The half-life of radium-226 is 1590 years. (a) A sample of radium-226 has a mass of 100 mg. Find a formula for the mass of the sample that remains after t years. (b) Find the mass after 1000 years correct to the nearest milligram. (c) When will the mass be reduced to 40 mg? SOLUTION (a) Let m(t) be the mass of radium-226 (in milligrams) that remains after t years. Then dm/dt = km and m(0) = 100, so this theorem gives m(t) = m(0)ekt = ekt. In order to determine the value of k, we use the fact that m(1590) = 1 2 . Thus e1590k = so e1590k = and 1590k = ln 1 2 = − ln(2) k = . Therefore m(t) = . We could use the fact that eln(2) = 2 to write the expression for m(t) in the alternative form m(t) = . (b) The mass after 1000 years is as follows. (Round your final answer to the nearest milligram.) m(1000) = ≈ mg

Answer:

d = 700.4 m

Explanation:

Given that,

The speed of sound through air at 32.0°C is 350.2 m/s.

Reginald sees a bolt of lightning and hears the thunderclap 2.00s later.

We need to find how far from Reginald did the lightning strike. Let the distance be d. So,

Speed = distance/time

d = vt

So,

d = 350.2× 2

d = 700.4  m

So, the required distance is 700.4  m.

Answer:

1.67 m/s²

Explanation:

Total force is;

ΣF = F_f + F_a

From the free body diagram attached, we see that the frictional force F_f is acting in a negative direction.

Thus;

ΣF = -15 + 30

ΣF = 15 N

Now, to get the acceleration, we will use the formula;

ΣF = ma

We are given m = 9 kg

Thus;

15 = 9a

a = 15/9

a = 1.67 m/s²

Answer:

A , power

Explanation:

Hope this is useful. Have a lovely rest of your day! God bless you.

We are to find the acceleration.

Answer:

-9.2 m/s²

Explanation:

Total force is expressed as;

ΣF = F_d + F_g

We are given;

F_d = 50 N

Mass of skydiver = 78 kg

Thus, F_g = 78 × -9.8

g is negative since it is a free fall

Thus;

F_g = -764.4 N

ΣF = 50 - 764.4

ΣF = -714.4 N

Formula for acceleration is;

ΣF = ma

a = -714.4/78

a ≈ -9.2 m/s²

Answer:

0 m/s

Explanation:

if an object is dropped we know the initial velocity is zero when in free fall

Answer:

A

Explanation:

Kinetic energy must be moving. Potential energy has the ability to move but is not doing so at the moment.

A is likely the answer. But there's lots involved in that kind of motion.

B If the ball is elevated, it implies it is not moving yet. It has potential energy.

C Again, the spring is compressed. It will push something when it moves, but it is not moving yet.

D The load gun's bullet is not moving. It's still potential energy.

E. The mouse trap is set, but it is not moving. When the mouse eats the bait then it's potential energy will transform into kinetic energy.

Answer:

I can infer that higher levels of CO2 result in warmer temperatures. The CO2 first exceeded 300 ppm in 1950.

Let me know if this helps!

The Work-Energy Theorem states that Work is equal to the change in kinetic energy, which is the first option . This theorem is an essential principle in physics and mechanics, so first option is correct.

Work (W) is a measure of the energy transferred to or from an object by a force acting on it. It is defined as the product of the force applied to the object and the displacement of the object in the direction of the force. When a force does positive work on an object, it transfers energy to the object, increasing its kinetic energy. Conversely, when a force does negative work on an object (opposite to its direction of motion), it takes energy away from the object, decreasing its kinetic energy. So, first option is correct.

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Answer:In this lesson, the mathematical relationship between the tube's length, the speed of sound through air, and the ... Thus, the length of the air column is equal to one-half of the wavelength for the first harmonic. ... Determine the fundamental frequency (1st harmonic) of an open-end air column that has a length of 67.5 cm.

Explanation:

Answer:

0.0s

Explanation:

I got it right in acellus

Answer: 0.0

Explanation:

Answer:

[tex]a=62.5\ m/s^2[/tex]

Explanation:

Given that,

The velocity of the object, v = 25 m/s

Radius of the circle, r = 10 m

We need to find the acceleration of the object. The centripetal acceleration act on it. It is given by :

[tex]a=\dfrac{v^2}{r}\\\\a=\dfrac{(25)^2}{10}\\\\a=62.5\ m/s^2[/tex]

So, the acceleration of the object is equal to [tex]62.5\ m/s^2[/tex].

