The amount Howie will pay back at the end of one year is $26000.00
The given parameters are:
-- the principal amount
-- the interest rate
--- the duration
The amount to pay back in this duration is then calculated using:
So, we have:
Express percentage as decimal
Multiply
Hence, the amount to pay back is $26000.00
Read more about simple interest at:
Hi there!
To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:
Answer:
First image attached
The error was done in Step E, because student did not multiply by the negative sign in numerator. Step E must be
.
Second image attached
The error was done in Step C, because the student omitted the of the algebraic identity
. Step C must be
Step-by-step explanation:
First image attached
The error was done in Step E, because student did not multiply by the negative sign in numerator. The real numerator in Step E should be:
Hence, Step E must be .
Second image attached
The error was done in Step C, because the student omitted the of the algebraic identity
. Step C must be
And further steps are described below:
Step D
Which according to the Quadratic Formula, represents a polynomial with complex roots. That is: (,
,
)
(Conjugated complex roots)
Step E
Step F