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3 years ago

Solve the Integral of 1/(1-y2)

1 answer:

5 0

−1/(y+1)(y−1) is the answer

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The core melt- down and explosions at the nuclear reactor in Chernobyl in 1986 released large amounts of strontium-90, which dec

elena-14-01-66 [18.8K]

If $S(t)$ is the amount of strontium-90 present in the area in year $t$ , and it decays at a rate of 2.5% per year, then

$S(t+1)=(1-0.025)S(t)=0.975S(t)$

Let $S(0)=s$ be the starting amount immediately after the nuclear reactor explodes. Then

$S(t+1)=0.975S(t)=0.975^2S(t-1)=0.975^3S(t-2)=\cdots=0.975^{t+1}S(0)$

or simply

$S(t)=0.975^ts$

So that after 50 years, the amount of strontium-90 that remains is approximately

$S(50)=0.975^{50}s\approx0.282s$

or about 28% of the original amount.

We can confirm this another way; recall the exponential decay formula,

$S(t)=se^{kt}$

where $t$ is measured in years. We're told that 2.5% of the starting amount $s$ decays after 1 year, so that

$0.975s=se^k\implies k=\ln0.975$

Then after 50 years, we have

$S(50)=se^{50k}\approx0.282s$

5 0

3 years ago

PLEASE HELP!!!

pogonyaev

Step-by-step explanation:

Part A:

Let $m$ be the number of mittens and $s$ be the number of scarves. Then we have the inequalities:

$s+m\leq 30.$ This says Nivyana and Ana cannot make more than 30 scarves

$50s+25m\geq 1000.$ This says that Nivyana and Ana have to earn at least $1000.

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)

8 0

2 years ago

What is 70% of 92? Please answer fast I need it done by tomorrow

mina [271]

The answer is 64.4 because you multiply 92 times 0.7 and get 64.4

8 0

3 years ago

Write and evaluate the expression. Then, complete the statements. Ten less than the quotient of thirty and a number Evaluate whe

Artyom0805 [142]

Answer:

expression: (30/t) - 10

evaluation: 30/2 - 10 = 5

Step-by-step explanation:

8 0

3 years ago

Dave has 10 poker chips, 6 of which are red and the other 4 of which are white. Dave likes to stack his chips and flip them over

Marina86 [1]

The number of 10 chips stacks that Dave can make if two stacks are not considered distinct is 110.

The solution

To get the symmetric stacks, one has to subtract the symmetric stacks to know the ones that are asymmetric.

The symmetric are flipped. Given that they are double counted what we have to do is to divide through by 2.

6/2 = 3

10/2 = 5

4/2 = 2

1/2(10C6) - (5C3) + (5C3)

0.5(210-10+10)

= 110

8 0

2 years ago