that the earth absorbs visible rays of higher energy, and radiation of infrared rays with lower energy, then from our definition, we can conclude that radiated waves will have a longer wavelength, and a lower frequency.

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Answer:

Length of the pipe = 53.125 cm

Explanation:

given data

harmonic frequency f1  = 800 Hz

harmonic frequency f2  = 1120 Hz

harmonic frequency f3  = 1440 Hz

solution

first we get here fundamental frequency that  is express as

2F = f2 - f1    ...............1

put here value

2F = 1120 - 800

F = 160 Hz

and

Wavelength is express as

Wavelength  = Speed ÷ Fundamental frequency    ................2

here speed of waves in air  = 340 m/s

so put here value

Wavelength  =340 ÷ 160

Wavelength   = 2.125 m

so

Length of the pipe will be

Length of the pipe = 0.25 × wavelength    ......................3

put here value

Length of the pipe = 0.25 × 2.125

Length of the pipe = 0.53125 m

Length of the pipe = 53.125 cm

Final answer:

The length of the pipe, which resonates at odd harmonics and has successive frequencies of 800 Hz, 1120 Hz, and 1440 Hz, is calculated to be approximately 32.2 centimeters. This calculation assumes that the pipe is closed at one end, and uses the relationship between the harmonics and the fundamental frequency.

Explanation:

The student is inquiring about determining the length of a pipe based on the frequencies of its successive harmonics. Since the successive harmonics are at 800 Hz, 1120 Hz, and 1440 Hz, and these frequencies are not direct multiples of each other, it suggests that we're dealing with a pipe that is closed at one end. Such pipes produce odd harmonics only. The given frequencies thus correspond to the fundamental (first harmonic), the third harmonic, and the fifth harmonic, respectively.

The frequency of the nth harmonic in a pipe closed at one end is given by:

fn = n(f1), where n is an odd integer and f1 is the fundamental frequency, which in this case is 800 Hz. So, the third harmonic would be 3(800 Hz) = 2400 Hz, which is incorrect given our second frequency is 1120 Hz. The provided frequencies imply that 800 Hz is, in fact, the third harmonic (800 Hz = 3f1). Hence, the fundamental frequency (f1) is 800 Hz / 3 = 266.67 Hz.

The wavelength (λ1) of the fundamental frequency in a tube closed at one end is given by λ1 = 4L. Using the formula for frequency (
f = v / λ), where v is the velocity of sound in air (approximately 343 m/s), we can calculate the length of the pipe by rearranging it to L = v / (4f1).

Therefore, L = 343 m/s / (4 * 266.67 Hz) = 0.322 meters or 32.2 cm.

Complete Question

The complete question is shown on the first uploaded image

Answer:

The gauge pressure that water has at the House A  [tex]P_A = 257020.68 Pa[/tex]

The gauge pressure that water has at the House B  [tex]P_B = 188454 \ Pa[/tex]

Explanation:

From the question we are told that

    The mass of water when full is  [tex]m_f = 7.41* 10^{5} kg[/tex]

Generally the volume of water in this tank is mathematically represented as

              [tex]V = \frac{m }{\rho}[/tex]

Where  [tex]\rho[/tex] is the density of water with a value of with a value of [tex]\rho = 1000 kg /m^3[/tex]

   substituting values

                  [tex]V = \frac{7.41 *10^5}{10^3}[/tex]

                  [tex]V = 741 m^3[/tex]

This volume is the volume of a sphere since the tank is spherical so

            [tex]V = \frac{4 \pi ^3}{3}[/tex]

  making r the subject of the formula

           [tex]r =\sqrt[3]{ \frac{741 *3 }{4\pi} }[/tex]              

        [tex]r = 5.6134 m[/tex]

Now we can use this parameter to obtain the diameter

  So

        [tex]d = 2 * r[/tex]

substituting values

        [tex]d = 2 * 5.6134[/tex]

        [tex]d = 11.23m[/tex]

The pressure  the water has at  faucet in House A is mathematically evaluated as

        [tex]P_A = \rho g h_A[/tex]

This height is obtained as follows

                       [tex]h_A = d+ 15[/tex]

The value 15 is gotten from the diagram

  so

          [tex]h_A = 15 + 11.23[/tex]

          [tex]h_A = 26.22 m[/tex]

Now substituting values

         [tex]P_A = 26.23 * 9.8 * 1000[/tex]

