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Komok [63]
3 years ago
14

Use separation of variables to solve dy dx − tan x = y2 tan x with y(0) = √3. Find the value of c in radians, not degrees

Mathematics
1 answer:
a_sh-v [17]3 years ago
3 0

Answer:

y(x)=tan(-log(cos(x))+\frac{\pi }{3} )

Step-by-step explanation:

Rewrite the equation as:

\frac{dy(x)}{dx}-tan(x)=y(x)^{2} *tan(x)

Isolating \frac{dy}{dx}

\frac{dy}{dx} =tan(x)+tan(x)*y^{2}

Factor:

\frac{dy}{dx} =tan(x)*(1+y^{2} )

Dividing both sides by (1+y^{2} ) and multiplying them by dx

\frac{dy}{1+y^{2} } =tan(x)dx

Integrate both sides:

\int\ \frac{dy}{1+y^{2} } = \int\ tan(x)  dx

Evaluate the integrals:

arctan(y)=-log(cos(x))+C_1

Solving for y:

y(x)=tan(-log(cos(x))+C_1)

Evaluating the initial condition:

y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)

\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1

Converting 60 degrees to radians:

60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}

Replacing C_1 in the diferential equation solution:

y(x)=tan(-log(cos(x))+\frac{\pi }{3} )

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Maggie runs in 5.20 minutes, Olivia runs in 4.35 minutes.

Step-by-step explanation:

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Olivia = can run a mile in 4.35 minutes (2.9/0.666666667)

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5 0
2 years ago
How would you convert 276 yards to inches?
valentinak56 [21]

Answer:

9936 inch.

Step-by-step explanation:

Note the measurements:

1 Yard = 3 Feet

1 Feet = 12 Inch

1 Yard = 3 Feet = (12)(3) Inches = 36 Inches; 1 Yard = 36 Inches

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276 x 36 = 9936

9936 inches is your answer.

~

6 0
3 years ago
How do I round these numbers?
olga nikolaevna [1]
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8 0
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A fisher usually catches 540kg of anchovies off El Niño,the fisher caught 85% less fish. How many kilograms of fish did the fish
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1. Which measure is equivalent to 16 quarts?
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Step-by-step explanation:

1quart=2pints

16quarts=32pints

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Read 2 more answers
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