An investigator collects a sample of a radioactive isotope with an activity of 490,000 Bq.48 hours later, the activity is 110,000 Bq. Part A For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution What is the half-life of the sample?
Answer:
The correct answer is "22.27 hours".
Explanation:
Given that:
Radioactive isotope activity,
= 490,000 Bq
Activity,
= 110,000 Bq
Time,
= 48 hours
As we know,
⇒ [tex]A = A_0 e^{- \lambda t}[/tex]
or,
⇒ [tex]\frac{A}{A_0}=e^{-\lambda t}[/tex]
By taking "ln", we get
⇒ [tex]ln \frac{A}{A_0}=- \lambda t[/tex]
By substituting the values, we get
⇒ [tex]-ln \frac{110000}{490000} = -48 \lambda[/tex]
⇒ [tex]-1.4939=-48 \lambda[/tex]
[tex]\lambda = 0.031122[/tex]
As,
⇒ [tex]\lambda = \frac{ln_2}{\frac{T}{2} }[/tex]
then,
⇒ [tex]\frac{ln_2}{T_ \frac{1}{2} } =0.031122[/tex]
⇒ [tex]T_\frac{1}{2}=\frac{ln_2}{0.031122}[/tex]
[tex]=22.27 \ hours[/tex]
what is the formula to calculate the speed
Answer:
speed=to distance ÷time , thank me later
2.
A rock, mass 4 kg, and a 1 kg stone fall freely from rest from a height of
100 m. After they fall for 2 seconds, the ratio of the rock's speed to the
stone's speed is
Answer:
44.72m/s
Explanation:
use th formula:vf²=vi²at
and then substitute the values
remember the units
If there is no air resistance, the speed of the free falling object from the same height will be the same. Therefore, the ratio of speed of the stone to that of rock for 2 seconds falling will be 1 : 1.
What is free falling ?An object freely falling under the force of gravitation is called the free falling body. Here, the acceleration of the object is the acceleration due to gravity.
For a freely falling body, the velocity v = g t
where g is the acceleration due to gravity and for earth g is 9.8 m/s².
Everybody falls with the same rate freely under the acceleration due to gravity if there is no air resistance at all.
Here, the time t = 2 s
then v = 9.8 m/s² × 2 s = 19.6 m/s.
the speed of both the rock and stone will be 19.6 m/s in the absence of air resistance. Hence, the ratio of their speed is 1 : 1.
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A stone was dropped off a cliff and hit the ground with a speed of 136 ft/s. What is the height of the cliff
Answer:
Explanation:
Use the equation
[tex]v^2=v_0^2+2a[/tex]Δx
In this dimension (the y dimension...the only one we have to care about for this problem), here's what we know:
a = -32 ft/s/s
v₀ = 0 m/s (since someone was holding the stone still before it was dropped)
v = 136 ft/s
Δx = ??
Filling in:
[tex]136^2=0^2+2(-32)[/tex]Δx so
Δx = [tex]\frac{136^2}{2(-32)}[/tex] so
Δx = -289 feet (negative because the stone dropped that many feet below the point from which it was dropped, but you would answer a height question with the positive of this number. If you were asked how far the stone dropped, it would be negative; if you're asked how tall the cliff is, that would be positive)
voltage needed to raise current to 3.75a using 20,20,200 resistor set
Answer: The voltage needed is 35.7 V
Explanation:
Assuming that the resistors are arranged in parallel combination.
For the resistors arranged in parallel combination:
[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}[/tex]
We are given:
[tex]R_1=20\Omega\\R_2=20\Omega\\R_3=200\Omega[/tex]
Using above equation, we get:
[tex]\frac{1}{R}=\frac{1}{20}+\frac{1}{20}+\frac{1}{200}\\\\\frac{1}{R}=\frac{10+10+1}{200}\\\\R=\frac{200}{21}=9.52\Omega[/tex]
Calculating the voltage by using Ohm's law:
[tex]V=IR[/tex] .....(1)
where,
V = voltage applied
I = Current = 3.75 A
R = Resistance = [tex]9.52\Omega[/tex]
Putting values in equation 1, we get:
[tex]V=3.75\times 9.52\\\\V=35.7V[/tex]
Hence, the voltage needed is 35.7 V
There are six different ways to arrange those resistors.
