Suppose that the voltage across the resistor is held constant at 40 volts. If the resistance is steadily decreasing at a rate of 0.2 ohms per second, at what rate is the current changing at the moment that the resistor reaches 5 ohms?

Answers

Answer 1

Answer:

The current is increasing at a rate of 0.32 ampere per second.

Explanation:

The voltage of the resistor is modelled after Ohm's Law, which states that voltage is directly proportional to current:

[tex]V = i\cdot R[/tex] (1)

Where:

[tex]V[/tex] - Voltage, measured in volts.

[tex]i[/tex] - Current, measured in amperes.

[tex]R[/tex] - Resistance, measured in ohms.

An expression for the rate of change in voltage is found by Differential Calculus:

[tex]\frac{dV}{dt} = \frac{di}{dt}\cdot R +i\cdot \frac{dR}{dt}[/tex]

[tex]\frac{dV}{dt} = \frac{di}{dt}\cdot R + \frac{V}{R}\cdot \frac{dR}{dt}[/tex] (2)

Where:

[tex]\frac{dV}{dt}[/tex] - Rate of change in voltage, measured in volts per second.

[tex]\frac{di}{dt}[/tex] - Rate of change in current, measured in amperes per second.

[tex]\frac{dR}{dt}[/tex] - Rate of change in resistance, measured in ohms per second.

If we know that [tex]\frac{dV}{dt} = 0\,\frac{V}{s}[/tex], [tex]R = 5\,\Omega[/tex], [tex]V = 40\,\Omega[/tex] and [tex]\frac{dR}{dt} = -0.2\,\frac{\Omega}{s}[/tex], then the rate of change in current is:

[tex]5\cdot \frac{di}{dt}-1.6 = 0[/tex] (3)

[tex]\frac{di}{dt} = 0.32\,\frac{A}{s}[/tex]

The current is increasing at a rate of 0.32 ampere per second.


Related Questions

The mass of a ship before launch is 55,000 metric tons. The ship is launched down a ramp and drops a total of 10 vertical meters before coming to rest in a lock containing 75,000 cubic meters of fresh water. The specific heat of water is 4200 joules per kilogram degree Celsius. Assume all energy is transferred from the ship to the water. Determine the change in temperature of the water in degrees Celsius .

Answers

Answer:

ΔT = 17.11 °C

Explanation:

In this case, we have a ship standing on a place with a given mass and it's about to be launched to a lock containing water.

At first, before launch, the ship has a potential energy, and when the ship hits the water after being launched, this potential energy is transformed into kinetic energy.

So, let's calculate first the potential energy of the ship:

E = mgh   (1)

We have the mass, gravity and height, so we need to replace the given data here. Before we do that, let's remember to use the correct units. A ton is 1000 kg, so replacing and converting we have:

E = (55000 ton * 1000 kg/ton) * (9.8 m/s²) * 10 m

E = 5.39x10⁹ J

Now this energy will be the same when the ship hits the water, only that is kinetic energy that will result in the rise of temperature. To get this rise we use the following expression:

E = m * C * ΔT   (2)

We have the energy, the mass of water (assuming density of water as 1 kg/m³) and the specific heat, so, replacing in (2) and solving for ΔT we have:

ΔT = E / m * C    (3)

ΔT = 5.39x10⁹ / 4200 * 75000

ΔT = 17.11 °C

Hope this helps

Candice is examining a cell under a microscope. She has identified a cell wall, a nucleus, and a chloroplast. What type of organism does this most likely belong to?
A. A plant B. An animal C. A fungus D. A bacterium

Answers

Answer:

A plant

Explanation:

because animals don't have cell walls, and fungus and bacteria dont have chloroplasts

Will mark BRAINLYEST

Answers

Answer:

A. shin guards is that answer

Answer:

Shin Guards Brainlyiest please

Explanation:

What is cutoff wavelength?

