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almond37 [142]
3 years ago
9

A plane flying horizontally at an altitude of 2 mi and a speed of 540 mi/h passes directly over a radar station. Find the rate a

t which the distance from the plane to the station is increasing when it is 5 mi away from the station. (Round your answer to the nearest whole number.)
Mathematics
1 answer:
Rasek [7]3 years ago
4 0

Answer:

The plane's distance from the radar station will increase about 8 miles per minute when it is 5 miles away from it.

Step-by-step explanation:

When the plane passes over the radar station, the current distance is the altitude h = 2. Then it moves b horizontally so that the distance to the station is 5. We can form a rectangle triangle using b, h and the hypotenuse 5. Therefore, b should satisfy

h²+b² = 5², since h = 2, h² = 4, as a result

b² = 25-4 = 21, thus

b = √21.

Since it moved √21 mi, then the time passed is √21/540 = 0.008466 hours, which is 0.51 minutes. Note that in 1 minute, the plane makes 540/60 = 9 miles.

The distance between the plane and the radar station after x minutes from the moment that the plane passes over it is given by the function

f(x) = \sqrt{((9x)^2 + 2^2)} = \sqrt{(81x^2+4)}

We have to compute the derivate of f in x = 0.51. The derivate of f is given by

f'(x) = \frac{162x}{2\sqrt{81x^2+4}}

also,

f'(0.51) = \frac{162*0.51}{2\sqrt{81*0.51^2+4}} = 8.2486

The plane's distance from the station will increase about 8 miles per minute.

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Answer:

Step-by-step explanation:

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x=\frac{-12\pm \sqrt{12^2-4*1*(-17)} }{2*1} \\=\frac{-12 \pm \sqrt{144+68} }{2} \\=\frac{-12 \pm \sqrt{212}}{2} \\=\frac{-12+2\sqrt{53}}{2}\\=-6 \pm \sqrt{53}

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If a denotes some​ event, what does upper a overbara ​denote? if ​p(a)equals=0.9930.993​, what is the value of ​p(upper a overba
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P(A) is the probability of not A (note that I am trying to place a bar over A. I hope you can see it, else it is because the editor did not show it as I intended)

Then, use the fact that the probability of A plus the probability not A is equal to 1:
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<h3>What is a slope?</h3>

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<h3>How to calculate the slope of a line?</h3>

Mathematically, the slope of a straight line can be calculated by using this formula;

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Read more on slope-intercept form here: brainly.com/question/1884491

#SPJ1

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