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svetoff [14.1K]
3 years ago
9

Solve the equation: b/5 + 15 =45 is answer 150

Mathematics
1 answer:
laila [671]3 years ago
4 0

Answer: The answer is 150.

Step-by-step explanation:

First of all, we need to use inverse operations to solve this arithmetical equation.

First, multiply both sides by 5.

5(B/5 + 15) = 5(45).

B + 75 = 225.

Now we need to use the inverse operation of addition to get B by itself.

The inverse operation of addition is subtraction. And so we must subtract each side by 75.

B + 75 - 75 = 225 - 75.

B = 150.

So it looks like you are correct. 150 is the answer.

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Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.
andreev551 [17]

The roots of an equation are simply the x-intercepts of the equation.

See below for the proof that \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0} has at least two real roots

The equation is given as: \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}

There are several ways to show that an equation has real roots, one of these ways is by using graphs.

See attachment for the graph of \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}

Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)

From the attached graph, we can see that \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0} crosses the x-axis at approximately <em>-2000 and 2000 </em>between the domain -2500 and 2500

This means that \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0} has at least two real roots

Read more about roots of an equation at:

brainly.com/question/12912962

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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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