Answer:

2)

Explanation:

Answer:

i believe it would be C

Explanation:

Answer:

v= 335 m/s

2∆t= 0.75 s

∆x= v.∆t → ∆x= 335×½×0.75 = 125.625 m

Answer:

The magnetic force was much stronger on Wednesday because the magnetic force is stronger closer to the magnets.

Explanation:

The magnetic force was much stronger on Wednesday than on Tuesday because the magnetic force is stronger closer to the magnets. Therefore claim 3B is more convincing.

Magnetic force can be described as a consequence of electromagnetic force which is caused due to the motion of charges. A moving charge surrounds itself with a magnetic field and the force that arises due to interacting magnetic fields.

The magnetic force between two moving charges is the effect exerted upon either charge by a magnetic field generated by the other. The magnetic force depends on the charge, the motion of each of the objects, and the separation between them.

The magnitude of the force is determined by the cross product of velocity and the magnetic field is equal to q.[v × B]. The resultant force can be described as perpendicular to the direction of the velocity and the magnetic field.

Therefore, the magnetic force was much stronger closer to the magnets.

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Answer:

2500 m

Explanation:

Given that,

Each lap is 500 m

Gareth takes 5 laps.

We need to find distance traveled by Gareth. The distance covered by him is given by :

d = 5×500

d = 2500 m

Hence, he will travel 2500 m.

When individuals improve their aerobic endurance, which body systems are affected?

Anwser: your heart and lungs

Answer:

the greater the speed, the greater the electromotive force

* The metal pole must be parallel to the field

* you must keep the ball of the field

Explanation:

To determine the advice to the runners, let's use the Farad equation to and

           fem = -N [tex]\frac{ d \phi}{dt}[/tex]  = -N [tex]\frac{ B A Cos \theta }{dt}[/tex]

how the runners are moving

                 fi = B l x

            fem = -N B l v

therefore the advice we can give are:

* the greater the speed, the greater the electromotive force

* The metal pole must be parallel to the field

* you must keep the ball of the field

Answer:

20 * .3 = 6N

Explanation:

The impulse on the ball kicked with a force of 20 N force 0.3 s is 6 Ns

From the question given above, the following data were obtained:

Force = 20 N

Time = 0.3 s

The impulse on the ball can be obtained as follow:

[tex]impulse \: = force \: \times time \\ impulse \: = 20 \: \times \: 0.3 \\[/tex]

Therefore, the impulse on the ball is 6 Ns

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Answer:

Explanation:

From the given information:

At state 1:

Initial Quality [tex]= x_1 = 0.85[/tex]

mass = 10.0 kg

At state 2:

Temperature [tex]T_2 = 320^0[/tex]

mass of the piston [tex]m_p = 204 \ kg[/tex]

area of the piston [tex]A_p = 0.00 5 \ m^2[/tex]

Atmospheric pressure [tex]P_{atm}= 100 \ kPa = 100 \times 10^3 \ Pa[/tex]

Gravitational acceleration = 9.81 m/s²

[tex]\mathbf{P= P_1=P_2}[/tex], This is because there exists no restriction to the movement of the piston and provided the process is frictionless. So, the process 1-2 is regarded as constant.

To calculate the applying force balance over the piston by using force balance in the vertical direction:

[tex]\mathbf{P_{AP} = P_{atmA_p} + m_pg}[/tex]

∴

(100 × 10³)×0.005 + 204 × 9.31 = P × 0.05

P = 500248 Pa

P = 500.25 kPa

At state 1:

[tex]\mathbf{P_1 = P = 500.25 \ kPa}[/tex]

[tex]x_1 = 0.85[/tex]

Hence, this is a saturated mixture of liquid and vapor

Using the steam tables at 500.25 kPa

[tex]V_f = 1.093 \times 10^{-3} \ m^3/kg \\ \\ V_g = 0.375 \ m^3/kg \\ \\ U_f = 639.72 \ kJ/kg \\ \\ U_g = 2560.72 \ kJ/kg[/tex]

∴

Specific volume at state 1 is given as:

[tex]V_1 = [ V_f +x_1(v_g -v_f) ] \ at \ 500.25 \ kPa \\ \\ V_1 = 0.319 \ m^3/kg[/tex]

volume at state 1 is given by:

[tex]V_1 = mV_1 = 10 \times 0.319 \\ \\ V_1 = 3.19 \ m^3[/tex]

Similarly, the specific internal energy is:

[tex]U_1 = [U_f +x_1 (U_o-Uf)] \ at \ 500.25 \ kPa[/tex]

[tex]U_1 = 639.72 +0.82 (2560.72 -639.72)[/tex]

[tex]U_1 = 2272.57 \ kJ/kg[/tex]

At state 2:

[tex]P = P_1 = P_2 = 500.25 \ kPa \\ \\ T_2 = 320^0 \ C[/tex]

Using steam tables at P = 500.25 kPa and T = 320° C

[tex]V_2 = 0.541 \ m^3/kg \\ \\ U_2 = 2835.08 \ kJ/kg[/tex]

∴

[tex]V_2 = mV-2 = 10 \times V_2 = 5.41 \ m^3[/tex]

[tex]\text{Now; Applying the 1st law of thermodynamics to the system}[/tex]

[tex]_1Q_2 -_1W_2 = \Delta V =m(u_2-u_1) \\ \\ where;\ _1W_2 = P(V_2-V_1) \\ \\ _1Q_2 -P(V_2-V_1) = m(u_2-u_1) \\ \\ _1Q_2 - 500.25(5.91 -3.19) = 10( 2835.08 -2272.57) \\ \\ \mathbf{ _1Q_2 = 6735.66 \ kJ}[/tex]

Answer:

8.82 m/s²

Explanation:

Formula for the free fall or gravitational acceleration is;

a = GM/r²

Where;

G is gravitational constant = 6.67 × 10^(-11) m³/kg.s²

M is mass of earth = 5.972 × 10^(24) kg

r is radius of earth = 6371 km

We are given that the satellite orbits Earth 350 km above Earth's surface.

Thus, new radius = 6371 + 350 = 6721 km = 6721000 m

Thus;

a = (6.67 × 10^(-11) × 5.972 × 10^(24))/(6721000²)

a = 8.82 m/s²

Answer:

Option C. 2, 2, 3

Explanation:

__KClO₃ —> __ KCl + __O₂

The above equation can be balance as illustrated below:

KClO₃ —> KCl + O₂

There are 2 atoms of O on the right side and 3 atoms on the left side. It can be balance by writing 2 before KClO₃ and 3 before O₂ as shown below:

2KClO₃ —> KCl + 3O₂

There are 2 atoms of K on the left side and 1 atom on the right side. It can be balance by writing 2 before KCl as shown below:

2KClO₃ —> 2KCl + 3O₂

Thus, the equation is balanced. The coefficients are: 2, 2, 3

Answer:

8. True

9. true

10. false

Explanation:

Answer:

false

true

false

the galaxies are moving away from each other, not towards each other.

Answer:

It leads to a higher pitch of sound which means the sound is louder.

Explanation:

When a sound is made, it will cause vibrations to occur.

The size of these vibrations are called amplitude while their speed is called frequency.

Now, the larger the vibrations implies that we will have high amplitude such that the sound is louder, whereas, the higher the frequency, the higher the pitch of sound and vice versa.

The larger the pitch, the louder the sound and vice versa.

Thus, increasing the frequency leads to higher pitch and ultimately louder sound.

Answer:

 F = 1.047 10⁻² N

Explanation:

Let's use kinematics to find the angular acceleration

             w = w₀ + α t

as for rest w₀ = 0

             w = α t

             α = w / t

let's reduce the magnitudes to the SI system

              w = 1000 rev / min (2π rad/ 1 rev) (1 min/ 60s) = 104.72 rad / s

              m = 1.00 g (1 kg / 1000 g) = 1,000 10⁻³ kg

              r = 10.0 cm (1 m / 100 cm) = 0.100 m

let's calculate

              α = 104.72 / 1

              α = 104.72 rad / s²

angular and linear variables are related

               a = α  r

               a = 104.72 0.100

               a = 10.47 m / s²

finally we substitute in Newton's second law

               F = 1 10⁻³ 10.47

               F = 1.047 10⁻² N

Answer:

F = 2985.125 N

Explanation:

Given that,

The radius of curvature of the roller coaster, r = 8 m

Speed of Micheal, v = 17 m/s

Mass of body, m = 65 kg  We need to find the net force acting on Micheal. Net force act the bottom of the circle is given by :

[tex]F=\dfrac{mv^2}{r}+mg\\\\F=m(\dfrac{v^2}{r}+g)\\\\=65(\dfrac{17^2}{8}+9.8)\\\\=2985.125\ N[/tex]

So, the net force is 2985.125 N.