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Sphinxa [80]
3 years ago
12

A scientist begins with 100 milligrams of a radioactive substance that decays exponentially. After 33 hours, 50 mg of the substa

nce remains. How many milligrams will remain after 59 hours? (Round your answer to two decimal places.)
Physics
1 answer:
Hoochie [10]3 years ago
4 0

Answer:

m\approx34.99

Explanation:

Radioactive decay behaves according to the law of exponential decay:

m(t)=m_0*e^{-rt}

Where:

r=Decay\hspace{3}rate

t=Time(In\hspace{3}days)

m_0=Initial\hspace{3}amount\hspace{3}of\hspace{3}substance

m(t)=Amount\hspace{3}of\hspace{3}substance\hspace{3}at\hspace{3}time\hspace{3}t

So we need to find the decay rate r. Let's find it using the equation and the data provide, but first, we need to convert the hours in days:

50h*\frac{1day}{24h}=\frac{25}{12}day\\  33h*\frac{1day}{24h} =\frac{11}{8}day

Now for t=\frac{11}{8},m=50 then:

m(\frac{11}{8} )=100*e^{-r(\frac{11}{8}) } =50

Divide both sides by 100:

e^{-r(\frac{11}{8}) } =\frac{1}{2}

Take the natural logarithm of both sides:

-\frac{11}{8}x=ln(\frac{1}{2} )

Multiply both sides by -8/11:

x=\frac{-8ln(\frac{1}{2} )}{11} \approx0.504107

Now we have found the rate decay r, let's find how many milligrams will remain after 59 hours (25/12 day):

m(\frac{25}{12} )=100*e^{-0.504107*\frac{25}{12}) } =100*e^{-1.050222917}=34.98597508\approx35.99

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If you do 1,000 J of work on a system and remove 500 J of heat from it, what is the change in its internal energy
DENIUS [597]
Here I advice doing thought experiment and not remembering equations. By doing thought experiment you will write down equation by yourself.

Doing some work on a system means that system will "absorb" that energy. Here, system absorbs 1000J of energy. Now you are cooling system down by removing 500J of energy. That means that system will lose 500J of energy

All of that can be written as 1000 - 500 = 500 which means that after cooling your system has 500J left.
6 0
3 years ago
Experiment 1: A study is done to determine which of two fuel mixtures allows a rocket to travel farther over a period of time. R
leva [86]

Answer: D

Experiment 1 has a confounding variable related to the mass of the rockets. Any variation in mass may cause a discrepancy in the distance traveled.

This is the answer to the question because:

  • Both experiments do have a confounding variable.
  • Experiment 1 doesn't have to stay constant.
  • A double-blind experiment will not do anything to the placebo.
  • High blood pressure people will not make the results confusing.

The answer has to be the option D. Hope this helps you!

3 0
4 years ago
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alexandr402 [8]

Answer:

Velocity Has vector Quantity

4 0
3 years ago
3) A driver in a 1000-kg car traveling at 24 m/s slams on the brakes and skids to a stop. If the coefticient of friction between
Natali5045456 [20]

Answer:

A) 37 m

Explanation:

The car is moving of uniformly accelerated motion, so the distance it covers can be calculated by using the following SUVAT equation:

v^2 -u^2 = 2ad (1)

where

v = 0 m/s is the final velocity of the car

u = 24 m/s is the initial velocity

a is the acceleration

d is the length of the skid

We need to find the acceleration first. We know that the force responsible for the (de)celeration is the force of friction, so:

F=ma=-\mu mg

where

m = 1000 kg is the mass of the car

\mu = 0.80 is the coefficient of friction

a is the deceleration of the car

g = 9.8 m/s^2 is the acceleration due to gravity

The negative sign is due to the fact that the force of friction is against the motion of the car, so the sign of the acceleration will be negative because the car is slowing down. From this equation, we find:

a=-\mu g

And we can substitute it into eq.(1) to find d:

v^2 -u^2 = 2(\-mu g) d\\d= \frac{v^2-u^2}{-2 \mu g}=\frac{0-(24 m/s)^2}{-2(0.80)(9.8 m/s^2)}=36.7 m \sim 37 m

7 0
4 years ago
What is the difference between a mineral and a rock
Sedbober [7]

A mineral is a naturally occurring, inorganic solid with a definite chemical composition and a crystalline structure formed by geological processes.

A rock is an aggregate of one or more minerals. It may also contain organic remains and mineraloids apart from regular mineral formations. Since rocks vary in their mineral and chemical composition, they are classified according to the process of their formation.

5 0
3 years ago
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