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# A plane flying horizontally at an altitude of $1 mi$ and a speed of $500 mi/h$ passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is $2 mi$ away from the station.(a) What quantities are given in the problem?(b) What is the unknown?(c) Draw a picture of the situation for any time $t.$(d) Write an equation that relates the quantities.(e) Finish solving the problem.

## a) $1 \mathrm{mi}, \quad 500 \mathrm{mi} / \mathrm{h}, 2 \mathrm{mi}$b) The rate at which the distance from the plane to the radar station is increasing, when the plane is 2 miles away from the stationc) See step for answerd) $y^{2}=x^{2}+1$e) 250$\sqrt{3} \mathrm{mi} / \mathrm{h}$

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JN

Jake N.

February 26, 2019

It's so hard to understand.. I get that english isn't your first language but you must get better with writing using PC because it's VERY sloppy and paired with the language barrier is bad.

WB

William B.

October 11, 2019

I really can't figure out what is being said and written

JR

Jp R.

November 4, 2019

HORRIBLE video.

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### Video Transcript

No. We're told that a plane flying horizontally at an altitude of one mile and the speed of 500 MPH passes directly over a radar station. We're asked to find the rate at which the distance from the plane to the station is increasing when it is two miles away from the station. Yes, to understand this problem first, we're gonna draw a diagram. So we have our station on the ground just constantly the we have our plane mile above the ground. What, and distance from the radar station to the plane. We'll call this why? And the horizontal distance from the station to the plane. We'll call this X lucky Mhm. Now. Hey, Jersey boys is entirely in part a positive grant, president. Right and years is were asked what quantities are given in the problem or clearly given that the altitude is one mile. We're also told that the plane is flying at a speed of 500 MPH and we're told that the distance other boys hair from the plains of the station is two miles. Yes. Then in part B, we are asked to find the unknown Well, the unknown is the rate at which the distance from the plane to the station is increasing. This, in other words, dy d t Yeah, mhm. So prison, then in part C rest to draw a picture. You've already drawn this picture? Yeah. So simply see the figure. Then in part D were asked to write an equation that relates to quantities. So by Pythagorean theorem, do you look at our figure? Yeah, we have that X squared plus one squared equals y squared or both x and wire functions of t. And so we differentiate both sides with respect to Time T And so we have two times x times dx DT is equal to two times y dy DT violence. Now we want to solve for dy DT So from this equation, it follows that dy DT equals X over y times dx DT, you see used it on your case. That man, that's what Right now, in order to solve this problem, he defined X At the moment y equals two miles to me to solve the equation. X squared plus one squared equals two squared. In other words, X squared equals four minus one is three so x equals in this case, plus or minus three. But because the plane is two miles away from the station and the rate at which the distance is increasing, yes, X is then positive three. Right now, plug these values into our shot equation for Dy DT. So this is Route 3/2 times the X DT, which we're told is 500. So this is 250 Route three mhm is and the units these are in miles per hour. There's a the soldiers. This is actually part E as well, so our answer is really 250 times route three MPH, said ST.

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Derivatives

Differentiation

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