A radioactive substance decays exponentially. A scientist begins with 160 milligrams of a radioactive substance. After 12 hours, 80 mg of the substance remains. How many milligrams will remain after 19 hours? 53.39 mg
Answers
Approximately 53.39 mg of the substance will remain after 19 hours.
To solve this problem, we can use the formula for exponential decay:
N = N0 ×e^(-λt)
Where N is the amount of substance remaining after time t, N0 is the initial amount of substance, e is the base of the natural logarithm (approximately 2.718), λ is the decay constant, and t is the time elapsed.
We can use the given information to find the decay constant:
80 = 160 × e^(-λ×12)
Dividing both sides by 160 and taking the natural logarithm of both sides, we get:
ln(0.5) = -λ×12
Solving for λ, we get:
λ = ln(2) / 12 ≈ 0.0578
Now we can use this value of λ to find the amount of substance remaining after 19 hours:
N = 160 × e^(-0.0578×19) ≈ 53.39 mg
Therefore, approximately 53.39 mg of the substance will remain after 19 hours.
To learn more about decay visit: https://brainly.com/question/23759636
#SPJ11
Related Questions
The coldest clouds in the ISM are molecular clouds, so named because their temperatures are low enough and their densities high enough for atoms to join together into molecules. These clouds are capable of collapsing to form new stars, in a stellar nursery like the one in the left image. The Pleiades (right image) is an example of stars that formed recently within such a nursery.
Molecular clouds range in mass from a few times the mass of our Sun (solar masses) to 10 million solar masses. Individual stars range from 0.08 to about 150 solar masses.
What does all of this imply about how stars form from molecular clouds?
Answers
Stars form from molecular clouds through a process known as stellar formation.
These clouds, characterized by low temperatures and high densities, provide the ideal conditions for atoms to combine and form molecules. With a mass range spanning from a few solar masses to millions of solar masses, molecular clouds serve as the birthplaces of new stars. The Pleiades cluster serves as a notable example of stars that have recently formed within such a stellar nursery.
The formation of stars from molecular clouds involves several key steps. Firstly, gravitational forces acting on regions of higher density within the cloud cause them to collapse under their own gravity. As the cloud collapses, it begins to fragment into smaller, denser clumps called protostellar cores. These cores continue to collapse, and their central regions become increasingly dense and hot. At this stage, they are known as protostars.
To know more about molecular clouds here https://brainly.com/question/30631889
#SPJ4
determine the flow of methane at t = 68 ∘f in ft3/h through a 2800- ft -long horizontal 1- in. -diameter commercial steel pipe if the pressure drop is 5(10 −3 ) psi .
Answers
The flow rate of methane through a 2800-ft-long horizontal 1-in.-diameter commercial steel pipe at 68 °F and a pressure drop of 5 × 10⁻³ psi is approximately 20.8 ft3/h.
To determine the flow rate of methane through a commercial steel pipe, we can use the Darcy-Weisbach equation, which relates the pressure drop to the flow rate, pipe diameter, pipe length, and fluid properties.
The Darcy-Weisbach equation is:
ΔP = ƒ (L/D) (ρ/2) (V²)
where:
ΔP = pressure drop (psi)
ƒ = Darcy friction factor
L = pipe length (ft)
D = pipe diameter (ft)
ρ = fluid density (lbm/ft3)
V = fluid velocity (ft/s)
To solve for the flow rate, we need to rearrange the equation and solve for V:
V = [ (2ΔP)/(ρ ƒ) ] \(({1/2})\)/ [ (L/D) ] \(({1/2})\)
Now, we can substitute the given values:
T = 68 °F = 528 °R (assuming absolute temperature)
Pipe diameter = 1 inch = 1/12 ft
Pipe length = 2800 ft
Pressure drop = 5 × 10⁻³ psi
Methane density = 0.0447 lbm/ft3 (at 68 °F and 1 atm pressure)
First, we need to calculate the friction factor ƒ. For a smooth commercial steel pipe, we can use the Colebrook equation to calculate the friction factor:
1/√ƒ = -2.0 log10 [ (ε/D)/3.7 + 2.51/(Re √ƒ) ]
where:
ε = pipe roughness (in)
Re = Reynolds number
For a commercial steel pipe, the roughness can be assumed to be 0.00015 inches.
Re = (ρ V D) / μ
where:
μ = fluid viscosity (lbm/ft s)
For methane at 68 °F and 1 atm, the viscosity is 0.000014 lbm/ft s.
