The correct question is:
Suppose x = c1e^(-t) + c2e^(3t) a solution to x''- 2x - 3x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c1 as c1 and c2 as c2.)
Answer:
x = c1e^(-t) + c2e^(3t)
is a solution to the differential equation
x''- 2x' - 3x = 0
Step-by-step explanation:
We need to verify that
x = c1e^(-t) + c2e^(3t)
is a solution to the differential equation
x''- 2x' - 3x = 0
We differentiate
x = c1e^(-t) + c2e^(3t)
twice in succession, and substitute the values of x, x', and x'' into the differential equation
x''- 2x' - 3x = 0
and see if it is satisfied.
Let us do that.
x = c1e^(-t) + c2e^(3t)
x' = -c1e^(-t) + 3c2e^(3t)
x'' = c1e^(-t) + 9c2e^(3t)
Now,
x''- 2x' - 3x = [c1e^(-t) + 9c2e^(3t)] - 2[-c1e^(-t) + 3c2e^(3t)] - 3[c1e^(-t) + c2e^(3t)]
= (1 + 2 - 3)c1e^(-t) + (9 - 6 - 3)c2e^(3t)
= 0
Therefore, the differential equation is satisfied, and hence, x is a solution.
Answer:
Option C - Simplify the right side using the "difference of two logs is the log of the quotient" property.
Step-by-step explanation:
Given : Expression 
To find : What is the first step in solving the expression ?
Solution :
Expression
Step 1 - Simplify the right side using the "difference of two logs is the log of the quotient" property.
i.e. 
Apply the first step we get,
Therefore, Option C is correct.
Answer:
1.01789228E-5
Step-by-step explanation:
hope this helped :)
Answer:
$5,843.9
Step-by-step explanation:
2016
Total health care cost in US = $1.7 trillion
= $1,700,000,000,000
Population in US = 290.9 million.
= 290,900,000
Average amount spent per person on health care = Total health care cost in US / Population in US
= 1,700,000,000,000 / 290,900,000
= $5843.9326228944
Approximately,
$5,843.9
To the nearest whole number
= $5,844