Answers

Answer:

The cutoff wavelength is the minimum wavelength in which a particular fiber still acts as a single mode fiber. Above the cutoff wavelength, the fiber will only allow the LP01 mode to propagate through the fiber (fiber is a single mode fiber at this wavelength).

Explanation:

What two air masses creates hurricanes?

Answers

Answer:

The warm seas create a large humid air mass. The warm air rises and forms a low pressure cell, known as a tropical depression.

Explanation:

Hurricanes arise in the tropical latitudes (between 10 degrees and 25 degrees N) in summer and autumn when sea surface temperature are 28 degrees C (82 degrees F) or higher.

Answer:

air

Explanation:

what is costant error​

Answers

Answer:

In a scientific experiment, a constant error -- also known as a systematic error -- is a source of error that causes measurements to deviate consistently from their true value.

Explanation:

Can you share me your answers ❤️❤️

Answers

Answer:

Depending, on how much it's push against together.

Explanation:

Since, the two objects are getting in contact. But, if it's a type of item/thing there's a different frictions, but I know it's normal friction when two objects comes in contact. But, its depending on how much you push it against the two items.

What principle does a heat engine take advantage of in order to use heat to perform work?

A. Magnets can convert motion into electrical energy
B. The speed of atoms increases when heat is added
C. Fluids expand when heat is added to them
D. Energy can be created from nothing​

Answers

B

Step by step explanation- I took the quiz
the answer is B have a great day but this is the right answer

1. With the exception to water, matter (expands, contracts) when it gets
hotter. *
A)Expands
B)Contracts

Answers

Matter expands when it gets hotter

The time required for one complete cycle of a mass oscillating at the end of a spring is 0.40 s. What is the frequency of oscillation?

Answers

Answer:

the  frequency of the oscillation is 2.5 Hz.

Explanation:

Given;

time to complete the oscillation, t = 0.4 s

number of oscillations, n = 1

The frequency of the oscillation is calculated as;

[tex]F = \frac{n}{t} \\\\F = \frac{1}{0.4} \\\\F = 2.5 \ Hz[/tex]

Therefore, the  frequency of the oscillation is 2.5 Hz.

4 of 1

Suppose that you begin on a street corner and walk one block in one minute. How would you express the rate of your motion?

O One block per minute.

O The information is insufficient.

O Fast

O One minute per block.

Answers

Answer:

The first choice, one block per minute.

Amy is in-line skating. Her mass is 50 kg. She is rolling forward (north) on a flat section of road at 10 m/s. The rolling friction acting on the wheels of her skates is 10 N backward (south). Air resistance creates a 15 N force also acting backward (south) on her. If these are the only horizontal forces acting on Amy. What is her horizontal acceleration as a result of these forces?

Answers

Answer:

The right solution is "0.50 m/s²". A further explanation is provided below.

Explanation:

The given values are:

Mass,

m = 50 kg

Speed,

v = 10 m/s

Rolling friction acting backward (south),

f = 10 N

Air resistance acting backward (south),

[tex]F_T[/tex] = 15 N

The total force acting will be:

⇒  [tex]F = -f-F[/tex]

On substituting the given values, we get

⇒      [tex]=-10-15[/tex]

⇒      [tex]=-25 \ N[/tex]

Now,

⇒  [tex]a = \frac{F}{m}[/tex]

On substituting the given values, we get

⇒     [tex]=\frac{-25}{50}[/tex]

⇒     [tex]=-0.50 \ m/s^2[/tex]

The horizontal acceleration will be "0.50 m/s²" because the (-)ve sign indicates it in south direction.

Which result is more accurate: the slope or the mean value

Answers

I think it is the mean as it gives more of an accurate result. Please give brainiest and thanks

Shanti is riding on a train that is moving at a speed of 90 km/h. He is carrying a power cord for his phone that is 1.2 m long.

Which describes the length of the power cord when Shanti gets off the train?

cannot be determined
less than 1.2 m
more than 1.2 m
equal to 1.2 m

Answers

Answer:

D. equal to 1.2

Explanation:

on edg

The length of the power cord will be equal to 1.2 m.

Describe about the length of power cord? The train is moving at a speed of 90 km /hr. Train was moving but the person in the train can be considered to be at rest. Shanti is the person travelling on the train. Her cord can be used only by her and the cord length of the phone will be 1.2 m.The length can be measured through the distance.The unit of length is meter.As we know the concept of motion and rest, there only the train in motion, shanti was at rest and shanti's power cord were also in the rest. Power cord length will be determined only at the time of manufacturing.If the power cord length to be change then the crimping process.So, the length will not change suddenly.

The length of the power cord when shanti gets off the train is equal to 1.2 m.

The Correct answer is Option D.

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A 2,000 kg rocket is launched 12 km straight up at a constant acceleration into the sky at which point the rocket is travelling at 750 m/s. a) How much work was done by the rocket? b) What is the magnitude of the acceleration of the rocket? c) How long did the flight take?

Answers

Answer:

797700000 J

Explanation:

From the question,

The work done by the rocket, is given as,

W = Ek+Ep............. Equation 1

Where Ek and Ep are the potential and the kinetic energy of the rocket respectively.

Ep = mgh............ Equation 2

Ek = 1/2mv²............. equation 3

Substitute equation 2 and equation 3 into equation 1

W = mgh+1/2mv².............. Equation 4

Where m = mass of the rocket, h = height, v = velocity of the rocket, g = acceleration due to gravity.

Given: m = 2000 kg, h = 12 km = 12000 m, v = 750 m/s, g = 9.8 m/s²

Substitute into equation 4

W = 2000(12000)(9.8)+1/2(2000)(750²)

W = 235200000+562500000

W = 797700000 J

What is the acceleration of a car that goes from 0 MS to 60 MS and six seconds

Answers

a = Δv/Δt
a = v2-v1/t2-t1
a = 60MS - 0MS / 6 seconds
a = 60 MS/ 6 seconds
a = 10 m/s^2

A 0.25 kg beach ball rolling at a speed of 7 m/s collides with a heavy exercise ball at rest. The beach ball bounces straight back with a speed of 4 m/s. That is the change in momentum of the beach ball? What is the impulse exerted on the beach ball? What is the impulse exerted on the exercise ball?

Answers

The impulse exerted on the beach ball is 2.75 kgm/s.

The impulse exerted on the exercise ball is - 2.75 kgm/s.

What is impulse?

This is the force applied to an object that acts over a period of time.

The impulse exerted on the beach ball is the change in the momentum of the ball and it is calculated as follows;

J = ΔP

J = m(v - u)

J = 0.25(7 - (-4))

J = 0.25(7 + 4)

J = 2.75 kgm/s

The impulse exerted on the exercise ball is equal in magnitude but opposite in direction to the beach ball.

Thus, the impulse exerted on the exercise ball is - 2.75 kgm/s.

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4 Two friction disks A and B are to be brought into contact withoutslipping when the angular velocity of disk A is 240 rpm counterclockwise. Disk A starts from rest at time t = 0 and is given a constantangular acceleration with a magnitude α. Disk B starts from rest attime t = 2 s and is given a constant clockwise angular acceleration,also with a magnitude α. Determine (a) the required angular acceleration magnitude α, (b) the time at which the contact occurs

Answers

This question is incomplete, the missing image is uploaded along this answer below;

Answer:

a) the required angular acceleration magnitude α is  π rad/s² or 3.14 rad/s²

b) the time at which the contact occur is 8 seconds

Explanation:

Given the data in the question;

first we convert the given angular velocity to rad/s

angular velocity = 240 rpm = ((240/60) × 2π ) = 8π rad/s

so

ωA = 8π rad/s

next we determine angular acceleration at point A; so

ωA = at

8π rad/s = at -------let this be equation

thus, angular acceleration of disk A is ωA and rotates in counter clockwise direction.

