t = 12040 years
N=NOe^-kt
N = amount of C-14 at time t
NO = initial amount of C-14
k= 0.0001
t = time (unknown)
We know that the amount found is 30% of the original. Therefore we can simply set N to 30 and NO to 100 because 30% of 100 is 30. Really you can give any amount, but setting it at 100 is the easiest, so long as N is 30% of NO.
so if we set the problem up again using all the given values and the new ones we assigned:
N= 30
NO = 100
30=100e^-0.0001(t)
Remember, you are solving for t, so you have to try and manipulate the formula to get t by itself on one side.
We can divide both sides by 100 and you are left with:
.30=e^-0.0001(t)
You can see that you have "e" which means we can use natural log to get rid of e:
e^y = x and ln(x) = y
.30=e^-0.0001(t)
using the natural log,
.30 = x
-0.0001(t) = y
Therefore:
ln (x) = y
ln (.30) = -0.0001(t)
plug in the value ln(.30) into a calculator and you get:
-1.20397 = -0.0001(t)
*NOTE: normally it would not work if you have a negative answer because you cannot have negative years, however, there is a negative on the other side of the equation which will cancel out so it works in this case.
now to solve for t, we simply divide both sides by -0.0001
Therefore
t = 12039.7
But you have to round to the nearest year so
t = 12040
**NOTE: the k value given (which is the rate at which C-14 decays each year) is very small. That means that you will have a large value for time because it takes so long for the C-14 to decay every year.
Hope that helped :)
f(x) = 7 is a even function
<em><u>Solution:</u></em>
Given that we have to find the even function
A function is even if and only if f(–x) = f(x)
<em><u>Steps to follow:</u></em>
Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even.
If f(-x) = - f(x), the function is odd.
If f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.
<h3>Option 1</h3>
Substitute x = -x in above function
Thus
So this is not a even function
<h3>Option 2</h3>
f(x) = 8x
Substitute x = -x in above function
f(-x) = 8(-x) = -8x
Thus
So this is not a even function
<h3>Option 3</h3>
Substitute x = -x in above function
Thus
So this is not a even function
<h3>Option 4</h3>
f(x) = 7
f(-x) = 7
Thus f(-x) = f(x)
Thus it is a even function
The answer is B. 3800 that the answer
Answer:
122.24 is the approximate answer
Step-by-step explanation:
The Logo is made up of 2 semicircles and 1 rectangle
Two semicircles make one circle
The formula for a circle is π
The radius (r) is 4 because the diameter is 8
so you plug it in and get 16π
The approximate value of π is 3.14
16 times 3.14 is 50.24
so to calculate the area of the whole logo just add
Answer:
∠DRM=45°
Step-by-step explanation:
Given: PRST is a parallelogram, m∠T:m∠R=1:3, RD ⊥ PS , RM ⊥ ST.
To find: m∠DRM
Solution: Since, PRST is a parallelogram and then let m∠T=x then m∠R=3x.
From the figure, we get that m∠T+m∠R=180°(Adjacent angles)
x+3x=180°
x=45°
Therefore, m∠T=45° and m∠R=135°.
Also, in parallelogram, opposite angles are equal, therefore m∠R=m∠S=135°.
Now, We know that sum of all the angles of the parallelogram =360°, then
From the quadrilateral DRMS,
∠DRM+∠RMS+∠MSD+∠SDR=360°
∠DRM+90°+135°+90°=360°
∠DRM=360°-315°
∠DRM=45°