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2 years ago

Which of these equations are in slope-intercept form?

Mathematics

1 answer:

maxonik [38]2 years ago

6 0

Answer:

y = mx + b

Step-by-step explanation:

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Find gradient xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to x, assuming y = y(x).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for dy/dx :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If y ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

PLEASE ANSWER THIS IS URGENT

mr Goodwill [35]

Answer:

i think its 48 but dont trust me im just doing this for points hope you get a good grade on it

Step-by-step explanation:

6 0

2 years ago

Can somebody help me? Thank you!

DiKsa [7]

Answer:

angel, side, angel

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Kellie is playing with a toy building block that has the shape of a rectangular prism.

Lena [83]

I think the volume is 200

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3 years ago

Please help and show work

shepuryov [24]

What’s the question????

5 0

2 years ago