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3 years ago

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Triangle ABC ≅ DEF. Each side of triangle ABC is 1.5 times longer than the corresponding sides of triangle DEF. If the perimeter

of triangle ABC is 36 centimeters, what is the perimeter of triangle DEF?

1 answer:

mina [271]3 years ago

5 0

Answer:

Step-by-step explanation:

see attachment

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Solve the initial value problem y'=2 cos 2x/(3+2y),y(0)=−1 and determine where the solution attains its maximum value.

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Answer:

$y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

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Step-by-step explanation:

We are given that

$y'=\frac{2cos2x}{3+2y}$

y(0)=-1

$\frac{dy}{dx}=\frac{2cos2x}{3+2y}$

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Taking integration on both sides then we get

$\int (3+2y)dy=2\int cos 2xdx$

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Using formula

$\int x^n=\frac{x^{n+1}}{n+1}+C$

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Substitute x=0 and y=-1

$-3+1=sin0+C$

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$sin0=0$

Substitute the value of C

$y^2+3y=sin2x-2$

$y^2+3y-sin 2x+2=0$

$y=\frac{-3\pm\sqrt{(3)^2-4(1)(-sin2x+2)}}{2}$

By using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$y=\frac{-3\pm\sqrt{9+4sin2x-8}}{2}=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

Hence, the solution $y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

When the solution is maximum then y'=0

$\frac{2cos2x}{3+2y}=0$

$2cos2x=0$

$cos2x=0$

$cos2x=cos\frac{\pi}{2}$

$cos\frac{\pi}{2}=0$

$2x=\frac{\pi}{2}$

$x=\frac{\pi}{4}$

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