The sum would be written as:
It goes from n=1 to =5 because it is the first 5 terms of the sum.
The sequence has a first term, a₁, of 1. The common difference, d, is 3. The explicit formula would then be:
Using the distributive property to simplify, we would have:
N=NOe^-kt
N=mass at time t
NO = initial mass
k= 0.1476
t= time, in days
We are asked to find the half-life, which means you want to find how long it will take for half of the substance to decay/disappear (depending on situation).
If we are looking for half-life, we can simply set N to half of NO (which we are given a value of 40grams for)
Therefore:
N = 20
NO = 40
plugging these values and the value given for k back into the equation you get:
20 = 40e^-0.1476(t)
We are looking for t, so we have to manipulate the formula to get t by itself on one side of the equation.
We can start by dividing 40 from both sides, and you get:
0.5 = e^-0.1476(t)
We have the exponential function "e".
To get rid of e, we can use natural log (ln)
if e^y=x then ln (x) = y
look back at our equation we can set
0.5 = x
-0.1476(t) = y
Rewriting it in natural log form:
ln (0.5) = -0.1476(t)
Plug in ln (0.5) on a calculator to find its value and we get:
-0.693147 = -0.1476(t)
*Note: normally, getting a negative value would suggest that we did something wrong, because you cannot have a negative value as your t (you cannot have negative days), but because there is a negative on both sides of the equation, they will cancel out in this case.
The last step is to simply divide both sides by -0.1476
therefore:
T = 4.696119
But it asks you for the answer to the nearest tenth (one place after decimal pt) so
T (half life) = 4.7 days
Hope that helps :)
Answer:
A Transaction by 8 units to the right and 5 units down
8 blocks because you multiply 20 by 2/5, then you get 4 multiplied by 2 and you get 8 blocks.
Curved surface area of a sphere =1256 cm
2
We know that, Curved surface area of a spehre =4πr
2
⟹1256=4×3.14×r
2
⟹r
2
=
4×3.14
1256
⟹r
2
=100
∴r=10 cm
Hence, the answer is 10 cm.
4186.66666666 volume of sphere
