Remember the formula
[tex]\\ \rm\Rrightarrow A(t)=A_o(0.5)^{\frac{t}{h}}[/tex]
h is half life[tex]\\ \rm\Rrightarrow A(7.82\times 10)=A(78.2)[/tex]
[tex]\\ \rm\Rrightarrow 4.11\times 10^{76}(0.5)^{\frac{78.2}{3.91\times 10^{5}}}[/tex]
[tex]\\ \rm\Rrightarrow 4.11\times 10^{76}(0.5)^{20\times 10^{-5}}[/tex]
[tex]\\ \rm\Rrightarrow 4.11\times 10^{76}(0.5)^{0.0002}[/tex]
[tex]\\ \rm\Rrightarrow 4.11\times 10^{76}(0.998)[/tex]
[tex]\\ \rm\Rrightarrow 4.10178\times 10^{76}[/tex]
Why no options matched?
That time given in end i.e 7.82×10
10 should contain some power to match our options .The number of nuclei of calcium-47 left after 7.82 x 10⁵s is 1.03 x 10¹⁶.
This can be found out using half life and laws of radioactive disintegration.
What are the laws of radioactive disintegration?
The Law of radioactive disintegration states the number of radioactive decay per unit time is proportional to the number of nuclei present in the sample initially.
So, ΔN/Δt = λN
Where, ΔN = number of radioactive nuclei decayed
Δt = time taken for decay
N = No of nuclei present initially
λ= decay constant
What is Half life?Half life is the time taken for the radioactive nuclei to reach half of its initial value.
Half life is given by
[tex]t_{1/2}[/tex] = λ/t
Given here, [tex]t_{1/2}[/tex] = 3/91 x 10.⁵s
N = 4.11 x 10¹⁶.
t = 7.82 x 10.⁵s
We see here that t = 2([tex]t_{1/2}[/tex])
Now, number of radioactive nuclei left undecayed in one half life is N/2
So number of nuclei left undecayed in 2 half lives will be 1/2(N/2) = N/4
So number of nuclei left in the sample will be N/4 = (4.11 x 10¹⁶.)/4
So Number of nuclei left in the sample = 1.03 x 10¹⁶.
Hence 1.03 x 10¹⁶is the correct answer.
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A 20 kg rock sits on the edge of a cliff that is 100 m high.
a. What potential energy does the rock-Earth system possess relative to the base of the cliff?
b. The rock falls without rolling from the cliff. What is its kinetic energy just before it strikes the ground?
c. What is the rock’s speed as it hits the ground?
The potential energy of the rock is 19600 J. Then, the kinetic energy when it hits the ground will be 19600 J. The velocity before it hits the ground will be 44.2 m/s.
What is potential energy ?The potential energy of an object is the energy by virtue of its position. It is related to the mass, m ,height h and acceleration due to gravity g as follows:
p = mgh.
Given m =20 kg
height = 100 m
g = 9.8 m/s²
then p = 20 kg × 100 m × 9.8 m/s² = 19600 J.
When the rock falls down as it approaches the ground, the potential energy converts to kinetic energy. Hence, the kinetic energy before it strike the ground will be 19600 J.
Ke = 1/2 mv² = 19600 J
then v = √ (2 Ke/m)
v = √(2× 19600 J/20 kg) = 44.2 m/s.
Therefore, the speed of the rock as it hits the ground is 44.2 m/s.
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Explore the role of friction when creating safety ramps and escalators. "Why is it important for people and object to move slowly on ramps and escalator?
The role of friction is of great importance when creating safety ramps and escalators because with the help of friction things move.
Why is it important to move objects slowly on ramps and escalator?It is important to move objects slowly on ramps and escalator because the ramps and escalator moves object in the opposite direction of gravity. If we did not move objects slowly, then the objects or a person get damaged.
So we can conclude that the role of friction is of great importance when creating safety ramps and escalators because with the help of friction things move.
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Question 12 (True/Faise Worth 5 points)
The presence of free electrons makes a material a good insulator.
O True
O False
What does the model below represent?
2CO + O2 ——-> 2002
O A. The production of oxygen
O B. An experiment
O C. A release of heat
O D. A chemical reaction
Answer:
D
Explanation:
Because we have two reactants and product
A generator is operating with 5% droop primary control. The generator is rated for 100 kW. Its secondary power command at this point in time (in other words, the power commanded to produce at 60 Hz) is 67 kW. The grid frequency is currently 59.9 Hz. What is the generator power
The generator power will be 59 kW. Power drop is the main factor for finding the generated power.
What is the power rating?The maximum power input allowed to pass through a piece of equipment is known as the equipment's power rating.
