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Wislar
Group Title
Please help!
One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is pi/6?
 2 years ago
 2 years ago
Wislar Group Title
Please help! One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is pi/6?
 2 years ago
 2 years ago

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experimentX Group TitleBest ResponseYou've already chosen the best response.1
perhaps the Q meant this dw:1350751784378:dw
 2 years ago

Wislar Group TitleBest ResponseYou've already chosen the best response.0
I thought this was related rates, but I'm in calc 3, and we are doing differentials and tangent approximations, so I'm kinda lost here. Plus, I don't really remember related rates too well
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1350751819497:dw yeah this is related rate.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1350751925717:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
Given that \( {x = 20} , {dx \over dt} = 3 \) \( {y = 30} , {dy \over dt} = 2 \) \[ A = {1 \over 2} xy \; \sin \theta \\ {dA \over dt} = 0, \\ \text{Find } {d \theta \over dt }\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
If i interpreted the problem correctly ...
 2 years ago

Wislar Group TitleBest ResponseYou've already chosen the best response.0
How did you get z=16.14?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
forget that ... it's not necessary.
 2 years ago

Wislar Group TitleBest ResponseYou've already chosen the best response.0
It's been along time since I've done related rates, so I may be wrong, but would I take the derivative of dA/dt first?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
also given that \( \theta = {\pi \over 6} \) differentiate the above ... put the values and get the rest.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
Given area is constant ... dA/dt = 0
 2 years ago

Wislar Group TitleBest ResponseYou've already chosen the best response.0
Would I differentiate A=.5 xysin(theta) ? What would I take the derivative with respect to?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
time ... t, also you are given the values of dx/dt and dy/dt
 2 years ago

Wislar Group TitleBest ResponseYou've already chosen the best response.0
dA/dt=.5 (dx/dt)ysin(theta)+x(dy/dt)sin(theta)+xy(theta)(cos(theta))(dtheta/dt) ?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yes ... put the values dA/dt = 0, all values are given, you only need to find the value of d(theta)/dt
 2 years ago

Wislar Group TitleBest ResponseYou've already chosen the best response.0
Got it! Thanks!
 2 years ago
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