0 = x because 0 + 5 = 5 plus 2 = 7
Answer: the value of the account after 10 years is $2606
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 1800
r = 3.7% = 3.7/100 = 0.037
t = 10 years
Therefore,
A = 1800 x 2.7183^(0.037 x 10)
A = 1800 x 2.7183^(0.37)
A = $2606 to the nearest dollar
The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
The sentence is converted into a mathematical equation will be 3n + 5 = n + n + 1/3. Then the correct option is C.
<h3>What is Algebra?</h3>
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Five more than three times the number is one-third more than the sum of the number and itself.
Let the number be n.
Then convert the sentence into a mathematical equation. Then the equation will be
3n + 5 = n + n + 1/3
The sentence is converted into a mathematical equation will be 3n + 5 = n + n + 1/3. Then the correct option is C.
The complete question is attached below.
More about the Algebra link is given below.
brainly.com/question/953809
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