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1 answer:
Answer:
For better understanding of the solution, see the attached figure of the problem :
1). From the diagram, since Yellowsburg is directly north of Blueville therefore AB will be perpendicular to BC and ∠ABC = 90
Now, In ΔABC, using Pythagoras theorem
AC² = AB² + BC²
158² = 141² + BC²
BC² = 158² - 141²
BC² = 5083
⇒ BC = 71.3 miles
Hence, Blueville is 71.3 miles away from Greentown.
2). The basketball court is in shape of rectangle whose dimensions are given by :
Length = 84 feet and Breadth = 50 feet
Since, Each angle of rectangle is 90 hence by using Pythagoras theorem in ΔPQR :
PR² = PQ² + QR²
PR² = 84² + 50²
PR² = 9556
PR = 97.75 feet
Hence, If a coach has her players sprint diagonally across the court, they need to run 97.75 feet
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The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.
<h3>Find the radius of convergence R and the interval of convergence:</h3>Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
= β
- If β < 1, then the series converges
- If β > 1, then the series diverges
- If β = 1, then the series inconclusive
Here =
and
=
Now limit is taken,
=
=
=
=
= < 1
- 1 < < 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
Learn more about radius of convergence here:
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