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3 years ago

Someone please help me answer this!!

Mathematics

1 answer:

Scrat [10]3 years ago

4 0

Answer:

b = 9cm is the answer.

Step-by-step explanation:

a = 12cm

b = ?

c = 15cm

By using the Pythagoras theorem,

a² + b² = c²

12² + b² = 15²

144 + b² = 225

b² = 225 - 144

b² = 81

b = 9cm.

∴ b = 9cm is the length of the missing leg.

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Solve this problem by using variation of parameters method. y''-y=coshx.

Gekata [30.6K]

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For the nonhomogeneous ODE

$y''-y=\underbrace{\cosh x}_{f(x)}$

we're looking for a particular solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\int\frac{y_2(x)f(x)}{W(y_1(x),y_2(x))}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(x)f(x)}{W(y_1(x),y_2(x))}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the two fundamental solutions.

We have

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so we're left with

$u_1=-\displaystyle\int\sinh x\cosh x\,\mathrm dx=-\dfrac12\cosh^2x$
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so that the particular solution is

$y_p=-\dfrac12\cosh^3x+\dfrac12x\sinh x+\dfrac14\sinh x\sinh2x$
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As $y_1$ already accounts for the $\cosh x$ term in $y_p$ , we're left with the general solution

$y=C_1\cosh x+C_2\sinh x+\dfrac12x\sinh x$

3 0

3 years ago

2x + 3 = 5 . Solve for x

STALIN [3.7K]

Answer:

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Step-by-step explanation:

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=> 2x = 2

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4 0

3 years ago

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Liula [17]

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4 years ago

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sertanlavr [38]

Answer:

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Step-by-step explanation:

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