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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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experimentXBest ResponseYou've already chosen the best response.1
perhaps the Q meant this dw:1350751784378:dw
 one year ago

WislarBest 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1350751819497:dw yeah this is related rate.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1350751925717:dw
 one year ago

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

experimentXBest ResponseYou've already chosen the best response.1
If i interpreted the problem correctly ...
 one year ago

WislarBest ResponseYou've already chosen the best response.0
How did you get z=16.14?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
forget that ... it's not necessary.
 one year ago

WislarBest 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?
 one year ago

experimentXBest 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.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Given area is constant ... dA/dt = 0
 one year ago

WislarBest ResponseYou've already chosen the best response.0
Would I differentiate A=.5 xysin(theta) ? What would I take the derivative with respect to?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
time ... t, also you are given the values of dx/dt and dy/dt
 one year ago

WislarBest 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) ?
 one year ago

experimentXBest 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
 one year ago
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