Not sure how to do this. (I'm aware this is wrong lol)

Mathematics

1 answer:

Bezzdna [24]3 years ago

3 0

I think the answer is 80 degrees. Think about it like you're moving the chunk with 100 degrees already filled in, to the space where you're trying to find the amount since they're the same. Vertical angles are supplementary and are equal to 180. So, 100+x = 180. x would equal 80 degrees.

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Find dy / dx for ex + y = y.

asambeis [7]

Answer: The required value of $\dfrac{dy}{dx}$ is $\dfrac{y}{1-y}.$

Step-by-step explanation: We are given to find the value of $\dfrac{dy}{dx}$ from the following equation :

$e^{x+y}=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Taking natural logarithm on both sides of equation (i), we have

$\ln e^{x+y}=\ln y\\\\\Rightarrow x+y=\ln y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Differentiating both sides of equation (ii) with respect to x, we get

$\dfrac{d}{dx}(x+y)=\dfrac{d}{dx}\ln y\\\\\\\Rightarrow 1+\dfrac{dy}{dx}=\dfrac{1}{y}\dfrac{dy}{dx}\\\\\\\Rightarrow \left(\dfrac{1}{y}-1\right)\dfrac{dy}{dx}=1\\\\\\\Rightarrow \dfrac{1-y}{y}\dfrac{dy}{dx}=1\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{y}{1-y}.$