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lana66690 [7]
3 years ago
8

When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17. After the reactor is

shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.
Required:
Write a differential equation that expresses the rate of change in the radiation level in terms of the radiation level.
Mathematics
1 answer:
wolverine [178]3 years ago
7 0

Answer:

The differential equation is \frac{dR}{dt} = -kR

Step-by-step explanation:

Differential equation for the rate of change in radiation level:

Radiation level is R.

Rate of change indicates that the radiation level R varies in function of time t, which mathematically means that we have:

\frac{dR}{dt}

After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.

Rate of change is k. Decreases means that k is negative. Proportional to the radiation level of R means that -k multiplies R. So the differential equation is:

\frac{dR}{dt} = -kR

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son4ous [18]

Answer:

The triangles aren't necessarily congruent. SAS postulate is side angle side, which means that the angle that is congruent must be between the two sides that are congruent. DF is congruent to MN, and DG is congruent to MP. This means, that angle D must be congruent to angle M.

However, we only know that D is congruent to P, not M.

These triangles are not necessarily congruent.

7 0
3 years ago
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There are 18 female teachers and 5 male teachers at Ashley's school. What is the ratio of the number of female teachers to the n
elena-14-01-66 [18.8K]

Answer:

The ratio of the number of female teachers to the number of male teachers is 18:5.

Step-by-step explanation:

First: Review how to write a ratio:

To write a ratio, take the two quantities, and put them on both sides of a colon (:). So, our two quantities our 18 and 5. But, they need to be in a specific order:

There are 18 female teachers and 5 male teachers at Ashley's school. What is the ratio of the number of female teachers to the number of male teachers?

Since, they mentioned the number of female teachers first, we put the quantity of female teachers first. So we will write 18 first and 5 after. So, the ratio is 18:5.

Thank you for reading

Topic: Ratios

6 0
2 years ago
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A random sample of 102 full-grown lobsters had a mean weight of 16 ounces and a standard deviation of 3.4 ounces. Construct a 98
pshichka [43]

Answer:

The best point estimate for a confidence interval estimating the population μ is 16 ounces.

The 98 percent confidence interval for the population mean μ is between 15.21 ounces and 16.79 ounces.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The best point estimate for a confidence interval estimating the population μ is

The sample mean, so 16 ounces.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 102 - 1 = 101

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 101 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.98}{2} = 0.99. So we have T = 2.36

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 2.36\frac{3.4}{\sqrt{102}} = 0.79

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 16 - 0.79 = 15.21 ounces

The upper end of the interval is the sample mean added to M. So it is 16 + 0.79 = 16.79 ounces

The 98 percent confidence interval for the population mean μ is between 15.21 ounces and 16.79 ounces.

4 0
2 years ago
Which is the more reasonable measurement of the distance between the tracks on a DVD: 7.4 ⋅ 10−4 mm or 7.4 ⋅ 104 mm? Justify you
EleoNora [17]

Answer:

A- 7.4 ⋅ 10−4 mm

Step-by-step explanation:

Well, to solve this problem, we must convert the number and / or the units in a more imaginable one.

We are given two choices:

a. 7.4 x 10^-4 mm

b. 7.4 x 10^4 mm

Converting the units and numbers into meters and general form, respectively. (What is meant by general form is not to write it in scientific notation).

a. 7.4 x 10^-4 mm (1 m / 1000 mm) = 0.00000074 m

b. 7.4 x 10^4 mm (1 m / 1000 mm) = 74 m

Now comparing the two values above, what do you think is the distance between the tracks on a DVD? Definitely NOT 74 m or else the DVD is extremely big. Therefore the correct is the smaller one.

8 0
1 year ago
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JulsSmile [24]
Harvey is 3 times as old as Jane." 
<span>h = 3j </span>

<span>"The sum of their ages is 48 years." </span>
<span>h + j = 48 </span>

<span>substitution </span>
<span>(3j) + j = 48 </span>
<span>4j = 48 </span>
<span>j = 12 </span>
<span>h = 3j = 36</span>
3 0
3 years ago
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