Answer:
see below
Step-by-step explanation:
The equation for half life is
n = no e ^ (-kt)
Where no is the initial amount of a substance , k is the constant of decay and t is the time
no = 9.8
1/2 of that amount is 4.9 so n = 4.9 and t = 100 years
4.9 = 9.8 e^ (-k 100)
Divide each side by 9.8
1/2 = e ^ -100k
Take the natural log of each side
ln(1/2) = ln(e^(-100k))
ln(1/2) = -100k
Divide each side by -100
-ln(.5)/100 = k
Our equation in years is
n = 9.8 e ^ (ln.5)/100 t)
Approximating ln(.5)/100 =-.006931472
n = 9.8 e^(-.006931472 t) when t is in years
Now changing to days
100 years = 100*365 days/year
36500 days
Substituting this in for t
4.9 = 9.8 e^ (-k 36500)
Take the natural log of each side
ln(1/2) = ln(e^(-36500k))
ln(1/2) = -36500k
Divide each side by -100
-ln(.5)/36500 = k
Our equation in years is
n = 9.8 e ^ (ln.5)/36500 d)
Approximating ln(.5)/365=-.00001899
n = 9.8 e^(-.00001899 d) when d is in days
Answer:
Step-by-step explanation:
let polynomial P(x)=ax³+bx²+cx+d
-3=-a+b-c+d
-2=d
-1=a+b+c+d
-1=a+b+c-2
a+b+c=1
-3=-a+b-c-2
a-b+c=1
a+b+c-(a-b+c)=1-1=0
2b=0
b=0
so a+c=1
6=8a+4b+2c+d
6=8a+4b+2c-2
8a+4b+2c=8
4a+2b+c=4
or 4a+0+c=4
4a+c=4
a+c=1
subtract
3a=3
a=1
1+c=1
c=0
reqd .P(x)=1x³-2=x³-2
Answer:
65
Step-by-step explanation:
Thats The Correct answer I dont really know how to explain
Answer: there were 345 pieces of chocolate in the box.
Step-by-step explanation:
Let x represent the number of pieces of chocolate there in the box.
0.55 of a box of chocolate are dark chocolate. This means that the number of dark chocolate in the box is 0.55x
0.3 are milk chocolate. This means that the number of milk chocolate in the box is 0.3x
The rest are white chocolate. This means that the number of white chocolate in the box is x(1 - 0.55 - 0.3) = 0.15x
There are 138 pieces more dark chocolate than white chocolate. This means that
0.55x - 0.15x = 138
0.4x = 138
x = 138/0.4
x = 345
Answer:
10
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64+36 = c^2
100 = c^2
Take the square root of each side
sqrt(100) = sqrt(c^2)
10 = c