Power drop = 5%
The relation of the frequency change with the power drop is;
[tex]\rm \frac{df}{dp} =5\%\\\\ \frac{f_{rated-f_1}}{P_{rated}-P_1}=0.05\\\\ \frac{f_{rated-60}}{100-61}=0.05\\\\ f_{rated}=61.95[/tex]
For the grid frequency, 59.9 Hz
[tex]\rm \frac{f_{rated-f_2}}{P_{rated}-P_2}=0.05[/tex]
[tex]\rm \frac{61.95-f_2}}{100-P_2} =0.05\\\\ 100-P_2 =20(61.95-59.9)\\\\P_2=100-41 \\\\ P_2=59 \ kW[/tex]
Hence, the generator power will be 59 kW.
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Which nuclear equation represents a spontaneous decay?.
Spontaneous fission is a nuclear equation represents a spontaneous decay.
Which nuclear equation represents a spontaneous decay?Spontaneous fission is another type of radioactive decay. In this process, the nucleus will split into two parts and free neutrons with the release of large amount of energy.
So we can conclude that spontaneous fission is a nuclear equation represents a spontaneous decay.
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The coefficient of dynamic friction between the grass and a 200 kg football blocking sled is 0.20. If a football player only pushes horizontally against the sled, how large must the horizontal force be to keep the sled moving at constant velocity
The horizontal force be to keep the sled moving at constant velocity is 392 N.
Horizontal force applied to the sled
The horizontal force applied to the sled to prevent it from moving is calculated from Newton's second law of motion.
F - Ff = ma
where;
a is acceleration of the sledat constant velocity, a = 0
F - μmg = m(0)
F - μmg = 0
F = μmg
F = 0.2 x 200 x 9.8
F = 392 N
Thus, the horizontal force be to keep the sled moving at constant velocity is 392 N.
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Clouds are formed when water vapor in the atmosphere becomes a liquid and condenses. Condensation is a result of the difference in which of the following?
A.
air temperature and dew point temperature
B.
air pressure and air temperature
C.
dew point temperature and ocean temperature
D.
air pressure and wind speed
Answer:
B temperature and dew point temperature
A 1200 kg car moving at 2.5 m/s is struck in the rear by a 2600 kg truck moving at 6.2 m/s. If the vehicles stick together after the collision, what is their speed immediately after colliding?
Velocity: m/s
Answer: 5.0 m/s
Explanation:i had this question on my test
100 % verified!
Conservation of linear momentum
[tex]\\ \rm\Rrightarrow m1v1+m2v2=(m1+M2)v3[/tex]
[tex]\\ \rm\Rrightarrow 1200(2.5)+2600(6.2)=(1200+2600)V3[/tex]
[tex]\\ \rm\Rrightarrow 3000+16120=3800v3[/tex]
[tex]\\ \rm\Rrightarrow 19120=3800v3[/tex]
[tex]\\ \rm\Rrightarrow V3=5m/s[/tex](Approx)
Describe the electric and magnetic fields of an electromagnetic wave.
Answer:The electric field and magnetic field of an electromagnetic wave are perpendicular (at right angles) to each other. They are also perpendicular to the direction of the EM wave. EM waves travel with a constant velocity of 3.00 x 108 ms-1 in vacuum.
Explanation:
When two forces act in the same direction on an object, the net force is found by ....................the forces.
1. adding
2.subtracting
3.multipling
4.dividing
Answer:
By ADDING the forces
Explanation:
A nuclear power plant is built alongside a river. what measurements should a monitoring station downstream record to be sure that the proper procedures are being followed at the power plant? density and radiation levels radiation levels and dust levels salt concentration and temperature temperature and radiation levels
Nuclear power plant should have monitoring units and water purifiers units, so thet they followed propress in the plant.
What is nuclear power plant?
Nuclear power plant is a structure that allows the generation of energy from the fission of toxic materials. It is usually due to the risk of accidents. Nuclear energy is very important for the generation of electricity in many countries.
Hence, water purifiers units should be used in the downstream to measure to protect river should be taken.
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Answer:
temperature and radiation levels
Explanation:
edge
Let each shake of the pennies or thumbtacks represent 1 year. what is the half life, in years, for the pennies in experiment 1? what is the half-life, in years, for the thumbtacks in experiment 2?
(5.4.3 lab - nuclear physics)
The half-life of the pennies in experiment 1 and 2 will be the time it takes for half the pennies to fall off after shaking.
What is Half-Life?Half-Life is the time required for half the amount one a given substance to disappear or decay.
The half-lives of substances are usually constant values.
For example, the Half-Life of radioactive carbon-14 is 5700 years.
Therefore, the half-life of the pennies in experiment one and two will be the time it takes for half the pennies to fall off after shaking.
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Water waves in a small tank are 6.6 m long. They travel at a speed of 2.9 m/s. What is the frequency of the water
waves?
Answer:
.439 Hz
Explanation:
Wavelength = 6.6 m
speed = 2.9 m/s
2.9 = 6.6 f
f = 2.9/6.6 = .439 Hz
A bag of frozen vegetables expanding in the microwave is a good example of how volume __________.
A. increases when temperature decreases
B. decreases when temperature increases
C. decreases when temperature decreases
D. increases when temperature increases
Answer:
D
Explanation:
because when the temperature increases things tend to rise and explode instead of decreasing
The _________ region is where a land or water air mass is formed.
Group of answer choices:
source
atmospheric
primary
hilly
Answer:
atmospheric
Explanation:
I think it’s atmospheric if I, wrong please tell me and I will fix it thanks!
A photon has an energy of 2.88 x 10^-18 j. convert this energy into ev.
Answer:
E = V Q voltage * charge
Since the charge on an electron is e = 1.6E-19 coulombs
the energy of 1 eV is 1.6E-19 joules
E = 2.88E-18 joules / 1.6E-19 joules/electron volt
E = 18 eV
When two forces act in the same direction on an object, the net force is found by ....................the forces.
Answer:
Net force is found by sum of the forces.
Answer:
The correct answer is When two forces act in the same direction on an object, the net force is found by the sum of the forces.
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Thankyou for joining Brainly communicty!!!Adrian plays basketball with Kevin on a basketball court that is completely level. After Adrian makes as basket, their ball rolls to a complete stop. what forces acted on the ball to cause it to stop rolling?
A. acceleration and gravity
B. friction and acceleration
C. gravity and friction
D. magnetic forces and friction
An 95 Watt TV is plugged into a 115 volt circuit.
The TV operates for 120 minutes. If the cost of energy is
8¢ per kW-hr, how much does it cost to run the TV
for 120 minutes?
120 min = 2 hours
95 x 2 : 1000 =0.19 kwh
8¢ x 0.19 kwh = 1.52¢
The cost of running the 95 W TV for 120 minutes if charged at 8 ¢ per kWhr is 1.52 ¢
How to determine the energyPower ( P) = 95 W = 95 / 1000 = 0.095 KWTime (t) = 120 mins = 120 / 60 = 2 hrEnergy (E) =?E = Pt
E = 0.095 × 2
E = 0.19 KWhr
How to determine the cost of operationEnergy (E) = 0.19 KWhrCost per KWhr = 8 ¢ Cost =?Cost = Energy × Cost per KWhr
Cost = 0.19 × 8
Cost = 1.52 ¢
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Active energy is a characteristic of _______ energy.
Answer:
Active energy is a characteristic of Kinetic energy
How can your physical health change with cardio activity? explain why.
Answer:
Other benefits include:
Increases blood flow and decreases chances of stroke.Improves memory and thinking ability.Combats decline in brain functioning with age.Helps protect against developing Alzheimer's disease.Fights osteoporosis and reduces chances for a hip fracture.Regular physical activity is one of the most important things you can do for your health. Being physically active can improve your brain health, help manage weight, reduce the risk of disease, strengthen bones and muscles, and improve your ability to do everyday activities.
Adults who sit less and do any amount of moderate-to-vigorous physical activity gain some health benefits. Only a few lifestyle choices have as large an impact on your health as physical activity.
Everyone can experience the health benefits of physical activity – age, abilities, ethnicity, shape, or size do not matter.
Tyra pushes the pedals of her bicycle with her feet to make it go faster. Which of Newton's laws is demonstrated by this action
The impressed force increases when Tyra pushes the pedals of her bicycle, the momentum of the bike increases hence it moves faster.
What are the laws of motion?The Newton's laws of motion lay the foundation for dynamics. According to Newton's second law, the rate of change of momentum is directly proportional to the impressed force.
Hence, as the impressed force increases when Tyra pushes the pedals of her bicycle, the momentum of the bike increases hence it moves faster.
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The long structure of small intestine is accommodated in small space within our body. Comment.
It would be really helpful if someone answered this.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
According to first law of reflection, we know that :
Angle made by the incident ray and normal [ i.e angle of incidence ] is always equal to Angle made by the reflected ray and normal [ i.e Angle of reflection ]
Therefore, we can say that the missing angle (angle of reflection) has the same value as the angle of incidence which is equal to 45°
Please read the statement through to understand the procedure ~
Help me pleaseee
a battery-operated toy draws 0.2 a of current from a battery pack. if the total resistance
of the boy is 362, what is the voltage of the battery pack?
What was the stated reason why Red Bull Stratos mission executed?
A.
Red Bull wanted a publicity stunt that caught the eye of consumers.
B.
A new one-manned capsule was invented and needed to use a human as its test pilot.
C.
The team needed to set itself apart from NASA and other private space companies.
D.
The team wanted to explore human limits for the future of space travel.
Show the molecular formula and electron structure of the simplest compound that forms with only carbon and hydrogen atoms.
The simplest compound of hydrocarbon is methane
The formula is CH_4It belongs to alkane group and has single bonds.The electron structure attached
write at least five electrical safety rules
a equals thirty five thats why the elephant strted to kiss the cat and the cat went upsidedown and started crying all over the ceiling
An ammeter is a device that measures _____.
the type of charge on a resistor
the current through a resistor
the voltage across a resistor
the potential of the battery
