Answer:
(5a+5b+3ab)/15
Step-by-step explanation:
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Directrix is x =1, so it is horizontal parabola.Vertex is between the focus and directrix on equal distance 5-x=x-1, 2x=6,
x=3. y -coordinate of the vertex for this parabola equals y-coordinate of the focus.
Vertex (3,2).
Focus has x=5 >1, so it is directed to the right.
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 :)
Answer:
No. The correct answer is x = 4i. The mistake is made on the penultimate step where "Mark" squares both sides, eliminating the negative sign.
Step-by-step explanation:
We can see that the answer is incorrect, because if we plug it back into the original equation, we get:
This of course is obviously incorrect. The mistake is made in squaring away the negative sign in solving the problem. An easier way to look at this is to get rid of √x, and substitute it for "n", and see what we get:
If we swap √x back in, we get:
√x = -2
x = 4i
let's solve it correctly: