Answer:
Explanation:
Half-life problems are modeled as exponential equations. The half-life formula is [tex]P=P_o\left (\dfrac{1}{2} \right)^{\frac{t}{k}}[/tex] where [tex]P_o[/tex] is the initial amount, [tex]k[/tex] is the length of the half-life, [tex]t[/tex] is the amount of time that has elapsed since the initial measurement was taken, and [tex]P[/tex] is the amount that remains at time [tex]t[/tex].
[tex]P=14.2\left (\dfrac{1}{2} \right)^{\frac{t}{8.0252}}[/tex]
Deriving the half-life formula
If one forgets the half-life formula, one can derive an equivalent equation by recalling the basic an exponential equation, [tex]y=a b^{t}[/tex], where [tex]t[/tex] is still the amount of time, and [tex]y[/tex] is the amount remaining at time [tex]t[/tex]. The constants a and b can be solved for as follows:
Knowing that amount initially is 14.2g, we let this be time zero:
[tex]y=a b^{t}[/tex]
[tex](14.2)=ab^{(0)}[/tex]
[tex]14.2=a *1[/tex]
[tex]14.2=a[/tex]
So, [tex]a=14.2[/tex], which represents out initial amount of the substance, and our equation becomes: [tex]y=14.2 b^{t}[/tex]
Knowing that the "half-life" is 8.0252 days (note that the unit here is "days", so times for all future uses of this equation must be in "days"), we know that the amount remaining after that time will be one-half of what we started with:
[tex]\left(\frac{1}{2} *14.2 \right)=14.2 b^{(8.0252)}[/tex]
[tex]\dfrac{7.1}{14.2}=\dfrac{14.2 b^{8.0252}}{14.2}[/tex]
[tex]0.5=b^{8.0252}[/tex]
[tex]\sqrt[8.0252]{\frac{1}{2}}=\sqrt[8.0252]{b^{8.0252}}[/tex]
[tex]\sqrt[8.0252]{\frac{1}{2}}=b[/tex]
Recalling exponent properties, one could find that [tex]\left ( \frac{1}{2} \right )^{\frac{1}{8.0252}}=b[/tex], which will give the equation identical to the half-life formula. However, recalling this trivia about exponent properties is not necessary to solve this problem. One can just evaluate the radical in a calculator:
[tex]b=0.9172535661...[/tex]
Using this decimal approximation has advantages (don't have to remember the half-life formula & don't have to remember as many exponent properties), but one minor disadvantage (need to keep more decimal places to reduce rounding error).
So, our general equation derived from the basic exponential function is:
[tex]y=14.2* (0.9172535661)^t[/tex] or [tex]y=14.2*(0.5)^{\frac{t}{8.0252}}[/tex] where y represents the amount remaining at time t.
Solving for the amount remaining
With the equation set up, substitute the amount of time it takes to cross the Pacific to solve for the amount remaining:
[tex]y=14.2* (0.9172535661)^{(31.8)}[/tex] [tex]y=14.2*(0.5)^{\frac{(31.8)}{8.0252}}[/tex]
[tex]y=14.2* 0.0641450581[/tex] [tex]y=14.2*(0.5)^{3.962518068}[/tex]
[tex]y=0.9108598257[/tex] [tex]y=14.2* 0.0641450581[/tex]
[tex]y=0.9108598257[/tex]
Since both the initial amount of Iodine, and the amount of time were given to 3 significant figures, the amount remaining after 31.8days is 0.911g.
What is matter ?
.......................
Answer:
Something which occupies space and have mass.
The answer is not B.
Answer:
D
Explanation:
15m/ s
i hope this helps
If a cup of coffee is at 90°C and a person with a body temperature of 36°C touches it, how will heat flow between
them?
O from the hand to the cup
from the cup to the hand
from the cup to the surrounding air
from the hand to surrounding air
Mark this and return
Save and Exit
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Submit
Answer:
if you pick it up the heat will flow to the hand until the Temperature of both evens out
Please help me!!
