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3 years ago

What is the range of g

Mathematics

1 answer:

denis23 [38]3 years ago

8 0

The range of g is -3,4

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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

a_sh-v [17]

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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3 years ago

How many triangles can be constructed with side lengths 5, 7, and 15?

IrinaVladis [17]

More than ne triangle

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Help me, please. Confused again.

vichka [17]

Answer:

Step-by-step explanation:

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3.) Duncan spent $70 and now has<br> $120. How much money did he have<br> before spending the 70?

frosja888 [35]

Answer:

He started with $190

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3 years ago

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PLEASE HELP AND EXPLAIN ALSO SHOW WORK

Goryan [66]

Answer:

x=10

Step-by-step explanation:

Make 2x the only variable on the left side of the equation. Do that by taking 3 and 5 to the left. Note: if you move/transpose any number the sign must change.

2x = 18+5-3

2x=20

Divide both sides of the equation by 2 to make x the only variable left.

x=10

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2 years ago