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2 years ago

Radium-226 has a half life of 1622 years. If you start off with a 200

Mathematics

1 answer:

sweet [91]2 years ago

3 0

Answer:

≈23.6 kg left.

Step-by-step explanation:

For determining this, we can simply use an exponential decay equation representing this scenario:

$y= a(0.5)^{\frac{t}{h} }$

a: the initial amount

t: the amount of time

h: the half life

Now, substitute the numbers into the equation:

$y=200(0.5)^{\frac{5000}{1622} }$

Now, solve this equation:

$y=220(0.5)^{3.08}$

Use a calculator to solve for y:

y= 200(0.118)

y≈23.6 kg left.

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gizmo_the_mogwai [7]

Answer:

α = π/3

γ = 2

x = -3π/4, -5π/12, π/4, 7π/12

Step-by-step explanation:

Easiest way to do this is in reverse.

γ sin(2x − α)

Angle sum/difference formula:

γ (cos α sin(2x) − sin α cos(2x))

Distribute:

γ cos α sin(2x) − γ sin α cos(2x)

Matching the coefficients:

γ cos α = 1

γ sin α = √3

Solve the system of equations. Divide to eliminate γ:

tan α = √3

α is between 0 and π/2, so:

α = π/3

γ = 2

sin(2x) − √3 cos(2x) = 1

Using the identity from before:

2 sin(2x − π/3) = 1

Solving:

sin(2x − π/3) = 1/2

2x − π/3 = π/6 + 2kπ or 5π/6 + 2kπ

2x = π/2 + 2kπ or 7π/6 + 2kπ

x = π/4 + kπ or 7π/12 + kπ

x is between -π and π, so:

x = -3π/4, -5π/12, π/4, 7π/12

7 0

3 years ago

A drawer contains 12 brown socks and 12 black socks, all unmatched. A man takes socks out at random in the dark. 21. Required in

avanturin [10]

Answer:

6 socks

Step-by-step explanation:

What we must do is calculate the probability of this happening, that he takes out two black socks in the first two taken out.

There are 12 black socks and in total they are 24, therefore the probability of drawing 1 is:

12/24

and now the probability of getting another one is 11 (there is one less outside) and in total they are 23:

11/23

the final probability is the multiplication of these events:

(12/24) * (11/23)

P = 0.24

Now, to know how many you should get, we multiply the probability by the total number of socks, that is:

0.24 * 24 = 5.76

So you must take out at least 6 socks for the above to happen.

6 0

3 years ago

What does absolute value mean?

Lynna [10]

Absolute value is the magnitude of a number without regard to its sign. for example, the absolute value of 5 is 5, and the absolute value of -5 is also 5!

4 0

3 years ago

Pls help need it ASAP can’t figure it out

Pie

Answer:

-25

Step-by-step explanation:

10^2 ÷ -2^2 = -25

That's why the answer is -25.

4 0

2 years ago

Answer please i need to pass this class

LuckyWell [14K]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers