urja asked in Science & MathematicsMathematics · 5 months ago

# Solve the following equation for the unknown value, n, using the appropriate number of significant figures.?

Solve the following equation for the unknown value, n, using the appropriate number of significant figures.

-246.0=1312(1/2^2 - 1/n^2) = +-

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• ?
Lv 7
5 months ago

-246.0 = 1312(1/2² - 1/n²)

-246.0 = 1312(1/4 - 1/n²)

-246.0 = 328 - 1312/n²

-246.0n² = 328n² - 1312

574.0n² = 1312

n² ≈ 2.286

n ≈ ±1.512..................ANS

• sepia
Lv 7
5 months ago

-246.0 = 1312(1/2^2 - 1/n^2)

Solutions:

n ≈ -1.51186

n ≈ -1.51186

• 5 months ago

Presuming that is:

-246.0 = 1312(1/2² - 1/n²)

"To the appropriate number of significant figures".  The first two have 4.  The others are in a fraction, so ignoring them as they aren't rounded, yet.

So the end result I'll round to 4DP.

I'll start by dividing both sides by 1312:

-246.0 = 1312(1/2² - 1/n²)

-0.1875 = 1/2² - 1/n²

Let's simplify the first term on the right side and subtract 1/4 (or 0.25) from both sides:

-0.1875 = 1/4 - 1/n²

-0.1875 - 0.25 = -1/n²

-0.4375 = -1/n²

Let's multiply both sides by -1 to get rid of the negatives, get the reciprocal of both sides, then simplify the left side again:

0.4375 = 1/n²

1/0.4375 = n²

10000/4375 = n²

16/7 = n²

Now we can get the square root of both sides:

n = ± 4 / √7

Using a decimal approximation to √7, then rounding the results to 4SF, we get:

n = ±1.512

If we weren't told to round, I would then simplify this and keep it as an irrational number by rationalizing the denominator:

n = ±(4/7)√7