         [tex]P_A = 257020.68 Pa[/tex]

      The pressure  the water has at  faucet in House B is mathematically evaluated as

        [tex]P_B = \rho g h_B[/tex]

This height is obtained as follows

                       [tex]h_B = d+ 15[/tex]

The value 15 is gotten from the diagram

  so

          [tex]h_B = d + 15 -h[/tex]

substituting values

         [tex]h_B =11.23 + 15 -7[/tex]

          [tex]h_A = 19.23 m[/tex]

Now substituting values

         [tex]P_B = 19.23 * 9.8 * 1000[/tex]

         [tex]P_B = 188454 \ Pa[/tex]

Answer:

The separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)

Explanation:

The relationship between energy and wavelength is expressed below:

E = hc/λ

λ = hc/EK - EL

Considering the condition of Bragg's law:

2dsinθ = mλ

For the first order Bragg's law of reflection:

2dsinθ = (1)λ

2dsinθ = hc/EK - EL

d = hc/2sinθ(EK - EL)

Where 'd' is the separation distance between the parallel planes of an atom, 'h' is the Planck's constant, 'c' is the velocity of light, θ is the angle of reflection, 'EK' is the energy of the K shell and 'EL' is the energy of the K shell.

Therefore, the separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)

Answer:

The diameter of the second pipe is [tex]D_2 = 1.095 D[/tex]

Explanation:

From the question we are told that

       The length of the connected pipe is  [tex]d = 2L[/tex]

        The pressure drop for the first pipe is  [tex]\Delta p __{1}} = 1.44* \Delta p__{2}}[/tex]

        The diameter of the pipe is  [tex]D[/tex]

The rate at which the fluid flows for laminar flow is mathematically represented as

          [tex]\r m = \frac{\pi D^4 \Delta p}{128 \mu L}[/tex]

Where L is the length of the pipe

           [tex]\mu[/tex] is the dynamic viscosity

          [tex]\Delta p[/tex] is the difference in pressure

          [tex]\r m[/tex] is the flow rate of the fluid

From the equation of continuity

         [tex]\r m_ 1 = \r m_2[/tex]

Where [tex]\r m_1[/tex] is the flow rate in pipe one

           [tex]\r m_2[/tex] is the flow rate in pipe two

So

        [tex]\frac{\pi D^4 \Delta p_1}{128 \mu L} = \frac{\pi D^4_2 \Delta p}{128 \mu L}[/tex]

Where [tex]D_2[/tex] is the diameter of the second pipe

=>     [tex]\frac{\pi D^4 (1.44 \Delta p_2)}{128 \mu L} = \frac{\pi D^4_2 \Delta p}{128 \mu L}[/tex]

=>   [tex]1.44 D^4 = D_2 ^4[/tex]

       [tex]D_2 =\sqrt[4]{ \frac{D ^4 }{1.44 } }[/tex]

      [tex]D_2 = 1.095 D[/tex]

Complete Question

An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick

Answer:

The  largest total area of the oil slick  [tex]A = 8.257 *10^{9} \ m^2[/tex]

Explanation:

From the question we are told that

     The volume of oil the escaped is  [tex]V = 18000 \ L[/tex]

    The refractive index of oil is [tex]n_o = 1.1[/tex]

     The refractive index of water is [tex]n_w = 1.33[/tex]

      The wavelength of the light  is [tex]\lambda = 485 \ nm = 485 * 10^{-9} \ m[/tex]

Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as

          [tex]d = m *\frac{\lambda}{2n_w}[/tex]

Where is the order of interference of the light and it value ranges from 1, 2, 3,...n

It is usually take as 1 unless stated otherwise by the question

substituting value

      [tex]d = 1 * \frac{485 *10^{-9}}{2 * 1.1}[/tex]    

      [tex]d = 218 nm[/tex]    

The are can be mathematically evaluated as

        [tex]A = \frac{V}{d}[/tex]

Substituting values

        [tex]A = \frac{18000}{218*10^{-8}}[/tex]

        [tex]A = 8.257 *10^{9} \ m^2[/tex]

Answer:

l = 10.16 m

Explanation:

In this case, we have the period of oscillation of the pendulum is 6.4 s. It is required to find the height of the tower.

We know that the pendulum executes SHM. Let l is the height of the tower. The time period of simple pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

g is acceleration due to gravity

We need to rearrange the above equation such that,

[tex]l=\dfrac{T^2g}{4\pi ^2}\\\\l=\dfrac{(6.4)^2\times 9.8}{4\pi ^2}\\\\l=10.16\ m[/tex]

So, the height of the tower is 10.16 m.

Answer:

a) 37.8 W

b) 2 Nm

Explanation:

180 g = 0.18 kg

We can also convert 180 revolution per minute to standard angular velocity unit knowing that each revolution is 2π and 1 minute equals to 60 seconds

180 rpm = 180*2π/60 = 18.85 rad/s

We can use the heat specific equation to find the rate of heat exchange of the steel drill and block:

[tex]\dot{E} = mc\Delta \dot{t} = 0.18*420*0.5 = 37.8 J/s[/tex]

Since the entire mechanical work is used up in producing heat, we can conclude that the rate of work is also 37.8 J/s, or 37.8 W

The torque T required to drill can be calculated using the work equation

[tex]E = T\theta[/tex]

[tex]\dot{E} = T\dot{\theta} = T\omega[/tex]

[tex]T = \frac{\dot{E}}{\omega} = \frac{37.8}{18.85} = 2 Nm[/tex]

Calculating the rate of working of a drill involves using the specific heat capacity, mass of the block, and rate of temperature increase to find the power. The torque can be derived from this power and the angular velocity of the drill.

The question involves calculating the rate of working of the drill in Watts and the torque required to drive the drill based on the information that all mechanical work is converted to heat that raises the temperature of the steel block and drill at 0.5 0C/s. Given the mass of the steel block and drill is 180 g and the specific heat capacity of steel is 420 J/(kgK), we can use the formula power (P) = mcigtriangleup T/igtriangleup t, where m is the mass, c is the specific heat capacity,  is the temperature change, and  is the change in time. To find the torque, we can use the power-torque relationship P = au imes w, where P is power in watts, au is the torque in Newton-meters, and w is the angular velocity in radians per second. As the drill makes 180 revolutions per minute (rpm), we'll convert that to radians per second to use in the power-torque equation.

Answer:

Explanation:

Let r be the radius of circular top and h be the height of the cylinder

Given

π r² h = 1000

Let cost of making side of can be p per unit area , the cost of making top and bottom will be 2p per unit area.

total cost

C = 2 x π r² x 2p + 2πrh x p

= 2(1000 / h) x 2p + 2π x (1000 / π) x  [tex]\frac{1}{\sqrt{h} }[/tex] x h x p

= 2(1000 / h) x 2p + 2π x (1000 / π) x √h x p

differenciating

dC / dh =  2(- 1000 / h²) x 2p + 2π x (1000 / π) x [tex]\frac{1}{2\sqrt{h} }[/tex] x p  = 0 for minimum cost

- 4 / h² + 1 / √h = 0

h³ = 16

h = 2.519 cm .

π r² h = 1000

π r²  x 2.519 = 1000

r = 11.24 cm

The cylinder will have height of 2.519 cm and radius of 11.24 cm.

Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize cost. This considers the volume constraint of 1000 cm³ and the different material costs for the top/bottom and side. Detailed steps involve deriving these dimensions mathematically.

Let's denote the radius of the base of the cylinder by r and the height by h. The volume V of the cylinder is given by V = πr²h. Given that the volume is 1000 cm³, we have:

Step 1: V = πr²h = 1000 cm³

Therefore, h = 1000 / (πr²).

Step 2: Next, we need to express the cost of the material. The cost for the top and bottom parts is double the cost of the side. The surface area A of the can is:

Area of the top and bottom (each): [tex]A_t[/tex] = πr²

Area of the side: [tex]A_s[/tex] = 2πrh

Total area A:

A = 2πr² + 2πrh

Considering the cost factor, the effective cost area C is:

C = 2(2πr²) + 2πrh

C = 4πr² + 2πrh

Step 3: Substitute h from the volume equation:

C = 4πr² + 2πr(1000 / (πr²))

C = 4πr² + 2000 / r

Step 4: To minimize the cost, take the derivative of C with respect to r and set it to zero:

[tex]\frac{dC}{dr}[/tex] = 8πr - 2000 / r² = 0

8πr = 2000 / r²

8πr³ = 2000

r³ = 250 / π

r ≈ 3.4198 cm

Step 5: Calculate the height h:

h = 1000 / (πr²)

h ≈ 1000 / (π * (3.4198)²)

h ≈ 27.2837 cm

In summary, Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize the cost.