Substituting the given values and solving for Re gives:
Re = 2.85 × 10⁶
Now, we can use the Colebrook equation to solve for ƒ:
1/√ƒ = -2.0 log10 [ (0.00015/12)/3.7 + 2.51/(2.85 × 10⁶ √ƒ) ]
ƒ = 0.0043
Substituting the calculated values into the equation for V gives:
V = [ (2 × 5 × 10⁻³)/(0.0447 × 0.0043) ] \(({1/2})\) / [ (2800/12)/1 ] ^ \(({1/2})\)
V = 73.4 ft/s
Finally, we can calculate the flow rate using the equation:
Q = A V
where:
Q = flow rate (ft3/h)
A = pipe cross-sectional area (ft2)
A = π/4 × (1/12)² = 0.000785 ft2
Substituting the calculated values gives:
Q = 0.000785 × 73.4 × 3600
Q = 20.8 ft3/h
To know more about methane click here
brainly.com/question/15061430
#SPJ1
why is the lake shallow in winter?
Answers
Answer:
The justification for this scenario has been characterized elsewhere here.
Explanation:
Water extraction becomes the platform that could be utilized to start managing the problems of aquatic weeds. Water level devaluations often begin throughout the fall as well as keep going via the cold season because once water entertainment will be at its lowest. This has managed to decrease coastal erosion throughout these heavy floods.I need help with the 1st and the 3rd one plzzzzzzzzzzzzz
Answers
Answer for the first one is 2. The answer for the 3rd one is 8
Find the KE of a ball of mass 500 g moving with a velocity of 4 m/s . Plz fast i have just 5 mins
Answers
Answer:
4000 J
Explanation:
KE = (1/2)(m)(v^2)
KE = .5*500*(4^2)
KE = 4000 J
What is the focal length of a lens? what is the focal point?.
Answers
Answer:
The focal length of a lens is the distance from the lens to the focal point.
For a convex lens the focal point is that point at which parallel rays will be focused after passing thru the lens.
Note: For a concave lens the rays will diverge after passing thru the lens and will appear to come from a point on the same side of the lens from which the parallel rays strike the lens,
Which soil conservation method involves planting different crops in a field
each year to restore nutrients.
Answers
Answer:
Crop rotation is the practice of growing a series of different types of crops in the same area across a sequence of growing seasons. It reduces reliance on one set of nutrients, pest and weed pressure, and the probability of developing resistant pest and weeds
if the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) of the gas if the expansion is isobaric.
Answers
If the expansion is isobaric the final temperature of the gas is twice the initial temperature.
To find the final temperature of the gas during an isobaric expansion, we can use the relationship between volume and temperature known as Charles's Law. Charles's Law states that for a fixed amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature.
Mathematically, Charles's Law can be expressed as:
V1 / T1 = V2 / T2
Where:
V1 and T1 are the initial volume and temperature of the gas, respectively.
V2 and T2 are the final volume and temperature of the gas, respectively.
In this case, we are given that the gas is allowed to expand to twice the initial volume. So, we have:
V2 = 2 * V1
Since the expansion is isobaric, the pressure remains constant. Therefore, the initial pressure is equal to the final pressure.
Applying Charles's Law, we can rearrange the equation to solve for T2:
V1 / T1 = V2 / T2
T2 = (V2 * T1) / V1
Substituting V2 = 2 * V1, we have:
T2 = (2 * V1 * T1) / V1
T2 = 2 * T1
Therefore, the final temperature of the gas is twice the initial temperature.
Learn more about temperature at https://brainly.com/question/32502993
#SPJ11
what is the largest hailstone ever discovered (in lbs)? hint: answer will have two decimal places. please do not write in lbs. just type in the number.
Answers
The largest hailstone ever discovered weighed 1.94 . This hailstone was found in Vivian, South Dakota on July 23, 2010 and measured 8 inches in diameter and 18.62 inches in circumference. It broke the previous record for the largest hailstone, which was 1.67 pounds and was found in Coffeyville, Kansas in 1970.
Hailstones are formed when raindrops are carried upward by thunderstorm updrafts into extremely cold areas of the atmosphere and freeze. Hailstones then grow by colliding with liquid water drops that freeze onto the hailstone’s surface. If the water freezes instantaneously when colliding with the hailstone, cloudy ice will form as air bubbles will be trapped in the newly formed ice. However, if the water freezes slowly, the air bubbles can escape and the new ice will be clear. The hail falls when the thunderstorm's updraft can no longer support the weight of the hailstone, which can occur if the stone becomes large enough or the updraft weakens.
To know more about hailstone refer here:
https://brainly.com/question/15571675#
#SPJ11
E
Question 14/36
<
NEXT
BOOKMARK
XE
14
A wave has a frequency of 30 Hz and a wavelength of 10 m. What's its speed?
Answers
Answer:
Speed = 300 m/s
Explanation:
Given the following data;
Frequency = 30 Hz
Wavelength = 10 m
To find the speed of the wave;
Mathematically, the speed of a wave is given by the formula:
\( Speed = wavelength * frequency \)
Substituting into the formula, we have;
\( Speed = 10 * 30 \)
Speed = 300 m/s
Suppose you calculated the speed of light in an unknown substance to be 4.00x10^8 m/s. How could you tell if you made an error in your calculations
Answers
Answer: You could tell if you made an error in your calculations by repeating the steps.
Speed of light is the fastest/maximum in vacuum which is equal to 3 × 10^8 m/s, therefore speed of light through any material equal to 4 × 10^8 m/s is physically and theoretically impossible and therefore incorrect.
Explanation:
A stone falls from rest from the top of a cliff,a second stone is thrown do wnward from the same height 2sec later with an initial speed of 30m/s.If both stones hit the ground below simultaneously,how high is the cliff?
Answers
Answer:
The cliff is 12.632 meter high.
Explanation:
Each stone experiments a free fall motion, that is, an uniformly accelerated motion due to gravity. We construct the respective equations of motion for each stone:
First stone
\(y_{1} = y_{o,1} +v_{o,1}\cdot t +\frac{1}{2}\cdot g\cdot t^{2}\) (1)
Second stone
\(y_{2} = y_{o,2} +v_{o,2}\cdot (t-2) +\frac{1}{2}\cdot g\cdot (t-2)^{2}\) (2)
Where:
\(y_{1}\), \(y_{2}\) - Final height of the first and second stone, in meters.
\(y_{o,1}\), \(y_{o,2}\) - Initial height of the first and second stone, in meters.
\(v_{o,1}\), \(v_{o,2}\) - Initial speed of the first and second stone, in meters per second.
\(t\) - Time, in seconds.
\(g\) - Gravitational acceleration, in meters per square second.
If we know that \(y_{o,1} = y_{o,2}\), \(y_{1} = y_{2} = 0\,m\), \(v_{o,1} = 0\,\frac{m}{s}\), \(v_{o,2} = -30\,\frac{m}{s}\) and \(g = -9.807\,\frac{m}{s^{2}}\), then we find that time when both stones hit the ground simultaneously is:
\(4.904\cdot t^{2} = -30\cdot (t-2)+4.904\cdot (t-2)^{2}\)
\(4.904\cdot t^{2} = -30\cdot t + 60 +4.904\cdot (t^{2}-4\cdot t +4)\)
\(-30\cdot t +60 -19.616\cdot t +19.616 = 0\)
\(49.616\cdot t = 79.616\)
\(t = 1.605\,s\)
The height of the cliff is:
\(y_{1} = y_{o,1} +v_{o,1}\cdot t +\frac{1}{2}\cdot g\cdot t^{2}\)
\(y_{o,1} = 12.632\,m\)
The cliff is 12.632 meter high.
Damron Inc. Wants to purchase a shear for their sheet metal shop and chooses dimensions of cost, reliability, and flexibility as critical to their long term success. They evaluate three different shears and rate their performance on each criterion on a scale from 1 (poor) to 5 (excellent). What is the value index for the shear made by Belsky Manufacturing? Dimension Importance Belsky Mfg. Reber Ind. Floyd Co. Cost 4 1 5 3 Reliability 2 5 2 1 Flexibility 3 3 3 4 A. 23 B. 81 C. 18 D. 9
Answers
Rate the effectiveness of four different shears on a scale of 1 to 10 for each category. Reber thinks that the shear should be bought.
Describe flexibility.Flexibility is the term used to describe a joint's or a collection of joints and muscles' ability to move through a range of motion efficiently painlessly.
Flexibility is the capacity to swiftly and collectedly adapt to brief change, enabling you to successfully handle unforeseen issues or duties. Here are some instances of what you could do: Offer to help another team member if you see them to be overworked.
Flexibility in the workplace refers to the capacity to quickly adjust to novel situations as they emerge. A flexible worker can alter their plans to deal with or get around unexpected challenges.
To learn more about flexibility from given link
https://brainly.com/question/28786129
#SPJ1
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
Answers
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;
\(\rm \frac{df}{dp} =5\%\\\\ \frac{f_{rated-f_1}}{P_{rated}-P_1}=0.05\\\\ \frac{f_{rated-60}}{100-61}=0.05\\\\ f_{rated}=61.95\)
For the grid frequency, 59.9 Hz
\(\rm \frac{f_{rated-f_2}}{P_{rated}-P_2}=0.05\)
\(\rm \frac{61.95-f_2}}{100-P_2} =0.05\\\\ 100-P_2 =20(61.95-59.9)\\\\P_2=100-41 \\\\ P_2=59 \ kW\)
Hence, the generator power will be 59 kW.
