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watchmath
 5 years ago
Find the height of the lamp post (see the attachment).
watchmath
 5 years ago
Find the height of the lamp post (see the attachment).

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watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1welcome to answer everybody :).

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1did you make this problem up or did you find it somewhere

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1It is from a book :). We give this as an assignment for our student :).

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1i think i'm fixing to figure out lol

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1if i can figure out P i'm done

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so far i have y1=2x0/y0 where P=(x0,y0) this is the way i'm suppose to go about it right?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1and where L representing the point of the bulb of the lamp post at (3,y1)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1so found the slope of the line containing P and the x intercept (5,0) and got m=(y10)/(3+5)=y1/8 and i found the derivative of the ellipse which is y'=x/4y i evaluated y' at (x0,y0) and got y'=x0/4y0 so this has to be equal to y1/8 so we have y1=2x0/y0

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1omg omg P=(1,1) so y1=2

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1ty so much for the problem :) i don't know if i went about the long way or not but i feel good about it

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Good job Miyaniya :) So you like it?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1yes im going to use it wow it took while for me to figure how to get P lol that was my problem for the longest time

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1is this way that you were thinking about finding the height? or is there a shorter way?

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Here what I will do to find \(P\). Let \(P=(a,b)\). Using \((a,b)\) and \((5,0)\) the slope is \(m=\frac{b}{a+5}\). Using implicit differentiation the slope is \(m=\frac{a}{4b}\). Setting the two to be equal, we have \(4b^2=a^25a\). But since \((a,b)\) is on the ellipse, \(4b^2=5a^2\). So \(a^25a=a^2+5\) which implies \(a=1\). It follows that \(4b^2=5a^2=4\). So \(b=\pm 1\). But \(b\) is above the \(x\)axis. So \(b=1\). Hence \(P=(1,1)\). Let \(h\) be the height that we are looking for. Using similar triangle we have \(\frac{h}{5+3}=m=\frac{1}{4}\). Then \(h=2\).

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1ok nice. you have less text than i have writing lol

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1thank you so much watchmath. i'm totally going to give this to my calculus students and let them work on it as a group project
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