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dos aviones parten de una ciudad con direcciones S32°E y E57°N¿ cuál es el angulo que forma sus direcciones?

Elan Coil [88]

Answer:

El ángulo formado entre las dos direcciones es aproximadamente 115º.

Step-by-step explanation:

Las direcciones dadas en el enunciado significan lo siguiente:

S32ºE - 32º al este del sur.

E57ºN - 57º al norte del este.

Vectorialmente hablando, cada dirección es la siguiente:

S32ºE

$A(x,y) = (\sin 32^{\circ}, -\cos 32^{\circ})$

$A(x,y) = (0.530, -0.848)$

E57ºN

$B(x,y) = (\cos 57^{\circ},\sin 57^{\circ})$

$B(x,y) = (0.545, 0.839)$

El ángulo formado entre los dos vectores unitarios ( $\theta$ ), medido en grado sexagesimales, puede determinarse mediante la siguiente ecuación vectorial:

$\theta = \cos^{-1} \frac{A\,\bullet \,B}{\|A\|\cdot \|B\|}$

Donde:

$\|A\|$ - Norma de $A(x,y)$ .

$\|B\|$ - Norma de $B(x,y)$ .

Si sabemos que $A(x,y) = (0.530, -0.848)$ , $B(x,y) = (0.545, 0.839)$ , $\|A\| = 1$ y $\|B\| = 1$ , entonces el ángulo formado entre los dos vectores es:

$\theta = \cos^{-1} \frac{(0.530)\cdot (0.545)+(-0.848)\cdot (0.839)}{(1)\cdot (1)}$

$\theta \approx 115^{\circ}$

El ángulo formado entre las dos direcciones es aproximadamente 115º.

4 0

3 years ago

The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased b

masha68 [24]

Answer:

The fraction is $\frac{4}{6}$

Option (B) is correct.

$3n-2d=0$ and $4n+8=3d+6$

Step-by-step explanation:

Let n denotes numerator and d denotes denominator of the fraction.

Given : The ratio of the numerator to the denominator of a fraction is 2 to 3.

That is $\frac{n}{d}=\frac{2}{3}$

Cross multiply , we get,

$3n=2d$

Or, $3n-2d=0$ ........(1)

Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4

That is $\frac{n+2}{d+2}=\frac{3}{4}$

Cross multiply , We get,

$4{n+2}={3}{d+2}$

$4n+8=3d+6$ .........(2)

$3d-4n=2$ .......(3)

Thus, from (1) and (2) , option (B) follows.

Solving equation (1) and (3) to get the original fraction using elimination method,

3n - 2d = 0 ............(1)

and 3d - 4n = 2 .........(3)

Multiply equation (1) by 3 , we get ,

9n - 6d = 0 ..........(4)

Multiply equation (3) by 2 , we get ,

-8n + 6d = 4 ..........(5)

Adding (4) and (5) , we get,

9n - 6d -8n + 6d = 4 + 0

⇒ n = 4

Put n = 4 in (1), we get

3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0 ⇒ 12 = 2d ⇒ d = 6

so, the numerator is 4 and the denominator is 6.

Thus, the fraction is $\frac{4}{6}$

6 0

3 years ago

Which table shows ordered pairs that satisfy the function y = x + 1?

const2013 [10]

Answer:

Knowledge Check The table of ordered pairs (x, y) gives an exponential function. Write an equation for the function. x y -1 6 0 12 1 1 24 2. 48 88 O х ? I Don't ...

Step-by-step explanation:

4 0

3 years ago

Mallory and five of her friends bought a box of 36 cookies. together they ate 2/3 of the cookies

Rzqust [24]

Answer:

24 cookies got eaten 12 weren't eaten

Step-by-step explanation:

36 divided by 3 = 12

12 x 2 = 24 ( since they ate 2/3)

36-24=12 (12 weren't eaten)

5 0

3 years ago

How would you write this number in numeric form?

liberstina [14]

22.0094
0.034
This should be the answer

3 0

3 years ago