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2 years ago

Complete the table for the radioactive iotope. (Round your anwer to 2 decimal place. Iotope : 239 Pu

Mathematics

1 answer:

Marizza181 [45]2 years ago

7 0

If the radio active isotope has the half life of 24100 years, then the initial quantity is 2.16 grams

The half life in years = 24100

Consider the quantity of the radio active isotope remaining

y = $Ce^{kt}$

When t = 1000 the y = 1.2

y = C/2 when t = 1599

Substitute the values in the equation

C/2 = $Ce^{24100k}$

Cancel the C in both side

1/2 = $e^{24100k}$

Here we have to apply ln to eliminate the e terms

ln (1/2) = 24100k

k = ln(1/2) / 24100

k = -2.87× 10^-5

To find the initial value we have to substitute the value of k and y in the equation

1.2 = Ce^{1000 × -2.87× 10^-5}

C = 1.2 / e^(-0.0287)

C = 2.16 gram

Hence, the initial quantity of the radioactive isotope is 2.16 gram

Learn more about half life here

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GIVE INEQUALITY thx !! will give brainilst!

abruzzese [7]

Answer:

y = 1/3 + 6

Step-by-step explanation:

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3 years ago

Scarlett bought an ant farm with 80 ants. From the following week forward, the ant population tripled every week. Let a(n) be th

pickupchik [31]

Answer:

$a(n) = 80(3)^{n}$

524880

Step-by-step explanation:

Scarlett bought an ant farm with 80 ants. From the following week forward, the ant population tripled every week.

So, the population of ant after 1st week will be (80 × 3) = 240

Again, after 2 weeks this will be (240 × 3) = 720

Therefore, the ant population is increasing in a geometric sequence and here the first term is 80 and the common ratio is 3.

Hence, if a(n) is the population of ant after n weeks then,

$a(n) = 80(3)^{n}$ (Answer)

Now, there will be $80(3)^{8} = 524880$ ants after 8 weeks. (Answer)

8 0

4 years ago

Read 2 more answers

Analyze the diagram below and complete the instructions that follow.

docker41 [41]

Answer:

x = 8 sqrt(2)

Step-by-step explanation:

Since this is a right triangle

sin 45 = opp side/ hypotenuse

sin 45 = 8/x

Multiply each side by x

x sin 45 = 8/x *x

x sin 45 = 8

Divide each side by sin 45

x sin 45 /sin 45 = 8 /sin 45

x = 8 / sin 45

We know sin 45 = 1/ sqrt (2)

x = 8 / 1 / sqrt(2)

x = 8 sqrt(2)

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4 years ago

Sin∅=√3-1/2 find approximate value of sec∅(sec∅+tan∅)/1+tan²∅

Neko [114]

Answer:

The approximate value of $f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}$ is 1.366.

Step-by-step explanation:

Let $f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}$ , we proceed to simplify the formula until a form based exclusively in sines and cosines is found. From Trigonometry, we shall use the following identities:

$\sec \theta = \frac{1}{\cos \theta}$ (1)

$\tan\theta = \frac{\sin\theta}{\cos \theta}$ (2)

$\cos^{2}+\sin^{2} = 1$ (3)

Then, we simplify the given formula:

$f(\theta) = \frac{\left(\frac{1}{\cos \theta} \right)\cdot \left(\frac{1}{\cos \theta}+\frac{\sin \theta}{\cos \theta}\right) }{1+\frac{\sin^{2}\theta}{\cos^{2}\theta} }$

$f(\theta) = \frac{\left(\frac{1}{\cos^{2} \theta} \right)\cdot (1+\sin \theta)}{\frac{\sin^{2}\theta + \cos^2{\theta}}{\cos^{2}\theta} }$

$f(\theta) = \frac{\left(\frac{1}{\cos^{2}\theta}\right)\cdot (1+\sin \theta)}{\frac{1}{\cos^{2}\theta} }$

$f(\theta) = 1+\sin \theta$

If we know that $\sin \theta =\frac{\sqrt{3}-1}{2}$ , then the approximate value of the given function is:

$f(\theta) = 1 +\frac{\sqrt{3}-1}{2}$

$f(\theta) = \frac{\sqrt{3}+1}{2}$

$f(\theta) \approx 1.366$

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3 years ago

Suppose on a certain test, fifty students earn a perfect score and fifty students earn a zero. determine the mean grade and stan

kodGreya [7K]

Answer:

Mean=50.

standard deviation=50.

Step-by-step explanation:

Let the perfect score be 100.

The mean(average) of a data is given by: $Mean=\frac{sum of data points}{number of data points}$

Here the number of data points are 100. out of which 50 attains a value 100,and 50 attains value 0.

so, sum of data points=50×100+50×0=5000.

$Mean=\frac{5000}{100}$

Mean=50.

"Now the standard deviation of data points are calculated by firstly subtracting mean from every entry and then square the number and take it as new entry and calculate the mean of the new data entry and lastly taking the square root of this new mean".

Here if 50 is subtracted from each entry the new entry will have 50 entries as '50' and 50 entries as '-50'.

next on squaring we will have all the 100 entries as '2500'.

now the mean of these entries is: $\frac{2500\times100}{100}$

=2500

taking it's squareroot we have $\sqrt{2500}=50$

Hence, standard deviation=50.

5 0

4 years ago

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