Answer:
C(p) = 4,96 (in thousands of dollars)
l = 2980 $ invest in labor
k = 2980 $ invest in equipment
Step-by-step explanation:
Information we have:
Monthly output P = 450*l*k ⇒ k = P/450*l
But the production need to be 4000
Then k = 4000/450*l
Cost of production = l * k (in thousands of dollars)
C(l) = l + 4000/450*l
Taking derivatives (both members of the equation)
C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0
45*l² - 400 = 0 ⇒ l² = 400/45
l = 2.98 (in thousands of dollars)
l = 2980 $ And
k = 400/45*l ⇒ k 400/45*2.98
k = 2.98 (in thousands of dollars)
C(p) = l + k
C(p) = 2980 + 2980
C(p) = 5960 $
Answer:
x = 6
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients/Degrees
- Expand by FOIL (First Outside Inside Last)
- Factoring
- Multiple Roots
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse
Step-by-step explanation:
<u>Step 1: Identify</u>
<em>a</em> = x + 3
<em>b</em> = x
<em>c</em> = √117
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [PT]: (x + 3)² + x² = (√117)²
- Expand [FOIL]: x² + 6x + 9 + x² = (√117)²
- Combine like terms: 2x² + 6x + 9 = (√117)²
- Exponents: 2x² + 6x + 9 = 117
- [SPE] Subtract 117 on both sides: 2x² + 6x - 108 = 0
- Factor out GCF: 2(x² + 3x - 54) = 0
- [DPE] Divide 2 on both sides: x² + 3x - 54 = 0
- Factor Quadratic: (x - 6)(x + 9) = 0
- Solve roots/solve <em>x</em>: x = -9, 6
Since we are dealing with positive values, we can disregard the negative root.
∴ x = 6
Answer:
21<em>a</em> − 8
Step-by-step explanation:
Answer:
a. Volume = π15.02 9.0=6361.73
b. I am very sorry, I don't know
Step-by-step explanation:
Answer:
5 m/min
Step-by-step explanation:
Initial speed = 6 m/ min
Final speedd = 4 m/ min
Average speed = 
Avg. Speed = 5 m / min.
