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2 years ago

Suppose a radioactive substance has a half-life of 1000 years. What fraction will be left after 1000 years?

Mathematics

2 answers:

Nezavi [6.7K]2 years ago

5 0

Answer:

1/2

Step-by-step explanation:

so if u do the waffalineneh times by arcimate it would equivently be the answer on top

salantis [7]2 years ago

3 0

Answer:

$\frac{1}{2}$

Step-by-step explanation:

The half life is the amount of time it takes a substance to decay to half of its original amount.

Since the radioactive substance has a half life of 1000 years, there will be half of it left after 1000 years.

So, the fraction that will be left after 1000 years is $\frac{1}{2}$

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Now Ann is x years old and her sister is eight years younger than her. After five years , Anne's age is twice the age of her sis

svp [43]

Answer:

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7 0

1 year ago

A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

$\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}$

Solve for S(t):

$\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}$

$e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}$

The left side is the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}$

Integrate both sides:

$e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt$

$e^{t/800}S(t)=64e^{t/800}+C$

$S(t)=64+Ce^{-t/800}$

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

$0=64+C\impleis C=-64$

and so (b) the amount of sugar in the tank at time t is

$S(t)=64\left(1-e^{-t/800}\right)$

As $t\to\infty$ , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0

3 years ago

Which function is the inverse of f(x)= 3x+5 over 7

Pani-rosa [81]

f(x) = (3x+5)/7

Step 1:

we write f(x) as y

y=(3x+5)/7

Step 2:

switch y by x and x by y

x=(3y+5)/7

Step 3:

solve for y,

x=(3y+5)/7

multiply both sides by 7

7x=3y+5

subtract 5 from left side

3y=7x-5

divide both sides by 3

y= (7x-5)/3

f⁻¹ (x) =(7x-5)/3

8 0

2 years ago

Melissa mows many lawns in her neighborhood. She mows lawns for $95 per lawn. She also offers full landscape maintenence for $12

olga55 [171]

9.52

125 * 4 = 500

500 * 9.52 = 4,760

6 0

2 years ago

Lindsay says all numbers that are multiples of 4 have 2 as a factor. Is lindsay correct?

m_a_m_a [10]

Answer:

Yes

Step-by-step explanation:

Let's take any random multiple of 4 as an example:

8 = 2 • 4

64 = 2 • 32

20 = 2 • 10

Try any multiple of 4—this pattern continues.

7 0

2 years ago