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3 years ago

Write the decimal as a fraction 0.272727

Mathematics

1 answer:

Oksana_A [137]3 years ago

7 0

.272727 written as a fraction is 272727/1000000

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All possible solutions for 6sin^2(3x)=-3

vova2212 [387]

Answer:

Please check the step-by-step explanation for the answer.

Step-by-step explanation:

Considering the trigonometric expression

$6sin^2\left(3x\right)=-3$

Steps

$\mathrm{Let:\:}\sin \left(3x\right)=u$

$6u^2=-3$

$\mathrm{Divide\:both\:sides\:by\:}6$

$\frac{6u^2}{6}=\frac{-3}{6}$

$u^2=-\frac{1}{2}$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$u=\sqrt{-\frac{1}{2}},\:u=-\sqrt{-\frac{1}{2}}$

$\mathrm{Simplify}\:\sqrt{-\frac{1}{2}}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}$

$=\sqrt{-1}\sqrt{\frac{1}{2}}$

$\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i$

$=i\sqrt{\frac{1}{2}}$

Similarly,

$-\sqrt{-\frac{1}{2}}=\quad -i\sqrt{\frac{1}{2}}$

So,

$u=i\sqrt{\frac{1}{2}},\:u=-i\sqrt{\frac{1}{2}}$

$\mathrm{Substitute\:back}\:u=\sin \left(3x\right)$

$\sin \left(3x\right)=i\sqrt{\frac{1}{2}},\:\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}$

So,

$\sin \left(3x\right)=i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}$

and

$\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}$

$\mathrm{Combine\:all\:the\:solutions}$

$\mathrm{No\:Solution\:for}\:x\in \mathbb{R}$

Keywords: trigonometric equation, solution

Learn more about trigonometric equation solution from brainly.com/question/1687218

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soldier1979 [14.2K]

X^2+y^2=z^2

x^2+96^2=100^2

x=sqrt(100^2-96^2)

x=28 so the distance from the base of the ladder and the base of the ladder is 28ft.

Hope this helps. Any questions please just ask. Thank you.

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