Each way leads to a different answer.
You didn't tell us how you want them connected.
The attached drawing shows them all.
A uniform copper wire has a resistance of 100 ohms. If the wire is cut into 10 equal lengths, what will be the resistance of each piece
Answer:
Since resistance is proportional to length R = K L / A
the resistance of each piece would be R / 10 = 10 ohms
A copper wire is the conductor wire. If the wire is cut into 10 equal lengths, the resistance of each piece will be 10 ohms.
What is resistance?Resistance is the opposition to the flow of electrons in the conductor wire.
Given is the total resistance of the wire is 100 ohms.
Resistance is directly proportional to the length of the wire. When the wire is cut into 10 pieces, the new resistance will be
[tex]\dfrac{R}{10} =\dfrac{100}{10} =10 \:\rm ohms[/tex]
Hence, the resistance of each piece will be 10 ohms.
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Two objects (48.0 and 25.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find (a) the acceleration of the objects and (b) the tension in the string.
Answer:
a. 3.09 m/s^2
b. 322.52 N
Explanation:
The computation of the acceleration of the object and the tension of the string is as follows:
The acceleration of the system is a
= (m1 - m2) × g ÷ (m1 + m2)
= (48 - 25) × 9.81 ÷ (48 + 25)
= 3.09 m/s^2
b. The tension in the string is T
= 2 × m1 × m2 × g÷ (m1+m2)
= (2 × 48 × 25 × 9.81) ÷ (48 + 25)
= 322.52 N
Which one will it be
Answer: D
The force decreases inversely proportional to 1/r(squared)
Explanation:
I looked it up im sure this is correct
Answer:
option d
Explanation:
Two objects are attracted to each other by a gravitational force F. ... As the distance r from the center of the planet increases, what happens to the force of gravity on the rocket? The force decreases inversely proportional to 1/r(squared) A spacecraft is orbiting Earth with an orbital radius r.
the force of gravity is represented as
F = GM1M2/r²
now the mass of warth and rocket is considered to be constant and G is a universal constant so it can be said
F is inverse to r²
therefore as the value of r increases that is distance between earth and rocket increases the force decreases
(Follows inverse square law)
What must be the same for two resistors that are connected in parallel?
Answer:
the voltage will be the same across all resistors
Explanation:
the total voltage supplied to the circuit will remain the same across all resistors
9. What part of the eye contains muscles that regulate the amount of light that is allowed to enter the eye?
Answer: the iris
Explanation: I looked it up
Answer:
Iris
Explanation:
Because (iris) has muscles that can expand/contract depends to the amount of light that pupil needs to process/figure out images.
The wheels on a skateboard have a diameter of 2.93 inches. If a skateboarder is traveling downhill at 23 miles per hour, determine the angular velocity of the wheels in radians per second.
Answer:
The angular velocity of the wheels is 276.314 radians per second.
Explanation:
The wheels are rolling, which is a combination of rotation and translation, whose center of rotation is the point of contact between the wheel and the ground and the geometrical center of the skateboard experiments pure translation. Then, the angular velocity can be found by using the following kinematic expression:
[tex]\omega = \frac{v}{R}[/tex] (1)
Where:
[tex]\omega[/tex] - Angular velocity, in radians per second.
[tex]v[/tex] - Velocity of the wheel at its center, in inches per second.
[tex]R[/tex] - Radius of the wheel, in inches.
If we know that [tex]v = 404.8\,\frac{in}{s}[/tex] and [tex]R = 1.465\,in[/tex], then the angular velocity of the wheels are:
[tex]\omega = \frac{404.8\,\frac{in}{s} }{1.465\,in}[/tex]
[tex]\omega = 276.314\,\frac{rad}{s}[/tex]
The angular velocity of the wheels is 276.314 radians per second.
A parallel-plate capacitor is connected to a battery of electric potential difference V. If the plate separation is decreased, do the following quantities increase, decrease, or remain the same: (a) the capacitor’s capacitance, (b) the potential difference across the capacitor, (c) the charge on the capacitor, (d) the energy stored by the capacitor, (e) the magnitude of the electric field between the plates, and (f ) the energy density of that electric field?
Answer:
a) increases.
b) remains the same.
c) increases.
d) increases.
e) increases.
f) increases.
Explanation:
a)
Since the capacitance of a parallel-plate depends only on geometric constants and the dielectric between the plates, we can use the following expression to asess the value of the capacitance:[tex]C = \epsilon_{0}*\frac{A}{d} (1)[/tex]
where ε₀ = permitivitty of free space
A = area of one of the plates
d= plate separation
As we can see, if the plate separation is decreased, the value of the capacitance must increase.b)
Per definition the capacitance explains the relationship between the charge on one of the conductors, and the potential difference between them, as follows:[tex]C = \frac{Q}{V} (2)[/tex]
Assuming that the capacitor remains connected to the battery when the plate separation is decreased, since the voltage can't change (as it must hold the same voltage than previously since it's directly connected to the battery) the potential difference between plates must remain the same.c)
From B, we know that V in (2) must remain constant. Since we know from (1) that C must increase, this means from (2) that Q must increase too.d)
The energy stored in the electric field between the plates can be expressed as follows in terms of the capacitance C and the potential difference V:[tex]U = \frac{1}{2}* C*V^{2} (3)[/tex]
From (1) in a) and from b) we know that the capacitance C must increase whilst V must remain the same, so U in (3) must increase also.e)
In the capacitor the magnitude of the Electric field between the plates is constant, and is related to the potential difference between them by the following linear relationship:[tex]V = E*d (4)[/tex]
Since we know that V must remain the same, if the distance d decreases, the electris field E must increase in the same ratio in order to keep the equation balanced.f)
The energy density of the electric field is defined as the energy stored between plates by unit volume, as follows:[tex]u = \frac{U}{v} = \frac{\frac{1}{2}* C*V^{2}}{A*d} =\frac{1}{2}* \epsilon_{0}*\frac{A*V^{2} }{A*d*d} = \frac{1}{2} *\epsilon_{0}*E^{2} (5)[/tex]
Since it's proportional to the square of the electric field, and we know from e) that the magnitude of the electric field must increase, u must increase too.what change occurs to the mass of an object when a unbalanced
Answer:
The mass decreases
Explanation:
Just smart
(a) Suppose that a NASCAR race car is moving to the right with a constant velocity of +96 m/s. What is the average acceleration of the car? (b) Twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed. What is the average acceleration of the car?
Give the missing ammeter reading a and b. suggest why more current flow through some bulbs than through others Grade 10 question and Answer
Answer:
becaude of electricity
can some one tell the answers
how can u tell matched forces act on objects?
Answer:If an object's speed changes, or if it changes the direction it's moving in,
then there must be forces acting on it. There is no other way for any of
these things to happen.
Once in a while, there may be a group of forces (two or more) acting on
an object, and the group of forces may turn out to be "balanced". When
that happens, the object's speed will remain constant, and ... if the speed
is not zero ... it will continue moving in a straight line. In that case, it's not
possible to tell by looking at it whether there are any forces acting on it
A rock is pulled back in a slingshot as shown in the diagram below. The elastic on the slingshot is displaced 0.2 meters from its initial position. The rock is pulled back with a force of 10 newtons.
When the rock is released, what is its kinetic energy?
Answer:
id
Explanation:
i don't know
The rock takes 8.16s to return to its release point. Given that the elastic band provides a speed of 40m/s to the rock in 10 cm stretch.
What will be the speed of the rock?Initial speed of the rock, u = 40m/s
Final position of the rock s = 0m taking the release point as reference. The rock takes 8.16s to return to its release point. Given that the elastic band provides a speed of 40m/s to the rock in 10 cm stretch.
