total profit is defined as total revenue, $r(x)$, minus total cost, $c(x)$, and is given by the function $p(x) = r(x) - c(x)$. given $r(x) = 59x - 0.3x^2$ and $c(x) = 2x + 12$, find each of the following.
a) $p(x)$
b) $r(100)$, $c(100)$, and $p(100)$

$p(x) = $
(type in descending powers of $x$.)

Question

total profit is defined as total revenue, $r(x)$, minus total cost, $c(x)$, and is given by the function $p(x) = r(x) - c(x)$. given $r(x) = 59x - 0.3x^2$ and $c(x) = 2x + 12$, find each of the following.
a) $p(x)$
b) $r(100)$, $c(100)$, and $p(100)$

$p(x) = $
(type in descending powers of $x$.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Function Evaluation" ], "new_concepts": [ "Profit Function", "Polynomial Subtraction" ], "current_concepts": [ "Linear Equations", "Function Evaluation", "Profit Function", "Polynomial Subtraction" ] } ## Find the profit function P(x) in descending powers of x $$ \begin{aligned} P(x) &= R(x) - C(x) \ P(x) &= (59x - 0.3x^2) - (2x + 12) \ P(x) &= -0.3x^2 + 59x - 2x - 12 \ P(x) &= -0.3x^2 + 57x - 12 \end{aligned} $$ ## Evaluate R(100), C(100), and P(100) $$ \begin{aligned} R(100) &= 59(100) - 0.3(100)^2 = 5900 - 0.3(10000) = 5900 - 3000 = 2900 \ C(100) &= 2(100) + 12 = 200 + 12 = 212 \ P(100) &= R(100) - C(100) = 2900 - 212 = 2688 \end{aligned} $$ ## Question 1 $P(x) =$ $-0.3x^2 + 57x - 12$ ## Question 2 $R(100) =$ $2900$, $C(100) =$ $212$, and $P(100) =$ $2688$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Subtraction" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the profit function P(x) in descending powers of x

Evaluate R(100), C(100), and P(100)

Answer:

Question 1

Question 2