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olya-2409 [2.1K]
2 years ago
8

La funcion que representa el beneficio obtenido por una empresa si vende x unidades de uno de sus productos es f(x)= -70x^2+2800

x-45000. ¿cuantas unidades tiene que vender para maximizar sus beneficios?
Mathematics
1 answer:
DerKrebs [107]2 years ago
3 0

Answer:

20

Step-by-step explanation:

La función es

f(x)=-70x^2+2800x-45000

Diferenciando con respecto a x obtenemos

f'(x)=-140x+2800

Igualar con cero

0=-140x+2800\\\Rightarrow x=\dfrac{2800}{140}\\\Rightarrow x=20

Doble derivada de la función

f''(x)=-140

Entonces, la función es máxima cuando el número de unidades vendidas,  x=20,

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The change in water vapor in a cloud is modeled by a polynomial function, C(x). C(x) = x^3+ 5x^2+3x+30 Describe how to find the
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Suppose the equation that describes the change in water vapor in a cloud (y) with respect to temperature (x): C(x) = x³ - 4x² - 7x + 10

You find the x-intercepts of the cubic equation by finding the roots. Let y be zero:

x³ - 4x² - 7x + 10 = 0

Now, find possible factors of the constant term in the equation: 10. These could be 1, 2, 5, and 10. Suppose we choose 1. We substitute x=1. If the answer is zero, then x=1 is one of the roots.

(1)³ - 4(1)² - 7(1) + 10 = 0

Hence, x=1 or x-1 = 0 is one of the roots. We use this to manipulate the rest of the terms in the original equation, such that you can factor out (x-1). Substitute -x² - 3x² to -4x³ because they are just equal. Same is true for +3x - 10x for -7x:

x³ -x² - 3x²+3x - 10x + 10 = 0

Factor out like terms such that they have a common factor of (x-1) as much as possible.

x³ -x² = x²(x-1)

- 3x²+3x = -3x(x-1)

- 10x + 10 = -10(x-1)

The factored equation is:

x²(x-1)-3x(x-1)-10(x-1) = 0

Factor out (x-1):

(x-1)(x²-3x-10) = 0

Now, we have the quadratic equation left to be solved:x²-3x-10

Use the quadratic formula to find the roots:

x = [-b +/- √(b²-4ac)]/2a,

The a, b and c coefficients are based on the general form of the quadratic equation: ax² + bx + c. Hence, a=1, b=-3 and c=-10. Substituting the values:

x = [-(-3) +/- √((-3)²-4(1)(-10))]/2(1)

x = 5, -2

Therefore, the roots of the cubic equations are x = 1, x = 5 and x =- 2. These are the x-intercepts of the equation. At temperatures °C, 5°C and -2°C, there is no change in water vapor in a cloud. The graph is shown in the attached picture

Step-by-step explanation:

7 0
2 years ago
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