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Elenna [48]
3 years ago
7

Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmospher

e by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 74% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.) yr
Mathematics
1 answer:
Artemon [7]3 years ago
5 0

Answer: 2500 years

Step-by-step explanation:

I'm not quite sure if I'm doing this right myself but I'll give it a shot.

We use this formula to find half-life but we can just plug in the numbers we know to find <em>t</em>.

A(t)=A_{0}(1/2)^t^/^h

We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For A_{0 let's just assume that there are 100 original  atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. <em>h</em> is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.

74=100(1/2)^t^/^5^7^3^0

Now, solve. First, divide by 100.

0.74=(0.5)^t^/^5^7^3^0

Take the log of everything

log(0.74)=\frac{t}{5730} log(0.5)

Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the <em>t</em> and get

5730\frac{log(0.74)}{log(0.5)} =t

Use your calculator to solve that giant mess for <em>t </em>and you'll get that <em>t</em> is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.

Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.

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Question 3
alexira [117]

Answer: when x = 7, y = 16

Step-by-step explanation: Here, we know that y varies inversely as x.

When we have two sets of inversely related coordinates, x₁ and y₁,

and x₂ and y₂, we can use the product rule, shown below,

to find the missing value.

<h2>x₁ y₁ = x₂ y₂</h2><h2 />

Here, we know that y = 14 when x = 8 so

one set of coordinates will be 8 and 14.

We want to know the value of y when x = 7.

So our other coordinates will be 7 and y.

So we have (8)(14) = (7)(y).

Simplifying, (8)(14) is equal to 112 and (7)(y) is equal to 7y.

So we have 112 = 7y.

Now we simply solve for y by dividing both sides of the equation by 7.

The 7's on the right side cancel out and

on the left, 112 divided by 7 is equal to 16.

So we have 16 = y.

So when x is equal to 7, y is equal to 16.

7 0
3 years ago
Consider the quadratic equation ax^2+bx+5=0, where a, b, and c are rational and the quadratic has two didstinct zeros if one zor
erica [24]

Answer:

It can either be rational or irrational

Step-by-step explanation:

Given the quadratic equation ax²+bx+5 = 0, to get the zeros of the function, we will factorize the function to have;

ax²+bx = -5

x(ax+b) = -5

x = -5 and ax+b = -5

From the second function we have;

ax+b = -5

ax = -5-b

x = -5-b/a

This shows that the other value of x can be rational or irrational depending on the values of a and b

3 0
3 years ago
1. The amount of extension in an elastic spring varies directly as the weight hung on it. If a weight of 150 gm produces an exte
gregori [183]

Answer:

900 g

Step-by-step explanation:

let e be extension and w be weight

given e varies directly as w then the equation relating them is

e = kw ← k is the constant of variation

to find k use the condition w = 150 , e = 2.9 , then

2.9 = 150k ( divide both sides by 150 )

\frac{2.9}{150} = k , that is

k = \frac{29}{1500}

e = \frac{29}{1500} w ← equation of variation

when e = 17.4 , then

17.4 = \frac{29}{1500} w ( multiply both sides by 1500 )

26100 = 29w ( divide both sides by 29 )

900 = w

3 0
3 years ago
I need help with 12 and 13 please.
Cerrena [4.2K]
Just add up all the angles hope you get it right
7 0
3 years ago
Carl is on the school track team. To prepare for an upcoming race, he plans to run 217 miles total over the next 31 days.
Tanya [424]

Answer:

Answer:

217/31=m

7 miles per day

Step-by-step explanation:

UR WELCOME 5 STAR PLS AND LIKE  IT

7 0
3 years ago
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