What is the answer for this question??

Mathematics

1 answer:

kotegsom [21]2 years ago

3 0

The correct answer is D: 10x = 1000, which simplifies to x = 100

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Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li

krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

$A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years$

First, let us calculate the decay constant (k)

$75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036$

Next, let us calculate the half-life as follows:

$\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years$

Therefore the half-life is between 600 and 700 years

5 0

2 years ago

The table below shows the coordinates of a figure that was transformed.

Dimas [21]

Answer:

I think it’s D

Step-by-step explanation:

8 0

3 years ago

On a map, 1 inch equals 100 miles. If Boston is 250 miles away from Dover, how far away is it on the map

12345 [234]

Answer:

2.5 inch i think because 1 inch equals 100 miles and .5 i think it is 50 miles

7 0

3 years ago

Can someone help me with this? I'm getting a 0 in a) but the book has -1/5 answer. I'm confused.

jok3333 [9.3K]

Replace the x values in the equation, then solve:

[(-2)^2+4]/[(-2)^2-2(-2)-48=

(4+4)/4+4-48=

8/8-48=

8/-40=

-1/5

7 0

2 years ago

Two lines, A and B, are represented by equations given below:

Ierofanga [76]

Set the equations equal to each other to find x
x - 2 = 3x + 4
-6 = 2x
x = -3

plug x into either equation
-3 - 2 = y
y = -5

(-3, -5)

the answer is B

4 0

2 years ago