1. For objects like insulators (plastics), they can get charged by ___.
2. For metals, where there are more loosely bound electrons, they can get charged without contact by ___.
3. For metals, they can also be charged by direct contact by ___.
a concave lens creates a virtual image at -47.0 cm and a magnification of +1.75. what is the focal length?
The focal length of given concave lens will be -26.85 cm
The height of an image to the height of an object is the ratio that is used to determine a lens' magnification. Additionally, it is provided in terms of object and image distance. It is equivalent to the object distance to image distance ratio.
Given concave lens creates a virtual image at -47.0 cm and a magnification of +1.75.
We have to find focal length
The focal length can be found out by following way:
Magnification = m = +1.75
m = hi/h
hi = -47 cm
1.75 = -47/h
h = -26.85 cm
So the focal length of given concave lens will be -26.85 cm
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Answer:
26.85
Explanation: I got it right on Acellus.
find the velocity and acceleration if x=t³ +2t²+4 at a time 2s
Answer:
[tex]\textsf {v = 20 m/s}[/tex]
[tex]\mathsf {a = 16 m/s^2}[/tex]
Explanation:
[tex]\textsf {To find velocity, let's differentatiate x :}[/tex] [tex]\implies \mathsf {v = \frac{dx}{dt} }[/tex]
⇒ [tex]\mathsf {v = \frac{d}{dx}(t^{3}+2t^{2}+4) }[/tex]
⇒ [tex]\mathsf {v = 3t^{2} +4t +0 }[/tex] [tex]\textsf {(By applying law of differentiation)}[/tex]
[tex]\textsf {Substitute t = 2 :}[/tex]
⇒ [tex]\mathsf {v = 3(2)^{2} + 4(2) }[/tex]
⇒ [tex]\textsf {v = 12 + 8}[/tex]
⇒ [tex]\textsf {v = 20 m/s}[/tex]
[tex]\textsf {To find acceleration, let's differentatiate v :}[/tex] [tex]\implies \mathsf {a = \frac{dv}{dt} }[/tex]
⇒ [tex]\mathsf {a = \frac{d}{dx}(3t^{2}+4t) }[/tex]
⇒ [tex]\textsf {a = 6t + 4}[/tex]
[tex]\textsf {Substitute t = 2 :}[/tex]
⇒ [tex]\textsf {a = 6(2) + 4}[/tex]
⇒ [tex]\textsf {a = 12 + 4}[/tex]
⇒ [tex]\mathsf {a = 16 m/s^2}[/tex]
Mark is diving to the bottom of a pool to pick up a penny. Which of the
following describes the fluid pressure on his ears as he dives?
A. The fluid pressure increases as he dives.
B. After he dives, the fluid pressure increases and then decreases as
he dives deeper.
C. The fluid pressure on his ears doesn't change as he dives.
D. The fluid pressure decreases as he dives.
Answer:
A
Explanation:
As you go deeper, the pressure increases because the water is going farther away from the air and atmosphere
Need help with this question!!
A beta particle or an electron is released during beta decay. The charges can be positive or negative. Co changes to Ni, Fe to Mn, Pb to Tl, and Pu to Am.
What is beta decay?Beta-decay is the radioactive decay that involves the release of the beta particle or the positron or the electron. The larger nucleus splits during nuclear fission and releases smaller nuclei.
The nuclear reactions are shown as:
⁶⁰Co₂₇ → ⁶⁰Ni₂₈ + ⁰e₋₁⁵⁶Fe₂₆ → ⁵⁶Mn₂₅ + ⁰e₋₁²¹⁰Pb₈₂ → ²¹⁰Tl₈₁ + ⁰e₋₁²⁴¹Pu₉₄ → ²⁴¹Am₉₅ + ⁰e₋₁Learn more about beta decay here:
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which of the following is NOT a type of scientist?
A. Geologist
B. Meteorologist
C. Botanist
D. Cryptologist
A cryptologist is not a type of scientist. The correct answer is a cryptologist and the correct option is (D).
