Two resistors are connected in parallel. If R1 and R2 represent the resistance in Ohms (Ω) of each resistor, then the total resistance R is given by 1R=1R1+1R2. Suppose that in fact, these two resistors are actually potentiometers (resistors with variable resistance) and R1 is increasing at a rate of 0.4Ω/min and R2 is increasing at a rate of 0.6Ω/min. At what rate is R changing when R1=117Ω and R2=112Ω?

Answers

Answer 1

Answer:

1/Re= 1/R1 + 1/R2

Explanation:

Answer 2

Two resistors are connected in parallel. If R1 and R2 represent the resistance in Ohms (Ω) of each resistor, then the total resistance R is given by  [tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex]. Thus, the rate of R changes when R₁ = 117 Ω and

R₂ = 112 Ω is 0.25 Ω/min

For a given resistor connected in parallel;

[tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex]

Making R from the left-hand side the subject of the formula, then:

[tex]\mathbf{R = \dfrac{R_1R_2}{R_1+R_2}}[/tex]

Given that:

[tex]\mathbf{R_1 = 117,}[/tex] [tex]\mathbf{R_2 = 112 }[/tex]

Now, replacing the values in the above previous equation, we have:

[tex]\mathbf{R = \dfrac{13104}{229}}[/tex]

However, the differentiation of R with respect to time t will give us the rate at which R is changing when R1=117Ω and R2=112Ω.

So, by differentiating the given equation of the resistor in parallel with respect to time t;

[tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex],   we have:

[tex]\mathbf{\dfrac{1}{R^2}(\dfrac{dR}{dt})=\dfrac{1}{R_1^2}(\dfrac{dR_1}{dt})+\dfrac{1}{R_2^2}(\dfrac{dR_2}{dt})}[/tex]

[tex]\mathbf{(\dfrac{dR}{dt})=R^2 \Bigg[ \dfrac{1}{R_1^2}(\dfrac{dR_1}{dt})+\dfrac{1}{R_2^2}(\dfrac{dR_2}{dt})\Bigg]}[/tex]

[tex]\mathbf{\dfrac{dR}{dt}=(\dfrac{13104}{229})^2 \Bigg[ \dfrac{0.4}{117^2}+\dfrac{0.6}{112^2}\Bigg]}[/tex]

[tex]\mathbf{\dfrac{dR}{dt}=3274.44 \Bigg[ (7.7052 \times 10^{-5} )\Bigg]}[/tex]

[tex]\mathbf{\dfrac{dR}{dt}=0.25\ \Omega /min}[/tex]

Therefore, we can conclude that the rate at which R is changing R1=117Ω and R2=112Ω is 0.25 Ω/min

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Related Questions

Describe the formation of the land, the atmosphere, and the oceans of earth

Answers

Land: Tectonic plate movement under the Earth can create landforms by pushing up mountains and hills. Erosion by water and wind can wear down land and create landforms like valleys and canyons. ... Landforms can exist under water in the form of mountain ranges and basins under the sea.

Atmosphere: (4.6 billion years ago)
As Earth cooled, an atmosphere formed mainly from gases spewed from volcanoes. It included hydrogen sulfide, methane, and ten to 200 times as much carbon dioxide as today's atmosphere. After about half a billion years, Earth's surface cooled and solidified enough for water to collect on it.

Ocean: After the Earth's surface had cooled to a temperature below the boiling point of water, rain began to fall—and continued to fall for centuries. As the water drained into the great hollows in the Earth's surface, the primeval ocean came into existence. The forces of gravity prevented the water from leaving the planet.

A copper wire has a mass of 29.33 mg/cm and has a length of 2.5 cm.

Find the weight of the copper wire.

Answers

The correct answer 73.325 mg

question is included in the picture!!! PUT REAL ANSWERS OR I WILL REPORT YOU​

Answers

Answer:

Explanation:

this is like rubbing a balloon on your head to make your hair stand up.  Do that to the can.    The balloon is filled , ofc,  and then just rub the balloon on the can.  This will charge the can with static electricity.   :P

Someone please help me...
the distance from the Earth to the sun equals 1 AU. Neptune is 30 AU from the sun. How far is Neptune from the Earth?

Answers

Answer:

1 astronomical unit, or AU, is the average distance from the Earth to the Sun; that's about 150 million km. So, Neptune's average distance from the Sun is 30.1 AU. Its perihelion is 29.8 AU, and it's aphelion is 30.4 AU.

Short Answer: it is 29

Explanation:

sorry if its wrong

Answer:

29

Explanation:

I just took a test! not only that but the other person who answered this question had the corrected answer.

35 POINTSS!!! PLSSSS HELLPPP!!!
Work is the transfer of power from one object to another.


Please select the best answer from the choices provided

T
F

Answers

Answer:

T

beacuse:

Energy can be transferred from one object to another by doing work. ... When work is done, energy is transferred from the agent to the object, which results in a change in the object's motion (more specifically, a change in the object's kinetic energy).

A 1-kg ball is 12 m above the ground, with an initial velocity = 0 m/s.

Use the following formulas
[ KE = 1/2 xm x V2]
[P.E = mxgxh] . g =9.8 m/s2
[ Mechanical energy = K.E + P.E]

Answers

Answer:

M = 117.6 J

Explanation:

Given that,

The mass of a ball, m = 1kg

The height of the ball, h = 12 m

At point A, its initial velocity, v = 0

The mechanical energy is the sum of kinetic and potential energy such that,

[tex]M=\dfrac{1}{2}mv^2+mgh\\\\M=0+mgh\\\\M=1\times 9.8\times 12\\\\M=117.6\ J[/tex]

So, the mechanical energy is equal to 117.6  J.

How much power is required to do 10 J of work on an object in 2 seconds?

Answers

Answer:

5 watts

power = work done ÷ time taken

10 j ÷ 2 = 5w

A 41.6-kg person, running horizontally with a velocity of +4.21 m/s, jumps onto a 14.6-kg sled that is initially at rest. (a) Ignoring the effects of friction during the collision, find the velocity of the sled and person as they move away. (b) The sled and person coast 30.0 m on level snow before coming to rest. What is the coefficient of kinetic friction between the sled and the snow?

Answers

Answer:

a)  v = 3.116 m / s,  b)  μ = 1.65 10⁻²

Explanation:

a) to find the velocity of the set, let's define a system formed by the person and the sled, so that the forces during the collision are internal and the moment is conserved

initial instant. Before the crash

        p₀ = M v₀

final instant. After the crash

        p_f = (M + m) v

the moment is preserved

       M v₀ = (M + m) v

       v = [tex]\frac{M}{M+m} \ v_o[/tex]

let's calculate

      v = [tex]\frac{41.6}{41.6 + 14.6} \ 4.21[/tex]

      v = 3.116 m / s

b) for this part let's use the relationship between work and kinetic energy

        W = ΔK

as the body has its final kinetic energy is zero

the work of the friction forces is

          W = - fr x

the negative sign is because the friction forces always oppose the movement

let's write Newton's second law

Y axis  

        N - W_sled -W_person = 0

        N = mg + M g

        N = (m + M) g

X axis

        fr = ma

the friction force has the expression

        fr = μ N

        fr = μ g (m + M)

we substitute

        - μg (m + M) x = 0- ½ (m + M) v²

          μ = [tex]\frac{1}{2} \ \frac{v^2 }{g \ x }[/tex]

let's calculate

        μ = [tex]\frac{1}{2} \ \frac{3.116^2}{9.8 \ 30.0}[/tex]

        μ = 0.0165

        μ = 1.65 10⁻²

Which is true regarding a child standing up for their own rights?

