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PolarNik [594]
3 years ago
14

Flying against the wind, an airplane travels 4560 kilometers in 6 hours. Flying with the wind, the same plane travels 3720 kilom

eters in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
Mathematics
1 answer:
Flura [38]3 years ago
7 0

Answer:

The speed rate of the plane in still air is 1006.67 km/h

The speed rate of the wind is 246.67 km/h

Step-by-step explanation:

To answer the question, we let the speed of the plane in still air = x  km/h

Let the speed of the wind = y km/h

Therefore,

4560/(x - y) = 6 hours and

3720/(x + y) = 3 hours

4560 = 6·x - 6·y.........(1)

3720 = 3·x + 3·y ........(2)

Multiplying equation (2) by 2 and add to (1) gives

12080 = 12·x

x = 12080/12 = 1006\frac{2}{3} km/h

Substituting the value of x in (1) gives

4560 = 6040 - 6·y

6·y = 1480

y = 1480/6 =  246\frac{2}{3}

The speed rate of the plane in still air = 1006.67 km/h

The speed rate of the wind = 246.67 km/h.

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Total number of ways so that one chicken and one beef Ramen selected = 450 + 450 = 900

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P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}

Required probability is:

\dfrac{900}{1140} = 0.789

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Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π
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The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of x can be found by concept of derivative, which is described below:

g(x) =  \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Where h is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of g if f(x) = \sin x and evaluate the resulting expression for x = \frac{\pi}{3}. Then, we have the following procedure below:

g(x) =  \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin h}{h}\cdot  \lim_{h \to 0} \cos x

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Now we evaluate g(x) for x = \frac{\pi}{3}:

g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}

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To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

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