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mestny [16]
3 years ago
13

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o

rganism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5556 years. Suppose C(t) is the amount of carbon-14 present at time t. The exponential decay differential equation that models this scenario is C'=-kC . Solve the differential equation to answer the following questions.
(a) Find the value of the constant k in the differential equation.
Mathematics
1 answer:
poizon [28]3 years ago
6 0
<span>As we know that the
 k = ln(2)/t½
so putting values
 = ln(2)/5556 years 
</span><span> =0.6931471/5556
</span> =0.0001247565yr⁻
You might be interested in
-3(1-2x)=3x+3(x-3)+6
deff fn [24]

Let's solve this problem step-by-step.

−3(1−2x)=3x+3(x−3)+6

Step 1: Simplify both sides of the equation.

−3(1−2x)=3x+3(x−3)+6

(−3)(1)+(−3)(−2x)=3x+(3)(x)+(3)(−3)+6(Distribute)

−3+6x=3x+3x+−9+6

6x−3=(3x+3x)+(−9+6)(Combine Like Terms)

6x−3=6x+−3

6x−3=6x−3

Step 2: Subtract 6x from both sides.

6x−3−6x=6x−3−6x

−3=−3

Step 3: Add 3 to both sides.

−3+3=−3+3

0=0

So, 0=0 or all real numbers.

6 0
3 years ago
The Rectangular rug has side lengths of 3 and 4 feet. What is the length of the diagonal?
lesya [120]

the formula to find the diagonal would be

a^2+b^2=c^2

3^2+4^2= 9+16=25

the square root of 25 is 5

5^2=25

so your diagonal is 5 ft

7 0
2 years ago
Please help!! (Number 73)
Rasek [7]
So hmm notice the picture below

one is 7x5x1.75 the volume of a rectangular prism is V = length * width * height

so 7*5*1.75 gives us 61.25 ft³

the second one, is larger by some width and length we dunno, but we know that it required that 61.25 plus an extra 17.5 to fill it up, so its volume is 61.25 + 17.5 or 78.75

the height is the same... so \bf V=l\cdot w\cdot h\qquad &#10;\begin{cases}&#10;l=length\\&#10;w=width\\&#10;h=height\\ --------\\&#10;h=1.75\\&#10;V=78.75&#10;\end{cases}\implies 78.75=lw\cdot 1.75&#10;\\\\\\&#10;\cfrac{78.75}{1.75}=lw\implies 45=lw

so.. if you factor 45, to two factors, one will be the length, the other the width

3 0
2 years ago
Can anyone pls help me to solve question 2 f and g and pls provide me a explanation I’m with that questions for three days
zvonat [6]

Answer:

  f)  a[n] = -(-2)^n +2^n

  g)  a[n] = (1/2)((-2)^-n +2^-n)

Step-by-step explanation:

Both of these problems are solved in the same way. The characteristic equation comes from ...

  a[n] -k²·a[n-2] = 0

Using a[n] = r^n, we have ...

  r^n -k²r^(n-2) = 0

  r^(n-2)(r² -k²) = 0

  r² -k² = 0

  r = ±k

  a[n] = p·(-k)^n +q·k^n . . . . . . for some constants p and q

We find p and q from the initial conditions.

__

f) k² = 4, so k = 2.

  a[0] = 0 = p + q

  a[1] = 4 = -2p +2q

Dividing the second equation by 2 and adding the first, we have ...

  2 = 2q

  q = 1

  p = -1

The solution is a[n] = -(-2)^n +2^n.

__

g) k² = 1/4, so k = 1/2.

  a[0] = 1 = p + q

  a[1] = 0 = -p/2 +q/2

Multiplying the first equation by 1/2 and adding the second, we get ...

  1/2 = q

  p = 1 -q = 1/2

Using k = 2^-1, we can write the solution as follows.

The solution is a[n] = (1/2)((-2)^-n +2^-n).

 

5 0
2 years ago
Please help explanation if possible
Novay_Z [31]

Answer:

Equation pf parallel line y = 4x + C

now this line pass through (-2,4) so it satisfies the eqn

Then, 4 = -8+C

C = 12

<h2>Hence required equation:- </h2>

<h2>y = 4x+12.....</h2>

hope it helps

4 0
2 years ago
Read 2 more answers
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