Answers

Answer:

hey mate......looks like the question is incomplete

Explain how grality and electric charge are different

Answers

A difference between the two forces is the fact that gravitation only attracts, while electrical forces attract when the electrical charges are opposite and repel if the charges are similar. Thus, gravitation is considered a monopole force, while electrostatics is a dipole force. Please mark me as a brainiest!!!

Drink water at least every
weather.
minutes while exercising in hot

Answers

what do you mean sorry

Answer:

Drink water at least every 5 to 20 minutes while exercising in hot weather.

Explanation:

Hope this helps brainliest please

What is the equation for frequency?
a. number of cycles +unit of time
b. number of cycles - unit of time
c. number of cycles ×unit of time
d. number of cycles/ unit of time ​

Answers

D. Number of cycles/ unit of time

Answer:

d

Explanation:

PLEASE HELP! I'LL GIVE BRAINLEST​

Answers

Answer:

Weight = 8.162 Newton.

Explanation:

Given the following data;

Mass = 2.2 kg

Acceleration due to gravity = 3.71 N/kg

To find the weight of the textbook;

Weight = mass * acceleration due to gravity

Weight = 2.2 * 3.71

Weight = 8.162 N

Therefore, the weight of the science textbook in mars is 8.162 Newton.

A moving man is lifting a box up an inclined plane. Halfway up he sets the box down and rests. Which of the following explains why the box does not slide back down the inclined plane?
a. The force of friction balances the force of gravity.
b. The force of gravity does not affect inclined planes.
c. The force of friction does not affect inclined planes.
d. The force of friction is less than the force of gravity.

Answers

Answer: A or B

Explanation: I’m guessing that they even each other out depending on the incline, gravity will help keeping it in place

Please answer the one you know!

Answers

#8 positive kinetic energy

What is the difference between a positively and negatively charged object?

Answers

Answer:

Positively charged objects have electrons; they simply possess more protons than electrons. Negatively charged objects have protons; it's just their number of electrons is greater than their number of protons.

The difference between a positively charged object and a negatively charged object is the number of protons and electrons. The imbalance in charge results into formation of charged objects.

What are Charged objects?

Charged objects have an imbalance of charge that is either more negative electrons than the positive protons or more positive protons than the negative electrons in the object. The neutral objects are those species which have a balance of charge with equal number of protons and electrons.

A positively charged object is formed when an atom has more protons than electrons. And, a negatively charged object is formed when an atom has more electrons than protons. As, electrons have a negative charge and protons have a positive charge.

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Determine a formula for the maximum height h that a rocket will reach if launched vertically from the Earth's surface with speed v0(v < vesc). Express in terms of v0, rE, ME, and G.

Answers

Initially, the energies are:

[tex]U_{i}=-\frac{G M_{\varepsilon} m}{r_{e}} \\ =K_{i}=\frac{1}{2} m v_{0}^{2}[/tex]

At final point, the energies are:

[tex]U_{f}=-\frac{G M_{\varepsilon} m}{r_{e}+h} \\ K_{f}=\frac{1}{2} m(0)^{2}=0[/tex]

Using conservation law of energy,

[tex]-\frac{G M_{e} m}{r_{e}}+\frac{1}{2} m v_{0}^{2} &=-\frac{G M_{e} m}{r_{\varepsilon}+h} \\ -\frac{G M_{e}}{r_{e}}+\frac{v_{0}^{2}}{2} &=-\frac{G M_{e}}{r_{e}+h} \\ \frac{-2 G M_{e}+r_{e} v_{0}^{2}}{2 r_{e}} &=-\frac{G M_{e}}{r_{e}+h} \\ \frac{r_{e}+h}{G M_{e}} &=\frac{2 r_{e}}{2 G M_{e}-r_{e} v_{0}^{2}}[/tex]

The equation is further simplified as:

[tex]r_{e}+h &=\left(\frac{2 r_{e}}{2 G M_{e}-r_{e} v_{0}^{2}}\right) G M_{e} \\ h &=\frac{2 r_{e} G M_{e}}{2 G M_{e}-r_{e} v_{0}^{2}}-r_{e} \\ &=\frac{2 r_{e} G M_{e}-2 r_{e} G M_{e}+r_{e}^{2} v_{0}^{2}}{2 G M_{e}-r_{e} v_{0}^{2}} \\ & h=\frac{r_{e}^{2} v_{0}^{2}}{2 G M_{e}-r_{e} v_{0}^{2}}[/tex]

A 51.0 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 10.0 m the floor is frictionless, and for the next 10.5 m the coefficient of friction is 0.17.
What is the final speed of the crate after being pulled these 20.5 meters?

Answers

Answer:

The final speed of the crate is 12.07 m/s.

Explanation:

For the first 10.0 meters, the only force acting on the crate is 225 N, so we can calculate the acceleration as follows:

[tex] F = ma [/tex]

[tex] a = \frac{F}{m} = \frac{225 N}{51.0 kg} = 4.41 m/s^{2} [/tex]

Now, we can calculate the final speed of the crate at the end of 10.0 m:

[tex] v_{f}^{2} = v_{0}^{2} + 2ad_{1} [/tex]                  

[tex] v_{f} = \sqrt{0 + 2*4.41 m/s^{2}*10.0 m} = 9.39 m/s [/tex]    

For the next 10.5 meters we have frictional force:

[tex] F - F_{\mu} = ma [/tex]

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

So, the acceleration is:

[tex] a = \frac{F - \mu mg}{m} = \frac{225 N - 0.17*51.0 kg*9.81 m/s^{2}}{51.0 kg} = 2.74 m/s^{2} [/tex]

The final speed of the crate at the end of 10.0 m will be the initial speed of the following 10.5 meters, so:

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

[tex] v_{f} = \sqrt{(9.39 m/s)^{2} + 2*2.74 m/s^{2}*10.5 m} = 12.07 m/s [/tex]  

Therefore, the final speed of the crate after being pulled these 20.5 meters is 12.07 m/s.  

I hope it helps you!                              

Pushing open door .action force and reaction

Answers

Answer: Newtons third law

Explanation: According to Newton's third law of motion, forces always act in equal but opposite pairs. Another way of saying this is for every action, there is an equal but opposite reaction. This means that when you push on a wall, the wall pushes back on you with a force equal in strength to the force you exerted.

Newton's third law we find that the reaction to the force is an out applied by the putting door towards to the person.

given parameters

  Push the door open

to find

  The reaction

Newton's third law states that the forces between bodies always occur in pairs, that is, the two bodies interacting with each other, therefore these forces are of equal magnitude, but opposite direction. Consequently each force acts on one of the bodies, these forces are called action and reaction.

By applying Newton's third law to the open door; we exert a force on the door therefore the door exerts a force of equal magnitude, but opposite direction on us.

Using Newton's third law we find that the reaction to the force is an out applied to the person.

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Disk A, with a mass of 2.0 kg and a radius of 70 cm , rotates clockwise about a frictionless vertical axle at 50 rev/s . Disk B, also 2.0 kg but with a radius of 50 cm , rotates counterclockwise about that same axle, but at a greater height than disk A, at 50 rev/s . Disk B slides down the axle until it lands on top of disk A, after which they rotate together. After the collision, what is their common angular speed (in rev/s) and in which direction do they rotate?

Answers

Answer:

    w = - 197.5 rad / s

The negative sign indicates that the rotations are clockwise

Explanation:

To solve this exercise, let's use the concept of conservation of the angular number.