Nuclear energy is a useful source of power but has disadvantages. The disadvantage of nuclear energy is it produces dangerous waste.
Initial speed of the rock, u = 40m/s
Final position of the rock s = 0m taking the release point as reference
From the second equation of motion:
solving above we get:
t = 0s or t = 8.16s, t =0 seconds is neglected since it represents the initial position which is the same as the final position at t = 8.16s
So, the rock takes 8.16 seconds to return to the release point.
Therefore, The rock takes 8.16s to return to its release point. Given that the elastic band provides a speed of 40m/s to the rock in 10 cm stretch.
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12. What type of lens is pictures below?
Oconverging lens
diverging lens
This is convex lens .
hence It's a converging lens .
The picture shown is a type of converging lens. The correct option is A.
What is a converging lens?A converging lens, also known as a convex lens, is a type of optical lens that is thicker in the middle than at the edges. It is shaped like a curved-outward disc and is commonly used in optical systems such as cameras, telescopes, and microscopes. When light passes through a converging lens, it bends inward and converges at a focal point located on the other side of the lens.
This focal point is determined by the curvature of the lens and its refractive index, which affects how much the light is bent. The distance between the lens and the focal point is called the focal length, and it determines the magnification and the image size produced by the lens. Converging lenses are used in many applications that require focusing and magnifying light, such as correcting vision problems and creating images in photography and microscopy.
Therefore, The correct answer is converging lens.
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Consider a simple pendulum that consists of a massless 2.00-meter length of rope attached to a 5.00-kg mass at one end. What is the period of oscillation for this simple pendulum
Answer:
2.8 seconds
Explanation: Given that a simple pendulum that consists of a massless 2.00-meter length of rope attached to a 5.00-kg mass at one end. What is the period of oscillation for this simple pendulum
The parameters given are :
Length = 2 m
Mass = 5kg
Using the formula below
T = 2 pi × sqrt ( L / g )
Substitute all the parameters into the formula.
T = 2 × 3.143 × sqrt ( 2 / 9.8 )
T = 2 × 3.143 × 0.4517
T = 2.838 s
Therefore, the period of oscillation for this simple pendulum is 2.8 s approximately.
If the temperature of the conductor is increased, the electrons’ speeds decrease
Answer:
HOPE IT HELPS YOU!!!
Explanation:
Mark FadedGirl25 as brainliest
which of the following is a correct statement. a. In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are constant. b. In dc steady state conditions, the voltages across the capacitors are zero and the currents through the capacitance are constant. The current through the inductors are constant and the voltage across the inductances are zero. c. In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are zero and the voltage across the inductances are constant. d. WIn dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are zero.
Answer:
d. In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are zero.
Explanation:
The current through a capacitor is given by i = CdV/dt where C = capacitance of capacitor and V = voltage across capacitor. At steady state dV/dt = 0 and V = constant. So, i = CdV/dt = C × 0 = 0.
So, in dc steady state, the voltage across a capacitor is constant and the current zero.
The voltage across an inductor is given by V = Ldi/dt where L = inductance of inductor and i = current through inductor. At steady state di/dt = 0 and V = constant. So, V = Ldi/dt = L × 0 = 0.
So, in dc steady state, the voltage across an inductor is zero and the current constant.
So, In dc steady state conditions, the voltages across the capacitors are constant and the currents through the capacitance are zero. The current through the inductors are constant and the voltage across the inductances are zero.
The answer is d.
Please solve this problem!
Answer:
Send a clear photo again
Explanation:
And tag me
turn this scentence to repirted speach.
i ate icecream
She said that..........
Answer:
dhfhffuththt9tr8tujtngigjtjrjrjrurur
13. How many electrons does a complete third electron shell hold?
Answer:
A) 8A complete third electron shell holds 8 electrons
---------------------------
hope it helps...
have a great day!!