Experts in the study of methods for secure communication and data security through encryption and decryption are known as cryptologists.
Even though they are considered scientists in the broadest sense, they are not typically classed with the other natural scientists (geologists, meteorologists, and botanists) stated in the alternatives.
Due to its emphasis on the methods and mathematical principles used in encryption and decryption, cryptology is more intimately related to computer science and mathematics.
Therefore, The correct answer is a cryptologist and the correct option is (D).
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If a 100 N block is resting on a steel table with a coefficient of
static friction μs = 0.68, then what minimum force is required to
move the block?
Answer:
6800
Explanation:
100 x 0.68=6800
Answer: 68
Explanation:
Which of the following measurement is most significant?
A. 66.000cm
B. 0.00066cm
C. 6.600cm
D. 6.6cm
Option C. The measurement with the most significant number is 6.600 cm.
What is significant number?
Significant numbers are numbers that have significance or meaning and give more precise details about the value of the entire numbers.
66.000 cm ------> 2 significant numbers0.00066 cm -------> 2 significant numbers6.600 cm ----------> 4 significant numbers6.6 cm ---------------> 2 significant numbersThus, the measurement with the most significant number is 6.600 cm.
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A radioactive contaminant gives an unfortunate lab rat a dose of 1500 rem in just 1 minute. Assuming that the half life of the radioactive isotope in the contaminant is much longer than 1 minute.What would the activity of the contaminant be if the contaminant is 1.1MeV Beta Emitter?
The activity of the contaminant will be 3.5 ×10⁻¹⁰ Bq if the contaminant is 1.1MeV Beta Emitter.
Disclaimer, here the m is taken as 0.5kg.
Given, REM = 1500
Time, t= 1 minute =60 seconds
For beta particles,
RBE (Relative Biological Effectiveness) =2.
Absorbed dose, D =REM/RBE= 1500/2 = 750rad
As 100 rad=1 J/kg,
750 rad=7.5 J/kg
So, D=7.5 J/kg
D= total energy absorbed (E)/mass (m)
7.5 J/kg=E/m
E =7.5 ×0.5 = 3.75J
Therefore, the number of beta particles absorbed is 3.75 J.
The number of beta particles absorbed,
As 1 MeV= 1.6 ×10⁻¹³J
So, converting 1.1 MeV in J, 1.1×1.6 ×10⁻¹³J=1.76×10⁻¹³J
Numbers of beta particles,
n=3.75J/1.76×10⁻¹³J
n=2.13×10⁻¹²
Hence, the number of beta particles is 2.13×10⁻¹².
Activity, A= n/t
where n is the number of beta particles and t is the time.
A= n/t=(2.13×10⁻¹²)/60
A= 3.5 ×10⁻¹⁰ Bq
So, the activity is 3.5 ×10⁻¹⁰ Bq.
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Calculate the estimated density of each ball. Use the formula
D = m/V
where D is the density, m is the mass, and V is the volume. Record your calculations in Table A of your Student Guide.
Given that the density of water is 1.0 g/cm3, make a prediction about whether each ball will float in water. Record your prediction in Table A.
What is the estimated density of the table tennis ball? Record your answer to the nearest hundredth.
0.07
g/cm3
What is the estimated density of the golf ball? Record your answer to the nearest hundreth.
The estimated density of the golf ball is 700 kg/m³
What is density?Density is defined as Mass per unit Volume.
In displacement method,
First , we measuring the volume of water displaced by an object which tell us the volume of the object then we will use the physical balance to determine its mass.
Then calculate the density by dividing the mass by the volume.
i.e. D = m/V
Given, Density of water is 1.0 g/cm³
Using displacement method , The estimated volume of golf ball is 100 cm³ and estimated mass is 7g
Then ,
Density = 10 cm³ / 7 g= 0.07 g/ cm³ = 700 kg/m³
So the estimated density of golf ball is 700 kg/m³
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. A vertical electric field is set up in space to compensate for the gravitational force on a point charge. What is the required magnitude and direction of the field when the point charge is: (a) an electron? (b) a proton? Comment on the obtained values.
(a) The required magnitude of the electric field when the point charge is an electron is 5.57 x 10⁻¹¹ N/C.
(b) The required magnitude of the electric field when the point charge is an proton is 1.02 x 10⁻⁷ N/C.
Magnitude of electric fieldThe magnitude of electric field is given by the following equation.
F = qE
But F = mg
mg = qE
E = mg/q
where;
E is the electric fieldm is mass of the particleg is acceleration due to gravityq is charge of the particleFor an electronE = (9.11 x 10⁻³¹ x 9.8)/(1.602 x 10⁻¹⁹)
E = 5.57 x 10⁻¹¹ N/C
For protonE = (1.67 x 10⁻²⁷ x 9.8)/(1.602 x 10⁻¹⁹)
E = 1.02 x 10⁻⁷ N/C
Thus, the required vertical electric field is greater when the charge is proton.
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A penny is dropped so that it reaches a terminal velocity of 13.3m/s. If the momentum is measured to be 0.0332kgm/s, what is the mass of the penny
Answer:
2.5 grams
Explanation:
p = mv
m = p/v
m = 0.0332 / 13.3
m = 0.0025kg
0.0025 x 1000 = 2.5
m = 2.5g
What can a line graph be used to do?
A. Make predictions
B. Make comparisons
C. Identify positive correlation
D. Identify negative correlation
Answer:
B
Explanation:
i's 100% paset bro.....
A sinewave has a period (duration of one cycle) of 460 μs. What is the corresponding frequency of this sinewave in kHz, expressed to three significant figures (see Study Note 7.1 in the Using numbers (maths) booklet)?
If the frequency of the sinewave is now reduced by a factor of 4.25, what will be the new period value? Express your answer in ms to three significant figures.
Note: in the second part of this question, to avoid rounding errors in your calculations, use the full frequency value from the first part, not the rounded value to three significant figures.
Answer:
See below
Explanation:
Frequency = 1 / period
= 1 / 460 X 10^-6
2173.91 Hz = ~ 2.17 Khz
2.17391 kHz / 4.25 = .511 kHz <====new frequency
period = 1/frequency
= 1955 microseconds =1.96 ms
Answer:
2.17 kHz1.96 msExplanation:
You want to know the frequency in kHz of a sine wave with a period of 460 μs, and its period if the frequency is reduced by a factor of 4.25.
UnitsWhen you are interested in the frequency in kHz, it is convenient to use milliseconds (ms) to express the period. Milliseconds and kilohertz are inverse units.
The period of the given sine wave can be expressed in milliseconds as ...
460 μs = 460×(0.001 ms) = 0.460 ms
FrequencyThe frequency of the wave is 1/(0.460 ms) ≈ 2.17 kHz.
PeriodBecause period and frequency are reciprocals of each other, reducing the frequency by a factor of 4.25 increases the period by the same factor.
The new period is 4.25×0.460 ms = 1.96 ms.
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A piece of steel expands 10 cm when ur is heated from 20 to 50 degrees Celsius. How much would it expand if it was heated from 20 to 60 degrees Celsius
The steel would expand by 4. 8 * 10^-3 cm
How to determine the linear expansionThe change in length ΔL is proportional to length L. It is dependent on the temperature, substance, and length.
Using the formula:
ΔL= α LΔT
where ΔL is the change in length L = 10cm
ΔT is the change in temperature = 60° - 20° = 40° C
α is the coefficient of linear expansion = 1.2 x 10^-5 °C
Substitute into the formula
ΔL = [tex]1.2 * 10^-5 * 10 * 40[/tex]
ΔL = [tex]4.8 * 10 ^-3[/tex] cm
Therefore, the steel would expand by 4. 8 * 10^-3 cm
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At a given temperature, lighter gas molecules:
A) have an average speed less than heavier gas molecules.
