This question has two parts. First, answer Part 1. Then, answer Part 2.

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

3 0

The answer will be a

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The slope of the line in the graph is 4. Fill in the y intercept. Choose the correct equation in the form y = mx + b The y inter

nikitadnepr [17]

Answer:

$\rm\implies y = 4x + 3$

Step-by-step explanation:

Given :-

The slope of the line in the graph is 4.

And we need to find the equation of the line. On looking at the graph we see that , it cuts y axis at (0,3) .So the y Intercept of the equation is 3 .

Slope Intercept Form :-

$\rm\implies y = mx + c$

Substituting the respective values :-

$\rm\implies y = 4*x + 3 \\\\\rm\implies y = 4x + 3$

Hence the equation of line is y = 4x + 3 

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3 years ago

Dy/dx = (cos x) e^(y+sinx) and y = 0 when x = 0. find the original equation

Korvikt [17]

Find the general solution by separating the variables then integrating:
dy / dx = cosx℮^(y + sinx)
dy / dx = cosx℮ʸ℮^(sinx)
℮^(-y) dy = cosx℮^(sinx) dx
∫ ℮^(-y) dy = ∫ cosx℮^(sinx) dx
-℮^(-y) = ℮^(sinx) + C
℮^(-y) = C - ℮^(sinx)
-y = ln[C - ℮^(sinx)]
y = -ln[C - ℮^(sinx)]

Find the particular solution by solving for the constant:
When x = 0, y = 0
-ln(C - 1) = 0
ln(C - 1) = 0
C - 1 = 1
C = 2
y = -ln[2 - ℮^(sinx)]

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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3 years ago