Next we determine the velocity of point C;

Vc = rA × ωA

where Vc is velocity at point C, rA is radius of A ( 150/1000)m,  { from the diagram }

so we substitute

Vc = 0.15m × 8π

Vc = 1.2π m/s

for angular velocity at point B;

Vc = rB × ωB

where rB is the radius of B ( 200/1000)m

we substitute

1.2π = 0.2 × ωB

ωB = 1.2π / 0.2

ωB = 6π rad/s

Thus, the wheel B rotates with an angular velocity of 6π rad/s in clock wise direction.

Now,

a) Determine the required angular acceleration magnitude α

we find the the angular acceleration of disk B after 2 seconds, using the expression;

ωB = at

where angular acceleration is a and t is time ( t - 2)

we substitute

ωB = at

6π = a( t - 2) -------- let this be equation 2

now, lets substract equation 1 form equation 2

(6π = a( t - 2)) - (8π = at)

(6π = at - 2a) - ( 8π = at)

-2π = 0 + -2a

2π = 2a

a = 2π/2

a = π rad/s² or 3.14 rad/s²

Therefore, the required angular acceleration magnitude α is  π rad/s² or 3.14 rad/s²

b) determine the time at which the contact occurs;

from equation 1

8π = at

we substitute in the value of a

8π = π × t

t = 8π / π

t = 8 seconds

Therefore, the time at which the contact occur is 8 seconds

You are explaining why astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn't so by calculating the acceleration of gravity 608 km above the Earth's surface in units of g. (The mass of the Earth is 5.97 x 1024 kg, and the radius of the Earth is 6380 km.)

Answers

Answer:

The answer is "83.1%".

Explanation:

Given:

[tex]\text{Mass of the earth}\ (M_E) = 5.97 \times 10^{24}\ \ kg\\\\\text{Radius of the earth}\ (R_E) = 6380 \ km = 6.38 \times 10^{6}\ \ m\\\\\text{acceleration of gravity}\ (g_E) = 608 \ \ km= 608,000 \ \ m \\\\G= 6.67 \times 10^{-11} \ \ \frac{N \cdot n^2}{kg^2}[/tex]

Using formula:

[tex]\to g_E = G \frac{M_E}{(R_E +h)^2}[/tex]

[tex]\to g_{608 \ km}=6.67\times10^{-11}\frac{5.97 \times 10^{24}}{(6.38 \times 10^{6}+ 608,000)^2}\\\\\to g_{608 \ km}=6.67\times10^{-11}\frac{5.97 \times 10^{24}}{(6,380,000+ 608,000)^2}\\\\\to g_{608 \ km} =6.67\times10^{-11}\frac{5.97 \times 10^{24}}{(6,380,000+ 608,000)^2}\\\\\to g_{608 \ km}=6.67\times10^{-11}\frac{5.97 \times 10^{24}}{(6,988,000)^2}\\\\\to g_{608 \ km}=6.67\times10^{-11}\frac{5.97 \times 10^{24}}{4.88 \times 10^{13}}\\\\[/tex]

[tex]\to g_{608 \ km}=6.67\times10^{-24}\frac{5.97 \times 10^{24}}{4.88}\\\\\to g_{608 \ km}=6.67\times \frac{5.97}{4.88}\\\\\to g_{608 \ km}=6.67\times 1.22336066\\\\\to g_{608 \ km}= 8.15 \ \frac{m}{s^2}[/tex]

Calculating the gravity on the Earth’s surface:

[tex]\to \frac{g_{608 \ km} }{ g_{\ earth \ surface}}[/tex] [tex]= \frac{8.15}{9.8} \times 100=83.1 \%[/tex]

A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 m/s at the bottom, what is the height of the hill?

Answers

Answer:

The height of the hill is 0.46 m.