Answer:
8
Explanation:
1. Why does the shape of the lens in your eye change?
To alter the amount of light that enters the eye
to focus the light
to alter the image sent to the brain
Answer:
to focus the link light
Explanation:
Because the lens is flexible and elastic, it can change its curved shape to focus on objects and people that are either nearby or at a distance. ... The ciliary muscles, which are part of the ciliary body, are attached to the lens and contract or release to change the lens shape and curvature.
Answer:
to focus the link light
Explanation:
vote brainliest I never got voted brainliest plssss
If you are driving a car with a velocity of -25 m/s and you have an acceleration of -2 m/s^2, are you speeding up or slowing down? Why?
Answer:
Hmmm...
This is a bit tricky
Ok...
Negative Velocity means you're Moving in the Opposite direction....
Negative Acceleration (deceleration) means you're slowing down.
Deceleration would mean slowing down if you were Moving with a Positive velocity.
But In this case...
You're Moving with negative velocity and Negative acceleration...
This simply means that the acceleration and velocity vector are in the same direction....
Its means that...
"YOU'RE SPEEDING UP"
Just that you're doing it in the opposite direction.
Hope this helps.
A 0.0780 kg lemming runs off a
5.36 m high cliff at 4.84 m/s. What
is its kinetic energy (KE) when it
is 2.00 m above the ground?
Answer:
0.913
Explanation:
k.e=1/2mv square
k.e=1/2×0.078g×23.4256m/s square
k.e=0.913J
The kinetic energy when the lemming is 2.00 m above the ground is approximately 2.56 J (Joules).
To calculate the kinetic energy (KE) of the lemming when it is 2.00 m above the ground, we need to consider the change in its potential energy (PE) as it falls.
The potential energy at a height h is given by:
PE = m g h
Where:
m is the mass of the lemming (0.0780 kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the height above the ground
Given:
Height of the cliff (h) = 5.36 m
Velocity of the lemming (v) = 4.84 m/s
Height above the ground (h') = 2.00 m
The lemming will lose potential energy as it falls from the cliff, which is converted into kinetic energy. Therefore, the kinetic energy when it is 2.00 m above the ground is equal to the difference between its total initial kinetic energy and the potential energy at that height.
Initial potential energy at the top of the cliff:
PE_initial = m g h
Potential energy when it is 2.00 m above the ground:
PE_final = m * g * h'
The change in potential energy is given by:
ΔPE = PE_final - PE_initial
The kinetic energy (KE) when it is 2.00 m above the ground:
KE = ΔPE = -ΔPE (due to energy conservation)
Let's calculate the potential energy at the top of the cliff and when it is 2.00 m above the ground:
PE_initial = m ×g × h
= 0.0780 kg × 9.8 m/s² × 5.36 m
PE_initial ≈ 4.09 J
PE_final = m ×g × h'
= 0.0780 kg ×9.8 m/s² ×2.00 m
PE_final ≈ 1.53 J
The change in potential energy (ΔPE) is:
ΔPE = PE_final - PE_initial = 1.53 J - 4.09 J
ΔPE ≈ -2.56 J
Since the change in potential energy is equal to the kinetic energy, the kinetic energy when the lemming is 2.00 m above the ground is approximately 2.56 J (Joules).
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The heat capacity of sodium metal is 1500 JK-1, if the mass of the sodium metal is 75 kg, the specific
heat capacity would be
Explanation:
the answer is in the image above
The position of a particle changes linearly with time, i.e. as one power of t, as given by the following: h(t) = ( 4.1 t + 5.5 ) meters. Find the speed of the particle, in meters per second.
Answer:
v = 4.1 m / s
Explanation:
Velocity is defined by the relation
v =[tex]\frac{dx}{dt}[/tex]
we perform the derivative
v = 4.1 m / s
Another way to find this magnitude is to see that the velocity on the slope of a graph of h vs t
v = [tex]\frac{\Delta x}{\Delta t}[/tex]
Δx = v Δdt + x₀
h= 4.1 t + 5.5
v = 4.1 m / s
x₀ = 5.5 m