B) have an average speed greater than heavier gas molecules.
C) ll move more slowly than heavier gas molecules.
At a given temperature, lighter gas molecules, have an average speed greater than heavier gas molecules.
What is temperature?Temperature is the measure of degree of hotness or coldness of a body. It is also the measure of average kinetic energy of a body.
As temperature increases, the average kinetic energy of a body increases.
K.E = ¹/₂mv²
v² = 2K.E/m
v = √( 2K.E/m)
where;
m is massv is velocityK.E is kinetic energyFrom the equation above, at a constant temperature, the speed of a gas molecule will decrease with increase in the mass of the molecules and vice versa.
Thus, at a given temperature, lighter gas molecules, have an average speed greater than heavier gas molecules.
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A metallic spoon is placed in a hot cup of coffee. If the coffee gives away 190 calories to the spoon to cool down by 0.75°C, what is the mass of the coffee? (Assume that ccoffee = 1.0 cal/gC°.)
According to the definition of calorimetry, the mass of the coffee is 253.33 g.
Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).
so, the equation that allows to calculate heat exchanges is:
Q = c× m× ΔT
where:
Q is the heat exchanged by a body of mass m.
c is the specific heat substance.
ΔT is the temperature variation.
Mass of coffee
In this case, Given is :
Q= 190 calories
c= 1
m= ?
ΔT= 0.75 C
Replacing in the equation that allows to calculate heat exchanges is:
190 cal = 1 × m× 0.75 C
Solving:
m= 190 cal÷ (1 × 0.75 C)
m=253.33 g
Finally, the mass of the coffee is 253.33 g.
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A car and a truck, starting from rest, have the same acceleration, but the truck moves twice the length of time. Compared with the car, the truck will travel
Compared with the car, the truck will travel four times as far.
The initial velocity of car and truck, u = 0
The acceleration of both the truck and car = a
The length of time for the acceleration = t
Let the time the truck accelerated be 2t
How to calculate the distance traveled by car and truck?The distance traveled by car is calculated as;
s = ut + ¹/₂at²
s₁ = 0(t) + ¹/₂at²
s₁ = ¹/₂at²
The distance traveled by truck
s = ut + ¹/₂at²
s₂ = 0(2t) + ¹/₂a (2t)²
s₂ = ¹/₂a x 4t²
s₂ = 4 (¹/₂at²)
s₂ = 4(s₁)
We can conclude that the Truck distance is four times the car distance.
Therefore, Compared with the car, the truck will travel four times as far.
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One principle of civil engineering is that when you design a highway you should have traffic flow in
the same direction and avoid interruptions to that flow as much as possible. Exit ramps tend to be
curved so that cars don't have to stop rather than having 90-degree angles that force stops and
starts. This is an application of which Gestalt principle?
The good continuation is an application of the Gestalt principle.
What is good continuation?
According to the Law of Good Continuation, figures with smooth edges are more likely to be perceived as continuous than those with abrupt or sharp angles.
One rule of civil engineering is that while designing a highway, traffic should move in one direction and be as free of interruptions as feasible.
Instead of having 90-degree angles that require stops and starts, exit ramps typically incorporate curves to prevent motorists from having to halt. Applying the Gestalt concept to a good continuation
Hence the good continuation is an application of the Gestalt principle.
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Ivan exerts 20 N of force to lift a basket 2 m. He then carries the basket 5 m across a room to place it on a shelf.
Ivan does work when he
.
The amount of work he does is
The amount of the work done will be 100 J. Work done is denoted by W.
What is work done?Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.
Work may be zero, positive and negative.it depends on the direction of the body displaced. if the body is displaced in the same direction of the force it will be positive.
The given data in the problem is;
F is the force applied = 20 N
d is the displacement = 5.0 m
The work done is found as;
W = F × d
W = 20 N × 5
W= 100 J
Hence, the amount of work done will be 100 J.