Explanation:

Given;

mass of the child and sled, m = 50 kg

initial velocity of the sled, u = 0

final velocity of the sled, v = 3 m/s

The height of the high is calculated from the law of conservation of energy;

P.E at top = K.E at bottom

mgh = ¹/₂mv²

gh = ¹/₂v²

[tex]h = \frac{v^2}{2g} \\\\h = \frac{3^2}{2\times 9.8} \\\\h = 0.46 \ m[/tex]

Therefore, the height of the hill is 0.46 m.

I WILL MAKE THE BRAINLEST

6. The front that moved over Roberto's area the last week of the month was humid. Based on the chart and your knowledge of fronts, what kind of front would this most likely be?

Answer choices
A. cold front
B. warm front
C. occluded front
D. stationary front ​

Answers

Answer:

warm front .,

Explanation:

...........

Please help 25 points!

Three waves with frequencies of 1 Hertz (Hz), 3 Hz, and 9Hz travel at the same speed. Which of the following statements is correct?

A. The 1 Hz wave contains the most energy.

B. The crests of all three waves are of equal height.

C. The wavelength of the 9Hz wave is three times that of the 3 Hz wave.

D. The 1 Hz wave has the longest wavelength.

Answers

Answer:

B

Explanation:

The crest of all three waves are of equal height

A 6 kg box with initial speed 8 m/s slides across the floor and comes to a stop after 2.4 s. A) What is the coefficient of kinetic friction?B) How far does the box move? C) You put a 5 kg block in the box, so the total mass is now 11 kg, and you launch this heavier box with an initial speed of 7 m/s. How long does it take to stop?

Answers

Answer:

A. Coefficient of kinetic friction, μ = 0.34

B. The box moves a distance of 9.64 m before coming to a stop

C. The heavier box will stop after 2.1 seconds

Explanation:

a. The coefficient of kinetic or sliding friction is given as: μ = F/R

where applied force, F = m × (∆v)/t

∆v = v - u

∆v = 0 - 8 m/s = -8 m/s; t = 2.4 s

R = normal reaction = m×g

where g = 9.8 m/s²

Substituting in the kinetic friction formula; μ = m∆v/t ÷ 1/m×g

μ = ∆v/g×t

μ = 8 / 9.8 × 2.4

μ = 0.34

b. Using the equation v² = u² + 2as to calculate the distance travelled by the box

where v = 0 m/s; u = 8.0 m/s; a = ? s = ?

From F = ma = μR

a = μR/m = (μ × m × g)/m

a = μg

a = 0.34 × 9.8

a = 3.32 m/s²

This is negative acceleration or deceleration

Substituting in the equation of motion

8² + 2 × -3.32 × s = 0

-6.64s = -64

s = 9.64 m

Therefore, the box moves a distance of 9.64 m before coming to a stop

c. The coefficient of friction is independent of mass.

Using the formula in (a): μ = ∆v/g×t

t = ∆v/μg

t = 7/0.34 × 9.8

t = 2.10 s

Therefore, the heavier box will stop after 2.1 seconds

The  coefficient of kinetic friction of the box is 0.34.

The distance traveled by the box is 9.6 m.

The time taken for the heavier box to stop is 2.1 s.

The coefficient of kinetic friction

The  coefficient of kinetic friction of the box is calculated as follows;

[tex]\mu mg = ma\\\\\mu g = a\\\\\mu g = \frac{v}{t} \\\\\mu = \frac{v}{gt} \\\\\mu = \frac{8}{9.8 \times 2.4} \\\\\mu = 0.34[/tex]

The distance traveled by the box

The distance traveled by the box is calculated as follows;

[tex]v^2 = u^2 + 2as\\\\2as = -u^2\\\\s = \frac{-u^2}{2a} \\\\s = \frac{-u^2}{2\mu g} \\\\s = \frac{-(8)^2}{2\times 0.34 \times 9.8} \\\\s = -9.6 \ m\\\\|s| = 9.6 \ m[/tex]

