Answer:
12,288
Step-by-step explanation:
aₙ = 3 (-2)ⁿ⁻¹
a₁₃ = 3 (-2)¹³⁻¹
a₁₃ = 12,288
Answer: d. (17, 20)
Step-by-step explanation:
We have the following system of equations:
(1)
(2)
Isolating 
from (1):
(3)
Substituting (3) in (2):
(4)
Isolating 
:
(5)
(6)
(7)
Substituting (7) in (1):
(8)
Isolating :
(9)
Hence, the correct option is d. (17, 20)
Answer:
"subtracting b, then dividing by m"
Step-by-step explanation:
To solve for a particular variable, look a the operations that are being performed on that variable. Then "undo" those operations in reverse order.
Here, the operations done to x are ...
• multiply by m
• add b to the product
Using the above recipe, first we "undo" the additon of b. We accomplish that by subtracting b from both sides of the equation. This gives ...
y - b = mx + b - b
y - b = mx . . . . . . . . . simplify
Next, we "undo" the multiplicatin by m. We accomplish that by dividing both sides of the equation by m.
(y -b)/m = mx/m
(y -b)/m = x . . . . . . . . simplify
This is your solution for x:
x = (y - b)/m
We found it by subtracting b, then dividing by m on both sides of the equation.
Answer:
a) 
, b) 
, c) 
, d) 
Step-by-step explanation:
a) Let assume an initial mass m decaying at a constant rate k throughout time, the differential equation is:
b) The general solution is found after separating variables and integrating each sides:
Where 
is the time constant and 
c) The time constant is:
The particular solution of the differential equation is:
d) The amount of radium after 300 years is:
