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3 years ago

Find the length of the missing side when x=3. Round the answer to the nearest tenth.

Mathematics

1 answer:

Juliette [100K]3 years ago

5 0

Answer/Step-by-step explanation:

The missing length can be found by applying pythagorean theorem. Thus:

Missing length = √((8x)² - (2x)²)

Missing length = √(64x² - 4x²)

✔️Missing length = √(60x²) = 2x√15

Plug in the value of x which is 3

Missing length = 2*3√15

✔️Length = 6√5

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$\displaystyle\\Answer:\ x=\sqrt{2}\ \ \ \ \ x=-\sqrt{2}\ \ \ \ \ x=\frac{ln5}{2}$

Step-by-step explanation:

$5x^2-x^2e^{2x}+2e^{2x}=10$

$Let:\ x^2=t \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}$

Prologarithmize both parts of the equation:

$ln5=lne^{2x}\\ln5=2x*lne\\ln5=2x*1\\ln5=2x\\$

Divide both parts of the equation by 2:

$\displaystyle\\x=\frac{ln5}{2}$

$t-2=0\\t-2+2=0+2\\t=2\\x^2=2\\x=\sqrt{2} \\x=-\sqrt{2}$

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