The time taken for the heavier box to stop is calculated as;

[tex]\mu = \frac{v}{gt} \\\\t = \frac{v}{\mu g} \\\\t = \frac{7}{0.34 \times 9.8}\\\\ t = 2.1 \ s[/tex]

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EXAMPLE

• A patient lying horizontally on a hospital bed is found to have an

enlargement of his blood vessel where the walls have weakened. The

cross-sectional area of the enlargement is 2.0A where A is the cross-

section of the normal aorta. The normal speed of blood through the

person's aorta is 0.40 m/s, and the density of blood is 1,060 kgm-3

Calculate

. a) the speed of blood in the enlargement.

• b) how much higher the pressure is in the enlargement.

Answers

Answer:

Explanation:

a ) The volume of blood flowing per second throughout the vessel is constant .

a₁ v₁ = a₂ v₂

a₁ and a₂ are cross sectional area at two places of vessel and v₁ and v₂ are velocity of blood at these places .

2A x v₁ = A x .40

v₁ = .20 m /s

b )

Let normal pressure be P₁ when cross sectional area is 2A and at cross sectional area A , pressure is P₂

Applying Bernoulli's theorem

P₁ + 1/2 ρv₁² = P₂ + 1/2 ρv₂²

P₁ - P₂ = 1/2  ρ(v₂² - v₁² )

= .5 x 1060 ( .4² - .2² )

= 63.6 Pa .

How much energy is required to move 2 electrons through a potential difference of 1.0 x 10^ 2 volts?

Answers

charge of electron = 1.6×10−¹⁹

(1.6×10−¹⁹)(1×10²) (2e)

= 3.2×10−¹⁷ J

The energy required to move 2 electrons through a potential difference of 1.0 x 10² volts is -3.2 x 10⁻¹⁷ joules.

What is the potential difference?

The potential difference, also known as voltage, is the difference in electrical potential energy per unit of charge between two points in an electrical circuit or an electric field.

In simpler terms, the potential difference is the amount of energy required to move a unit of electric charge from one point to another in an electric field or an electrical circuit. It is measured in volts (V) and can be calculated using the equation:

V = W/Q

Where V = is the potential difference,

W =  is the work done in moving the charge Q from one point to another,

Q =is the amount of charge that is moved.

Potential difference is an essential concept in electrical engineering and physics, as it governs the flow of electric current in a circuit and determines the behavior of electrical devices such as resistors, capacitors, and batteries.

Here in this question,

The energy required to move an electron through a potential difference is given by the formula:

E = qV

Where

E = is the energy required,

q = is the charge of the electron,

V = is the potential difference.

The charge of one electron is -1.6 x 10⁻¹⁹coulombs.

Therefore, for two electrons, the total charge is:

q = 2 x (-1.6 x 10⁻¹⁹coulombs) = -3.2 x 10⁻¹⁹ coulombs

The potential difference is given as 1.0 x 10² volts.

Now, the energy required to move 2 electrons through a potential difference of 1.0 x 10² volts is:

E = (-3.2 x 10⁻¹⁹ coulombs) x (1.0 x 10² volts) = -3.2 x 10⁻¹⁷ joules.

Note: that the negative sign indicates that the electrons lose potential energy as they move through the potential difference.

Therefore, The required energy is -3.2 x 10⁻¹⁷ joules.

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If a biker rides west for 50 miles from his starting position, then turns and bikes back east for 80 miles. What is his displacement?

Answers

Answer:

Displacement = 30 miles due east.

Explanation:

Let the distance due west be A

Let the distance due east be B

Given the following data;

A = 50 miles

B = 80 miles

To find the displacement;

Displacement can be defined as the change in the position of a body or an object. It is a vector quantity because it has both magnitude and direction.

Thus, the displacement would be calculated by subtracting distance A from distance B because the rider rode in opposite directions.

