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Phoenix [80]
3 years ago
14

Division A reports the following data: Sales = $180,000, Net income = $18,000, Average'assets

Mathematics
1 answer:
Karolina [17]3 years ago
3 0

Company A is operating more efficiently

Step-by-step explanation:

Given parameters:

Division A:

Sales = $180,000

Net income = $18,000

Average assets = $72,000

Division B:

Sales = $60,000

Net income = $9,600

Average assets = $48,000

Unknown:

Division operating more efficiently = ?

Solution:

Efficiency measures the relationship between the output from a business and the input into it. Here, the efficiency is the relationship between the net income and the average assets. it can be expressed as a percentage or ratio.

The net income is the profit derived from sales of a company's products.

The higher the value the more efficient a company is.

 Efficiency = \frac{net income}{Average assets} x 100

 Efficiency of division A = \frac{18000}{72000} x 100 = 25%

 Efficiency of division B = \frac{9600}{48000} x 100 = 20%

Division A has a higher efficiency compared to B

Learn more:

Economic goals brainly.com/question/8951463

#learnwithBrainly

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Se tiene un lote baldío de forma triangular bardeado. La barda de enfrente tiene una medida de 4 m,las otras dos bardas no es po
dybincka [34]

Answer:

a) La medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m. b) El triángulo en cuestión <em>no es un triángulo rectángulo</em>, es decir, ninguno de sus ángulos internos es <em>recto </em>(90 grados sexagesimales). En estos casos, no se puede aplicar el Teorema de Pitágoras o la simple utilización de las razones trigonométricas; se aplican, en cambio, leyes para la resolución de triángulos oblicuángulos (o triángulos no rectángulos).

Step-by-step explanation:

Este problema no se puede resolver "aplicando sólo las razones trigonométricas o el teorema de Pitágoras" porque es sólo aplicable a <em>triángulos rectos</em>, es decir, uno de los ángulos del triángulo es recto o igual a <em>90</em> grados sexagesimales. Los dos restantes triángulos suman 90 grados sexagesimales, o se dice, son <em>complementarios</em>.

La resolución de triángulos que no son rectos (conocida en algunos textos como solución de problemas de triángulos oblicuángulos) pueden resolverse usando, la <em>ley de los senos (o teorema del seno)</em>, <em>ley de los cosenos</em> y <em>la ley de las tangentes</em>. El caso propuesto en la pregunta se ajusta a la <em>ley de los senos</em>:

\\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)} = \frac{c}{\sin(\gamma)}

Es decir, la razón entre el lado de un triángulo y el seno del ángulo que tiene frente a él es igual para todos los lados y ángulos del triángulo.

El triángulo de la pregunta no tiene un ángulo recto

La suma de los ángulos internos de un triángulo es de 180 grados sexagesimales:

\\ \alpha + \beta + \gamma = 180^{\circ}

En la pregunta tenemos que la suma de los dos ángulos propuestos es:

\\ 34^{\circ} + 64^{\circ} + \gamma = 180^{\circ}

\\ 98^{\circ} + \gamma = 180^{\circ}

Restando 98 grados sexagesimales a cada lado de la igualdad:

\\ 98^{\circ} - 98^{\circ} + \gamma = 180^{\circ} - 98^{\circ}

\\ 0 + \gamma = 180^{\circ} - 98^{\circ}

\\ \gamma = 82^{\circ}

Con lo que se deduce que no hay ningún ángulo recto en el triángulo propuesto y no se podría usar el Teorema de Pitágoras o simples razones trigonométricas para resolverlo.

Resolución del lado del triángulo

De la pregunta tenemos:

  • La barda de enfrente tiene una medida de 4m. El ángulo que está enfrente de esta barda (barda frontal) es de 34°.
  • No se sabe el valor del lado que está enfrente del ángulo de 64°, pero se puede calcular usando la Ley de los senos.

Digamos que:

\\ a = 4m, \alpha = 34^{\circ}

\\ b = x, \beta = 64^{\circ}

Entonces, aplicando la <em>Ley de los senos</em>:

\\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)}

Multiplicando a cada lado de la igualdad por \\ \sin(\beta)

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = \frac{b}{\sin(\beta)}*\sin(\beta)

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*\frac{\sin(\beta)}{\sin(\beta)}

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*1

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b

Sustituyendo cada valor en la expresión anterior:

\\ b = \frac{a}{\sin(\alpha)}*\sin(\beta)

\\ b = \frac{4m}{\sin(34^{\circ})}*\sin(64^{\circ})

\\ b = 4m*\frac{0.8988}{0.5592}

\\ b = 6.4292m

En palabras, la medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m.

El lado <em>c</em> puede obtenerse de manera similar considerando que \\ \gamma = 82^{\circ}.

6 0
3 years ago
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