We create a system formed by the two discs, in this case the forces last the shock are internal

initial instant .. just before shock

           L₀ = I₀ w₀ + I₁ w₁

instnte final. Right after crash

           L_f = (I₀ + I1) w

angular momentum is conserved

           I₀ w₀ + I₁ w₁ = (I₀ + I₁) w

           w = I₀ w₀ + I₁ w₁ / Io + I1

The moment of inertia of a disk with an axis passing through its thermometric center

          I₀ = ½ m² r₀²

          I₁ = ½ m₁ r₁²

         we substitute

          I₀ = ½ 2.0 0.70²

          I₀ = 0.49 kg m

          I₁ = ½ 2.0 0.5²

          I₁ = 0.25

₁  

let's reduce the magnitudes the SI system

          w₀ = -50 rev / (2pi rad / 1rev) = -314.15 rad / s

          w₁ = 70 rev (2pi rad / 1rev) = 439.82 rad / s

we will assume that the counterclockwise turns are positive

           w = -0.49 314.15 + 0.25 439.82 / (0.49 + 0.25)

            w = (- 4.696 + 1.0995) 102) / 0.74

            w = -197.75 + 0.25

            w = - 197.5 rad / s

The negative sign indicates that the rotations are clockwise

if one stand of DNA reads as AATTCCGGATCG, what would the opposite strand bases be?

Answers

TTAAGGCCTAGC

hope this helps

assuming weightless pulleys and 100% efficiency, what is the minimum input force required to lift a 120 N weight using a single fixed pulley?

A. 21 N
B. 61 N
C. 121 N
D. 241 N

Answers

May be b I’m not for sure tho

40 POINTS!!! PLEASE HELPP!!!
Please select the word from the list that best fits the definition

One form of energy changes to one other form

(A.) single transformation
(B.) multiple transformation

Answers

Answer:

A

Explanation:

if it was B it would say from one to another to another

Answer A



Single transformation

Which climate zone has hot summers, cold winters, and average amounts of precipitation throughout the year?
A. Equator
B. Polar
C. Temperate
D. Tropical

Answers

Answer:

i believe its temperate

Explanation:

The climate zone that has hot summers, cold winters, and average amounts of precipitation throughout the year is the temperate climate zone. So, option C is correct.

What is meant by climatic zone ?

Climatic zones are defined as the areas that have different climatic conditions over the world.

Here,

The climate zone that hot summers, cold winters and average amounts of precipitation throughout the year is the temperate climate zone.

The temperate climate zones are the areas that have mild temperature condition that are located between the subtropical and the polar regions. These are zones with moderate rainfall that is throughout the year. The temperature in this zone will change greatly between the summer and winter seasons. These zones are hotter during the summer and very cold during the winter.

The temperate zone has an average precipitation of 800 mm.

Hence,

The climate zone that has hot summers, cold winters, and average amounts of precipitation throughout the year is the temperate climate zone.

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PLEASE HELP NO LINKS NEED HELP FAST
Use the scenario to answer the question.

An astronomer discovers a new galaxy using a telescope. The astronomer wants to investigate how the galaxy is moving relative to the Milky Way galaxy.

In one or two sentences, make a hypothesis about the movement of the galaxy and explain at least one way to test the hypothesis.

Answers

Answer:

The galaxies outside of our own are moving away from us, and the ones that are farthest away are moving the fastest. This means that no matter what galaxy you happen to be in, all the other galaxies are moving away from you

Explanation:

The hypothesis about the movement of the galaxy is that galaxies are moving far from each other continuously.

What is the milky way galaxy?

The milky way galaxy is a galaxy that contains over a hundred billion stars and it also includes our solar system.  Its name describes its appearance when viewed from the earth. All the individual stars in the whole sky are a portion of the Milky Way Galaxy, the term "Milky Way" is because of the band of light.

The astronomer has discovered a new galaxy which means our universe is continuously expanding. This is because the universe encloses everything that exists.

Galaxies are moving in space and since the universe space is continuously expanding so the galaxies continuously move from each other. The farther the galaxy is from the milky way which is an observable part, the faster will be moving the galaxy and the closer the galaxy is to the milky way, the slower will be movement of the galaxy.

