12x3+27x2+23x+10/ 4x+5
3x2 + 3x + 2
The annual income tax paid by the person is: $4,500.
<h3>Annual income tax</h3>
Using this formula
Annual income tax=[Salary÷(1-percentage deduction)]- Salary
Let plug in the formula
Annual income tax=[40,500÷(1-10%)]-40,500
Annual income tax=45,000-40,500
Annual income tax=4500
Therefore the annual income tax paid by the person is: $4,500.
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Answer:
- y = 81-x
- the domain of P(x) is [0, 81]
- P is maximized at (x, y) = (54, 27)
Step-by-step explanation:
<u>Given</u>
- x plus y equals 81
- x and y are non-negative
<u>Find</u>
- P equals x squared y is maximized
<u>Solution</u>
a. Solve x plus y equals 81 for y.
y equals 81 minus x
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b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.
P equals x squared left parenthesis 81 minus x right parenthesis
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c. Find the domain of the function P found in part b.
left bracket 0 comma 81 right bracket
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d. Find dP/dx. Solve the equation dP/dx = 0.
P = 81x² -x³
dP/dx = 162x -3x² = 3x(54 -x) = 0
The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...
P is maximized at (x, y) = (54, 27).