Displacement = B - A

Displacement = 80 - 50

Displacement = 30 miles due east.

A spring is stretched 5 mm by a force of 125 N. How much will the spring stretch
when 250 N force is applied?

Answers

Answer:

10 mm

Explanation:

We'll begin by calculating the spring constant of the spring. This can be obtained as follow:

Extention (e) = 5 mm

Force (F) = 125 N

Spring constant (K) =?

F = Ke

125 = K × 5

Divide both side by 5

K = 125 / 5

K = 25 N/mm

Finally, we shall determine how much the spring will stretch when a 250 N force is applied. This can be obtained as follow:

Force (F) = 250 N

Spring constant (K) = 25 N/mm

Extention (e) =?

F = Ke

250 = 25 × e

Divide both side by 25

e = 250 / 25

e = 10 mm

Thus, the spring will stretch 10 mm when a 250 N force is applied.

The half-life of iodine-131 is 13 hours. If a sample of radium-226 has an original
activity of 400 Bg, what will its activity be after:
i) 26 hours?
ii) 39 hours?
iii) 52 hours

Answers

Answer:

I. 100 Bg

II. 50 Bg

III. 25 Bg

Explanation:

I. Determination of the activity after 26 hours.

We'll begin by calculating the number of half-lives that has elapse. This can be obtained as follow:

Half-life (t½) = 13 hours

Time (t) = 26 hours

Number of half-lives (n) =?

n = t / t½

n = 26 / 13

n = 2

Finally, we shall determine remaining activity

Original activity (N₀) = 400 Bg

Number of half-lives (n) = 2

Activity remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2² × 400

N = 1/4 × 400

N = 100 Bg

II. Determination of the activity after 39 hours.

We'll begin by calculating the number of half-lives that has elapse. This can be obtained as follow:

Half-life (t½) = 13 hours

Time (t) = 39 hours

Number of half-lives (n) =?

n = t / t½

n = 39 / 13

n = 3

Finally, we shall determine remaining activity.

Original activity (N₀) = 400 Bg

Number of half-lives (n) = 3

Activity remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2³ × 400

N = 1/8 × 400

N = 50 Bg

III. Determination of the activity after 52 hours.

We'll begin by calculating the number of half-lives that has elapse. This can be obtained as follow:

Half-life (t½) = 13 hours

Time (t) = 52 hours

Number of half-lives (n) =?

n = t / t½

n = 52 / 13

n = 4

Finally, we shall determine remaining activity

Original activity (N₀) = 400 Bg

Number of half-lives (n) = 4

Activity remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2⁴ × 400

N = 1/16 × 400

N = 25 Bg

A fish of 108 N is attached to the end of a dangling spring, stretching the spring by 14.0 cm. What is the mass of a fish that would stretch the spring by 23.0 cm?

Answers

Answer:

The mass of the fish is 18.1 kg.

Explanation:

Given;

weight of the fish, F = 108 N

extension of the spring by the given weight, x = 14 cm = 0.14 m

First, determine the elastic constant of the spring by applying Hook's law;

F = kx

where;

k is the spring constant

k = F/x

k = 108 / 0.14

k = 771.43 N/m

When the spring is stretched to 23cm, the mass of the fish is calculated as follows;

[tex]F = mg = Kx\\\\m = \frac{Kx}{g} \\\\m = \frac{771.43\times 0.23}{9.8} \\\\m = 18.1 \ kg[/tex]

Therefore, the mass of the fish is 18.1 kg.

Allison and Heather are going to conduct an experiment to see whether salt affects the growth of plants. They assemble five groups of identical plants and give the plants in each group water with a different salt concentration. What is the outcome variable (dependent variable) for their experiment?
A. Salt concentration in plant tissue
B. Salt concentration in plant water
C. Amount of water absorbed by plants
D. Average mass of plants in each group

Answers

Answer:b

Explanation:

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