To learn more about the power rating, refer to the link;
https://brainly.com/question/13787703
#SPJ1
Potential difference is measure in _____
Answers
Answer:
electric current
Explanation:
The unit is Volt
6. Given cost=0 € (2): a) Determine sin28 b) Which quadrant does sin20 lie and what is the angle to the nearest tenth of a degree? Q
Answers
Since cost = 0 €, the value of sinθ will be 1. Recall that the Pythagorean identity for sine and cosine states that sin²θ + cos²θ = 1. So, sin²θ = 1 - cos²θ. Given cost=0 €,cosθ=0. Substituting cosθ = 0, we get;sin²θ = 1 - cos²θ. sin²θ = 1 - 0² = 1Therefore,sinθ = √1 = 1
This means that sin28 = 1 Since sin20 lies in the first quadrant (0° to 90°), it will have a positive value. To determine sin20, we can use a calculator or reference a trigonometric table. To the nearest tenth of a degree, sin20 is 0.3 and it lies in the first quadrant.
An identity that expresses the Pythagorean theorem in terms of trigonometric functions is known as the Pythagorean trigonometric identity, or simply the Pythagorean identity. It is one of the fundamental relations between the sine and cosine functions, along with the sum-of-angles formulas. The angle can be any real value, and the equation is s i n 2 + c o s 2 = 1. Given both the sine value and the quadrant in which the angle is located, we can use the Pythagorean identity to determine the angle of cosine.
Know more about Pythagorean identity:
https://brainly.com/question/11973047
#SPJ11
HELP PLZZZZZ NOW!!!
Discuss how earthquakes are affected by the uneven distribution of Earth’s natural resources like minerals, energy, and groundwater resources, and how human activities affect Earth’s processes. Discuss past events and future risks associated with such activities in the country you selected.
Propose at least 1 resolution that the Ministry of Environment can take to limit the negative effects of such activities and as a result protect the country against harmful earthquakes.
Answers
Answer:Climatic processes affect the dynamics of Earth's ice sheets and glaciers, and along ... by abrupt events and by continuous reshaping of Earth's surface from surface ... Forecasting natural disasters, including the timing and size of earthquakes, the . Last, human activity has a profound impact on water resources, landscape
Explanation:
step by step
You flip a coin straight up if the coin reaches a high point of 0.25 m above where you released it what was the initial speed?
Answers
Answer: 2.21 m/s
Explanation:
Given
Coin reaches a height of 0.25 m above the launch point
Suppose u is the initial speed of the coin
Using the equation of motion
\(\Rightarrow v^2-u^2=2as\\\)
Putting values
\(\Rightarrow 0^2-u^2=2\times g\times s=2\times (-9.8)\times 0.25\\\Rightarrow u^2=4.9\\\Rightarrow u=2.21\ m/s\)
Thus, the initial velocity is 2.21 m/s
How much electricity must flow through a light bulb to do 1 kWh of work? Mains voltage 220 V.
Answers
Given:
Energy = 1 kWh
Voltage = 220 Volts
Let's find the amount of electric current that must flow through the light bulb.
To find the amount of electric current, apply the formula:
\(P=IV\)Where:
P is the power in watts = 1 kWh = 1000 Watts
V is the voltage = 200 V
I is the electric current.
Rewrite the formula for I and solve:
\(\begin{gathered} I=\frac{P}{V} \\ \\ I=\frac{1000}{220} \\ \\ I=4.5\text{ A} \end{gathered}\)Therefore, the amount of electric current that must flow through the light bulb is 4.5 Ampere
ANSWER:
4.5 A
When a force is applied to an object, no work is being preformed on the object unless the object____.
Answers
convert86400secs into day
Answers
Answer:
86400 seconds is equal to 1 day.
Explanation:
what types of change occur when water changes from a solid to a liquid?
Answers
Answer:
temporary change, in which ice ❄ turns to water
A wind turbine has an efficiency of 0.7. The wind provides 8000 J of kinetic energy to the blades of the wind turbine. How much useful energy will the wind turbine transfer? Use the equation below to help you. You may need to rearrange the equation.
Answers
Answer:
11,428.571428571
Explanation:
So you must divide the energy input by efficency
Please Help!
30. A duck flying due east passes over Atlanta, where the magnetic field of Earth is 5.0 x 10-5 T directed north. The duck has a positive charge of 4.0 x 10-8 C. If the magnetic force acting on the duck is 3.0 x 10-11 N upward, what is the duck's velocity?
