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3 years ago

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b. From where the shoes spilled (48°N, 161°W) to where they were found on May 22nd 1996 (54°N, 133°W), how many kilometers did t

hey travel? How many days did they take to travel that distance (use April 30 as the date found)? What was their rate of travel in kilometers per hour?

1 answer:

dsp733 years ago

3 0

To find kilometers using latitude and longitude:

distlon = lon2 - lon1 = 133-161 = -23

distlat = lat2 - lat1 = 54-48 = 6

a = (sin(distlat/2))^2 + cos(lat1) * cos(lat2) * (sin(distlon/2))^2

a = (sin(6/2)^2 + cos(48)*cos(54)* sin(-23/2)^2

c = 2 * arctan2( sqroot(a), sqroot(1-a) )

d = R * c (where R is the radius of the Earth, 6373 km's)

d = 2052 km's

April 30th to May 22nd is 23 days.

23 days x 24 hours per day = 552 hours.

Rate of travel = 2052 / 552 = 3.717 km per hour ( round answer as needed.)

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El valor de <em>x</em> es igual a 20 o <em>x</em> = 20.

Step-by-step explanation:

Lo primero que se debe saber es que <em>dos ángulos complementarios suman un ángulo recto o 90º</em>.

Supongamos que el valor de un ángulo $\\ \alpha$ y un ángulo $\\ \beta$ valen:

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Sumamos los factores comunes entre si:

$\\ (2x + x) + (10 + 20) = 90$

Para la primera expresión debemos recordar que se suman sólo los coeficientes. Así:

$\\ (2 + 1)x + (10 + 20) = 90$

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Para despejar la incógnita <em>x</em>, debemos tener en cuenta que <em>una igualdad no se altera si se suma, se resta, se multiplica o divide un mismo valor a cada lado de ella</em>. Por esta razón, para despejar 3x, lo primero que podemos hacer es sumar -30 a cada lado de la expresión (lo que es igual a restar 30 a cada lado de la misma). Así tenemos:

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$\\ 3x + 0 = 90 - 30$

$\\ 3x = 60$

Ahora dividimos cada miembro de la igualdad entre 3 (o multiplicamos cada lado de la igualdad por $\\ \frac{1}{3}$ ):

$\\ \frac{3}{3}x = \frac{60}{3}$

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$\\ \frac{3}{3} = 1$

Entonces:

$\\ 1*x = \frac{60}{3}$

$\\ x = \frac{60}{3}$

$\\ x = 20$

De esta manera, el valor de <em>x</em> es igual a 20 o x = 20.

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$\\ \alpha = 2x + 10$ [1]

Sustituimos x por el valor de 20:

$\\ \alpha = 2*20 + 10 = 40 + 10 = 50$

$\\ \beta = x + 20$ [2]

Hacemos lo mismo para [2]:

$\\ \beta = 20 + 20$

$\\ \beta = 40$

De esta manera:

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$\\ 50 + 40 = 90$

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