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tamaranim1 [39]
3 years ago
7

Find three consecutive odd integers with the sum of 51.

Mathematics
1 answer:
Levart [38]3 years ago
3 0
Well.. hmmmm

bear in mind that, if you multiply any integer, odd or even, by 2, you get an even, no matter how you slice it and dice it, you always get an even number, 17 *2, 34*2, or whatever * 2, is always an EVEN integer.

you can always get an ODD integer, by simply adding or subtracting 1 from any even,  say  4 - 1, or 4 + 1, is 3 and 5 respectively, both odd ones.

and you can always get another consecutive odd integer, by simply jumping 2 units from any odd, so 3, 5, 7, 9, 11 and so on, notice, you simply hop two spots from one, on either direction back or forth, and you get another ODD integer.

alrite, with that in mind, let's pick a reference value, say "a" is our reference integer.

so, 2*a or 2a, we know is an EVEN integer, however, we also  know that 2a + 1 is an ODD integer, well, there you have it, our first odd integer is 2a + 1.

now, let's hop twice from there to get our second consecutive odd one, (2a + 1) + 2, or 2a + 3, now, let's hop again to get the next consecutive odd one, (2a + 3) + 2, or 2a + 5.

there you have it, our reference integer is "a", our odd integers are those.

alrite... now, we know their sum gives 51, alrite

\bf (2a + 1) + (2a + 3) + ( 2a + 5) = 51
\\\\\\
2a + 1 + 2a + 3 +  2a + 5 = 51
\\\\\\
2a + 2a + 2a +1 + 3 ++ 5 = 51\implies 6a+9=51\implies 6a=51-9
\\\\\\
6a=42\implies a=\cfrac{42}{6}\implies \boxed{a=7}

now, recall, "a" is only our reference integer, so... if you want to get the consecutive odd integers, well, they're just 2a + 1, 2a + 3 and 2a + 5, and since you already know what "a" is, well, just plug it in to get the integers.
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The exponential model A = 661.7 e^0.011t describes the population, A, of a country in millions, t years after 2003. Use the mode
faust18 [17]

Answer:

661.7 million

Step-by-step explanation:

Given the exponential model :

A = 661.7 e^0.011t

The general form of an Exponential model is expresses as :

A = A0 * e^rt

Where A = final value ; A0 = Initial value ; r = growth rate and t = time elapsed

From the question t = time after 2003

Therefore, A0 = initial population, which is the population in 2003

Therefore, A0 = 661.7

Or we could put t = 0 in the equation and solve for A

A = 661.7 e^0.011(0)

A = 661.7 * 1

A = 661.7

Hence, population in 2003 is 661.7 million

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3 years ago
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}.

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Answer:

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0.75 * 35 == 26.25

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