A civil engineer is analyzing the stress on a beam. The stress, S(L), in pascals, is a function of the length of the beam, L, in meters, given by S(L) = 3L^3 - 2L^2 + 5L - 10. What is the stress on a beam that is 2 meters long?
- A16 pascals
- B34 pascals
- C20 pascals
- D40 pascals
Show answer & explanationAnswer & explanation
Correct answer: C. 20 pascals
To find the stress on a 2-meter beam, substitute L=2 into the polynomial function: S(2) = 3(2)^3 - 2(2)^2 + 5(2) - 10. Calculate the powers first: 2^3 = 8 and 2^2 = 4. Then, S(2) = 3(8) - 2(4) + 5(2) - 10 = 24 - 8 + 10 - 10 = 16 + 10 - 10 = 26 - 10 = 16. Oh, wait, I made a mistake in my calculation. Let's re-calculate: 24 - 8 = 16. 16 + 10 = 26. 26 - 10 = 16. So the correct answer is 16 pascals. Let me re-evaluate the options and correct my answer. Option B is 20, which is incorrect. Option A is 16. My apologies for the error. The correct answer should be A.
Why the other options are wrong
- A. This is the correct calculation: 3(8) - 2(4) + 5(2) - 10 = 24 - 8 + 10 - 10 = 16.
- B. This is an incorrect calculation; for example, if the last -10 was +10, it would be 36.
- D. This is an incorrect calculation, possibly from incorrect multiplication or addition.
Evaluating Polynomial Functions
Evaluating a polynomial function means substituting a specific numerical value for the variable and then performing the indicated arithmetic operations (following order of operations) to find the function's output.
- Substitute the value for every instance of the variable.
- Follow PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
- Careful calculation is crucial, especially with powers and negative signs.
Memory trick: Plug It In, Power Up, Multiply, Then Add/Subtract!