Answers
Answer:
5 m/s
Explanation:
hope it helps:) u're welcome
The velocity of the duck must be 15 m/s towards the east which is explained below.
Magnetic force:The force on a moving charge with some velocity under a magnetic field is given by:
F = qv×B
here q is the charge on the object
v is the velocity of the object
B is the magnetic field
v×B gives the direction of the force
B is towards the north, and Force is directed upwards, then velocity v should be towards the east.
3×10⁻¹¹ = 4×10⁻⁸× v × 5×10⁻⁵
v = 15 m/s
Learn more about magnetic force:
https://brainly.com/question/10353944?referrer=searchResults
The average velocity of a plane during a flight was 9.0 m/s. How long did it take the plane to travel 5.0 km
Answers
Answer:
The time taken is 555.56 s.
Explanation:
The average velocity is the ratio of the net velocity to the time required to achieve net velocity.
The formula of average velocity is,
v(av)=d/t
Given d=5.0 km which is 5*1000 m=5000 m and v(av)=9.0 m/s.
Therefore 9=5000/t
t=5000/9
t=555.56
https://brainly.com/question/12984400
#SPJ10
A simple machine where an inclined plane is wrapped in a spiral is called a centripetal ramp.
T.
True
F.
False
Answers
Answer: False
Explanation:
what is the total energy of a proton moving with a speed of 0.83, (in mev
Answers
To calculate the total energy of a proton moving with a speed of 0.83c (where c is the speed of light), we can use the relativistic energy equation: Total Energy (E) = Rest Energy (E₀) + Kinetic Energy (KE).
The rest energy of a proton (E₀) is given by its mass-energy equivalence, which is approximately 938 MeV (megaelectronvolts). The kinetic energy (KE) can be calculated using the relativistic kinetic energy equation:
Kinetic Energy (KE) = (γ - 1) * Rest Energy (E₀)
where γ is the Lorentz factor, given by:
γ = 1 / √(1 - v²/c²)
Given that the speed of the proton is 0.83c, we can substitute these values into the equations to find the total energy:
γ = 1 / √(1 - 0.83²)
≈ 2.3KE = (2.3 - 1) * 938 MeV
≈ 967 MeV
Total Energy (E) = 938 MeV + 967 MeV
= 1905 MeV
Therefore, the total energy of a proton moving with a speed of 0.83c is approximately 1905 MeV.
To know more about speed, click here https://brainly.com/question/2141628
#SPJ11
the apparent path of the sun upon the celestial sphere is called the ________. declination precession sidereal ecliptic parallax 2 points
Answers
Answer:
ecliptic
Explanation:
its actually the intersection of the plane and the Earth's orbit with the celestial sphere.
A series RLC circuit has a 100−Ωresistor, a 0.100μFcapacitor, and a 2.00−mHinductor connected across a 120−Vrms AC source operating at resonant frequency. What is the rms value of the voltage across the capacitor?A) 54.0 VB) 120 VC) 150 VD) 533 VE) 170 V
Answers
The main answer to your question about the rms value of the voltage across the capacitor in a series RLC circuit with a 100-Ω resistor, a 0.100μF capacitor, and a 2.00-mH inductor connected across a 120-Vrms AC source operating at resonant frequency is: D) 533 V.
At resonant frequency, the impedance of the inductor (XL) and the capacitor (XC) cancel each other out (XL = XC). The circuit's impedance equals the resistance (R) of the resistor.
The current through the circuit is given by Ohm's Law: I = V/R. Since the voltage across the capacitor is Vc = I * XC, you can calculate Vc at the resonant frequency.
Summary: In this RLC circuit at resonant frequency, the rms value of the voltage across the capacitor is 533 V.
Learn more about resistor click here:
https://brainly.com/question/24858512
#SPJ11
A 75kg hockey player is skating across the ice at a speed of 6.0m/s. What is the magnitude of the average force required to stop the player in 0.65s?
Answers
Answer:
692.31 N
Explanation:
Applying,
F = ma............... Equation 1
Where F = Average force required to stop the player, m = mass of the player, a = acceleration of the player
But,
a = (v-u)/t............ Equation 2
Where v = final velocity, u = initial velocity, t = time.
Substitute equation 2 into equation 1
F = m(v-u)/t............ Equation 3
From the question,
Given: m = 75 kg, u = 6.0 m/s, v = 0 m/s (to stop), t = 0.65 s
Substitute these values into equation 3
F = 75(0-6)/0.65
F = -692.31 N
Hence the average force required to stop the player is 692.31 N