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3 years ago

5

The accepted value of the average distance between Earth and the moon is 384, 467 km. If a scientist measures that the moon is 3

84,476 km form the Earth, what is the measurement's percentage error?

1 answer:

Karo-lina-s [1.5K]3 years ago

4 0

Answer:

Percentage error is 0.0024 %

Step-by-step explanation:

Initial average distance between Earth and moon = 384467 km

Distance measure by the scientist = 384476 km

Total variation in the distance calculation = 384476 – 384467 = 9 km.

Now we can find the percentage by dividing the variation in distance from the initial measurement and then multiply with hundred.

Percentage error = ( 9 / 384467 ) × 100 = 0.0024 %

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Answer:

See attached picture.

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3 years ago

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IgorC [24]

Hey there, hope I can help!

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$\mathrm{Factor\:out\:coefficient\:of\:square\:terms} \ \textgreater \ -4\left(x^2-8x\right)+9\left(y^2+4y\right)=64$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}4$
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$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}9$
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$\mathrm{Convert}\:x\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x^2-8x+16\right)+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert\:to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)$

$\mathrm{Convert}\:y\:\mathrm{to\:square\:form}$
$-\frac{1}{9}\left(x-4\right)^2+\frac{1}{4}\left(y^2+4y+4\right)=\frac{16}{9}-\frac{1}{9}\left(16\right)+\frac{1}{4}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
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For me I used
$\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}= 1$
$As\;\mathrm{it\;\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}$

I know yours is an equation which is why I did not go any further because this is the standard form you are looking for. I would rewrite mine to get my hyperbola standard form. However the one I have provided is the form you need where mine would be.
$\frac{\left(y-\left(-2\right)\right)^2}{2^2}-\frac{\left(x-4\right)^2}{3^2}=1$

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andrey2020 [161]

I will assume that this question is about scientific notation (also assuming that the first number is 3.4*10^2), where you can arrange the numbers by the exponent of the 10, so from least to greatest:
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3 years ago