Wyatt should choose a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm for the metal can to minimize the cost, given the volume constraint of 1000 cm³.

Answer:

The required power by the engine is 33.0 hp

Explanation:

Solution

Newton's second law says that, the net force Fnet on an object of mass m will accelerates the object

Where

Fnet = ma

a = acceleration

θ = angle of incline,

m = mass of the 30 skiers,

f = frictional force

N = normal force

mg sinθ, mg cos θ are components of weight skier

F = the force applied by engine

Now,

The skier mass  is 65 kg

We calculate the mass of the 30 skier

m = 30 (65kg) = 1950 kg

Calculate the net force acting on the skiers along the x-axis

Fnet, x=ma

Now,

F-mg sin θ - f = 0

F= mg sin θ + f -----(1)

The kinetic frictional force is denoted by

f = μk N ------(2)

μk = The coefficient of the kinetic friction

We now, calculate the net force acting on the skiers along y axis

Fnet, y = ma

N- mg cos θ = 0

so,

N = mg cos θ

This value is  substituted in equation (2)

f = μk mg cos θ

we substitute the value for equation (1)

F = mg sin θ + μk mg cos θ

mg =  sinθ + μk cos θ)-----(3)

The next step is to calculate the work done by the engine in pulling the skiers, the incline top by applying the equation 3

W = Fx

= mg ( sinθ + μk cos θ)x

x = the displacement

we now substitute 1950 kg for m, 23° for θ, 0.10 for μk and 320m for x

so,

W = mg ( sinθ + μk cos θ)x

= (1950 kg) (9.81 m/s²) (sin 23° + (0.10) cos 23°) (320 m)

= 2.99 * 10 ^6 J

Then,

The time from minute to s is converted

t =(2.0min) ( 60sec/1.0min) = 120 sec

Now we calculate the power needed by the engine to pull the skiers at the incline top

Thus,

P = W/t

we substitute  2.955 * 10 ^6 J for W and  120 s for t

we have,

P = 2.955 * 10 ^ 6 J/ 120 s

= ( 2.4625 * 10 ^ 4 W) (1.0 hp/746 W)

= 33.0 hp

In conclusion the required power by the engine is 33.0 hp

To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. By plugging in the given values into the appropriate equations, we can find the required horsepower of the engine.

To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. First, we find the net force of the skier parallel to the incline by subtracting the force due to friction from the component of the skier's weight parallel to the incline. Then, we calculate the work done against friction and gravity using the formula W = Fd. Finally, we convert the work done to horsepower using the conversion factor 1 hp = 746 W.

The work done against friction and gravity is:

W = F_net * d

The power required is:

P = W / t

And finally, we convert the power to horsepower:

Power (hp) = P / 746

By plugging the given values into these equations and multiplying the final power by 30 (for 30 skiers), we can find the required horsepower of the engine.

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Answer:

It is perceived as louder.

Explanation:

Amplitude affects the loudness of sound.

Frequency and wavelength affect the pitch of the sound.

Answer:3m/s

Explanation:

mass(m)=50kg

Kinetic energy =225 joules

Kinetic energy=(m x (velocity)^2)/2

225=(50 x (velocity)^2)/2

Cross multiplying we get

225x2=50x(velocity)^2

450=50x(velocity)^2

Divide both sides by 50

450/50=(50x(velocity)^2)/50

9=(velocity)^2

Taking the square root of both sides we get

√9=velocity

3=velocity

Velocity=3m/s

Answer:

Decrease the voltage,and do not change the resistance,the current will also decrease

Explanation:

Decrease the voltage,and do not change the resistance, the current will also decrease, because voltage is directly proportional to current

Answer:

B.If we decrease the voltage, and do not change the resistance, then the current will also decrease.

Explanation:

i just take the (pre)test

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Answer:

Explanation:

Half width - 3.75 m

Rainfall intensity - 90 mm/hr

Longitudinal slope - 0.75%

Cross slope - 2.25%

Allowable limit of gutter flow, Q road = (Design constant x Intensity of rain x Area) / 360

= (0.91×90×(9×L1×10∧-4)/360 = 0.000204 L1

Using the standard design chart, allowable limit of gutter flow =0.018 m3/s

Therefore,0.018 = 0.000204 L1

L1 = 0.018 / 0.000204 = 88.24

Inlet spacing to be adapted is 88m