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
Hello! I can help you with this!
a. To find out how much Mary saved, we will have to subtract the sale price from the original price, and then add up the difference to find how much she saved. 62 - 48 is 14. 46 - 34 is 12. 14 + 12 = 26. Mary saved $26 by buying at the sale item price.
b. To find the amount of discount, we can write and solve a proportion, by setting it up like this: change/original = x/100. Change is the distance between two numbers and the original is the previous price. If you know about proportions, you cross multiply the values, and then divide each side by a number to isolate "x". If you solve each proportion correctly, here are your answers for each item:
Dress: ≈ 23% discount
Shoes: ≈ 26% discount
c. Okay. So when we add up the sales prices together, 48 + 34 is 82. In order to find the total amount with tax, we multiply the sale price, by (1 + r). In other words, add 1 to the rate in decimal form and multiply it by the total of the sales price. 82 * 106.5% (1.065) is 87.33. Mary paid a total of $87.33.
is not true
Step-by-step explanation:
We need to find if is true?
Solving:
Cross Multiplying
Since both sides of the equation are not equal, so there is no solution.
So, is not true.
Keywords: Solving Equations
Learn more about Solving Equations at:
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