1. Round to the nearest hundredth.
2 answers:
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Answer:
11.51
Step-by-step explanation:
In general, a calculator is required to evaluate the irrational sum ...
π + √70
<h3>Calculator result</h3>The result from a readily-available online calculator is shown in the attachment.
π + √70 ≈ 11.51
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<em>Additional comment</em>
You have probably memorized pi to several digits: 3.1416. To obtain the required estimate means you need to approximate √70 to about the same level of precision.
For a number n = a² +b, the square root can be approximated by the continued fraction ...
√n ≈ a +b/(2a +b/(2a +...))
Effectively, the root (r) can be iterated from the recursive formula ...
r' = a +b/(a +r)
For √70, we have 70 = 8² +6 ⇒ a=8, b=6
If the initial approximation of the root is r0≈a=8, then a couple of iterations gives ...
r1 = 8 + 6/(8 +r0) = 8 + 6/(8 +8) = 8 3/8
r2 = 8 + 6/(8 +r1) = 8 +6/(8 +8 3/8) = 8 48/131
This has sufficient accuracy for the purpose. The decimal equivalent of the sum then becomes ...
3.1416 +8.3664 = 11.5080 ≈ 11.51
The values of a and b are 1/4 and 1/5 respectively
<h3>How to determine the true statement?</h3>The function is given as:
16x^2 - 25y^2 = 1
The above function is a horizontal hyperbola.
A horizontal hyperbola that passes through the origin is represented as:
Rewrite 16x^2 - 25y^2 = 1 as
By comparison, we have:
Solve for a and b
Hence, the values of a and b are 1/4 and 1/5 respectively
Read more about hyperbola at:
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