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mamaluj [8]
3 years ago
12

an aircraft flies from its base 200 km on a bearing 162 degree, then 350km on a bearing 260 degree and then returns directly to

base. Calculate the length and bearing of the return journey
Mathematics
1 answer:
Anastasy [175]3 years ago
4 0
X=200cos(162+90)+350cos(260+90)

y=200sin(162+90)+350sin(260+90)

x≈282.88

y≈-250.99

So the length of the return trip is:

d^2=x^2+y^2

d^2≈143017.0745

d≈378.18

tanα=-250.99/282.88

α=arctan(-250.99/282.88)

α≈-41.58°  that's the standard angle relative to the positive x-axis...

We need to be going in the exact opposite direction when returning so...

180-41.58=138.42°  again this angle is standard notation.  To convert this to a bearing we need to subtract 90°...

So the bearing is 138.42-90=48.42°

So the return trip will be 378.18km on a bearing of 48.42°

(I have assumed that the bearing was relative to true north, or the positive y axis....)
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Step-by-step explanation:

For the first limit, plug in x=8 in the expression (9x-3), that's the answer for linear equations and limits.

So we have:

9x-3\\9(8)-3\\72-3\\69

The answer is 69


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\frac{x^2+8x-9}{x^2-1}\\\frac{(x+9)(x-1)}{(x-1)(x+1)}\\\frac{x+9}{x+1}

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Choose the model that represents the function
kirill [66]

Answer:

OPTION D

Step-by-step explanation:

We have to determine which option determines the function given above.

To determine the function, just substitute the values and compare LHS and RHS.

we have $ f(4) = 18 $

$ f(-2) = -12 $

$ f(0) = -2 $

$ f(-3) = -17 $

Here, $ x $ is the domain and $ f(x) $ is the co-doamin.

Therefore, $ x = \{4, -2, 0, -3\} $

Now, OPTION A: $ f(x) =  2x - 5 $

Substitute x = 4. We get f(x) = 3 $ \ne $ 18.

So, OPTION A is rejected.

Similarly, OPTION B: $ f(x) = 5x + 2 $

Substitute x = 4. We get f(4) = 22 $ \ne $18.

It is rejected as well.

Now, for OPTION C: $ f(x) = \frac{x}{2} - 5 $

Substitute x = 4. We get f(4) = -3 $ \ne $ 18.

So, OPTION C is also rejected.

OPTION D: $ f(x) =  5x - 2 $

Substitute x = 4. We get f(4) = 18.

Substitute the remaining points in domain as well. We notice that it exactly matches the given function. So, OPTION D is the answer.

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