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Which lists the springs in order of increasing spring constant?
W, Y, X, Z
OW, Y, Z, X
O Z, X, Y, W
OX,Z,Y, W

Answers

Answer:

is there supposed to be a picture?

Explanation:

The correct order of the springs in increasing spring constant is: W, Y, X, Z. The correct option is A.

What is the spring constant?

Spring constant, also known as force constant or stiffness, is a measure of the resistance of a spring to deformation when a force is applied to it. It is defined as the amount of force required to stretch or compress a spring by a given distance.

The formula for the spring constant is:

k = F/x

Where

k = is the spring constant,

F = is the applied force,

x =is the displacement or deformation of the spring.

The unit of spring constant is newtons per meter (N/m) in the SI system of units, or pounds per inch (lb/in) in the Imperial system.

A higher spring constant means that a spring is stiffer and requires more force to be stretched or compressed by a given distance. A lower spring constant means that a spring is more flexible and requires less force to be stretched or compressed by a given distance. The spring constant is an important property of springs, which are used in various applications, such as in suspension systems, mattresses, and mechanical watches.

Here in the Question,

In order to determine the order of increasing spring constant, we need to compare the given springs and see which one requires more force to stretch or compress.

Therefore, The correct order of the springs in increasing spring constant is: W, Y, X, Z. This is because the spring constant increases as we move from W to Z.

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Can someone help me here

Answers

Answer:

1. grass Can survive by itself because it is not dependent on food, it is self-sustaining. and since grass it's not dependent on food it is a producer.

2. and 3. they would all decrease, since the prairie dogs are herbivores they eat basically plants such as grass and if half of the grass is gone then they would have less to eat and therefore decrease.

since ferrets eat prairie dogs, if the prairie dogs population decreases the ferrets would have less to eat and therefore decrease as well.

one of the predators of ferrets are foxes and if the ferrets decrease then the fox would also decrease since it will have less to eat.

4. if we would continue advancing years soon the ferret, prairie dogs and foxes would be no more because if there is less grass they would keep on decreasing over the years until they would be extinct.

A wave has a frequency of 2 Hz. Find its period

Answers

It’s period would be 0.5 seconds or 1/2. I think
T=1/f where f=2Hz => T=1/2 or 0,5 seconds.

(20 points) You are at the center of a boat and have been rowing the boat for a long time. You weigh only 80 kg and your 120 kg buddy Bubba has been riding at the front of your 60 kg, 4 m long boat. You come to a stop in the water and then switch places. A) What is the center of mass before you switch places

Answers

Answer:

Explanation:

From the given information:

Let the first weight be [tex]m_ 1[/tex] = 80 kg

The weight of the buddy be [tex]m_2[/tex] = 120 kg

The weight of  Bubba be [tex]m_3[/tex] = 60 kg

Also, since you and Budda are a distance of 4m to each other, then the length to which both meet buddy will be:

[tex]x_1 = x_3 = \dfrac{4}{2} \\ \\ = 2[/tex]

The length of the boat be [tex]x_2[/tex] = 4 m

We can find the center of mass of the system by using the formula:

[tex]X_{CM} = \dfrac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3} \\ \\ X_{CM} = \dfrac{(80 \times 2)+(120\times4)+(60\times2)}{80+120+60} \\ \\ X_{CM} = \dfrac{160+480+120}{260} \\ \\ \mathbf{X_{CM} = 2.923}[/tex]

A rod that is 96.0 cm long is made of glass that has an index of refraction equal to 1.60. The rod has its ends ground to convex spherical surfaces that have radii equal to 8.00 cm and 19.1 cm. An object is in air on the long axis of the rod 19.9 cm from the end that has the 19.1-cm radius.
(a) Find the image distance due to refraction at the 19.1-cm radius surface.
(b) Find the position of the final image due to refraction at both surfaces.
(c) Is the final image real or virtual?

Answers

your answer is B! find the position of the final image due to refraction at both surfaces
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