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Answer:
lifts the basket, 40J
Explanation:
which of the following statements is true about the suns energy and earth
The correct statement about the sun and the earth is that only about half of the suns energy hits the earths surface.
What is the sun?The sun is the source through which energy reaches the earth. The sun is a large star that produces energy by the process of nuclear fusion.
Hence, the correct statement about the sun and the earth is that only about half of the suns energy hits the earths surface.
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Which sentence describes an object that has kinetic energy?
Answer:
Kinetic energy is referred to the energy associated with movement and or motion, thus the only object that is moving would be A boat sailing across the ocean.
Explanation:
An object is released from an aeroplane which is diving at an angle of 30° from the horizontal with a speed of 50m/s. If the plane is at a height of
4000m from the ground when the object is released, find
(a) the velocity of the object when it hits the ground.
(b) the time taken for the object to reach the ground.
please I need the solution urgently.
a)The velocity of the object when it hits the ground will be 1.12 × 10⁵ m/sec
b) The time taken for the object to reach the ground will be 11.4 × 10³ sec.
What is projectile motion?The motion of an item hurled or projected into the air, subject only to gravity's acceleration, is known as projectile motion.
The velocity in the x-direction;
[tex]\rm v_x = (vcos \theta)^2 +2gh \\\\ v_x = (50 cos 30)^2+ 2 \times 9.81 \times 4000 \\\\ v_x = 80355 m/sec[/tex]
Velocity in y-direction;
[tex]\rm v_ y = (vsin \theta)^2 + 2gh \\\\ v_ y = (25)^2+2 \times 9.81 \times 4000 \\\\ v_y =79105 \ m/sec[/tex]
The resultant velocity is found as 1.12 × 10⁵ m/sec.
The time taken to reach the ground is found as;
[tex]\rm v = u+gt \\\\ 1.12 \times 10^5 \ m/sec = 50 \ m/sec + 9.81 \times t \\\\ t = 11.4 \times 10^3 \ sec[/tex]
Hence, the velocity of the object when it hits the ground will be 1.12 × 10⁵ m/sec, and the time taken for the object to reach the ground will be 11.4 × 10³ sec.
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What is the weight of a 0.145kg baseball on the moon if the gravitational acceleration on the moon is approximately 1.625 m/s2
Answer:I would say that it would be about 2/3rds as fast as the moon and i have seen a similar question but it asked different info about it. I also believe that the basketball would have a lower weight due to it being in space. I feel bad saying this but i know that i got some info off this website when working with this and i hope it helps.
Explanation:
Note- I am new to Brainly so sorry if this isn't as helpful as you expected this to be.
a person walk at first constant speed 5 m/s then back alone the straight line from B to A at a constant speed 3 m/s a) what is his average speed over the entire trip b) what is his average velocity over the entire trip
Answer:
3.75 m/s
Explanation:
Comment
Let's deal with the second question first. The average velocity is 0 because the displacement (distance between the starting point and ending point) is 0.
The first question is a little harder. You don't seem to have enough information. When that happens, you can just make things up. Now there's an interesting solution. You could do it with algebra, but it is easier to see with numbers.
Givens
d = 150 m. between A and Br1 = rate from A to B = 5 m/sr2 = rate from B to A = 3 m/stime A to B = t1time B to A = t2Formulas
t1 = d / r1
t2 = d/r2
average rate = total distance / total time
Solution
t1 = 150 m / 5 m/s = 30 seconds
t2 = 150 m / 3 m/s = 50 seconds
Total distance = 150 m + 150 m = 300 m
Total time = 30 seconds + 50 seconds = 80 seconds
Average speed = 300 m / 80 s
Answer
Average speed = 3.75 m/s
What does the first law of thermodynamics state about energy?
The first law states that the internal energy change of that system is given by Q − W . Since added heat increases the internal energy of a system, Q is positive when added to the system and negative when removed from the system.
Which object has the least thermal energy?
Answer:
2kg brick
Explanation:
2kg brick at 25 degrees.
Answer: A 2kg brick at 20*C
Explanation: