Answer:
The age of the pottery bowl to the nearest year is 15606 years.
Step-by-step explanation:
Let the initial amount of C-14 in the bowl i.e. 
and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.
Therefore, from the given equation we can write
{Since, k is give to be 0.0001}
⇒ 
Now, taking ln on both sides we get
ln 0.21 = - 0.0001t (ln e) {Since, 
}
⇒ - 1.560647 = - 0.0001t {We have ln e = 1}
⇒ t = 15606.47 years ≈ 15606 years
Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is 
<h3>How to determine the equation of the hyperbola?</h3>
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
So, we have:
Evaluate
Hence, the equation of the hyperbola is
Read more about hyperbola at:
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Well first do this
12.00 - 9.30 = 2.30
2.30 + 6.30 = 9
You slept 9hrs
Hello there! Thank you for asking your question here at Brainly. I will be assisting you today with how to handle this problem, and will teach you how to handle it on your own in the future.
First, let's evaluate the question.
"The circumference of a circle is 6.28. What is the area of a circle?"
Now, let's remember the different formulas for area and circumference.
The circumference is "2•3.14•r", while the area is "3.14•r•r".
We have our circumference, 6.28.
However, we are looking for the area. Since we have the circumference, we need to narrow down to the radius (so we can solve for the area).
Let's set this up as an equation;
C = 2 • 3.14 • r
Plug in the value for our circumference.
6.28 = 2 • 3.14 • r
Multiply 2 by 3.14 and r to simplify the right side of the equation.
2 • 3.14 • r = 6.28 • r = 6.28r
We're now left with:
6.28 = 6.28r
Divide both sides by 6.28 to solve for r.
6.28 / 6.28 = 1
6.28r / 6.28 = r
We are now left with the radius:
R = 1.
Now, we can solve for the area.
Remember our formula for the area.
A = r • r • 3.14.
Plug in 1 for r.
A = 1 • 1 • 3.14
A = 3.14.
Your area is 3.14 units^2.
I hope this helps, and has prepared you for your future problems in relation to this topic!
Complete the square
isolate x terms
y=(x^2-14x)+53
take 1/2 of -14 and square it ((-7)^2=49
add plus and minus of that inside the parntehasees
y=(x^2-14x+49-49)+53
factor perfect suqrae
y=((x-7)^2-49)+53
get rid of parnthasees
y=(x-7)^2-49+53
y=(x-7)^2+4
C isi answer
