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AveGali [126]
2 years ago
12

Practice with Conversions

Mathematics
1 answer:
mylen [45]2 years ago
3 0

Answer:

1) Newbury Park → The distance is accurate.

2) Thousand Oaks → The distance is not accurate.

3) Los Angeles → The distance is not accurate.

Step-by-step explanation:

It is important to remember that:

1\ mile=1.609\ kilometers

Knowing this, you can make the corresponding conversions:

1) Newbury Park

10 miles to kilometers:

(10\ mi)(\frac{1.609\ km}{1\ mi})=16.0\ km

The distance shown in that California highway sign is accurate.

2) Thousand Oaks

13 miles to kilometers:

(13\ mi)(\frac{1.609\ km}{1\ mi})=20.9\ km

The distance shown in that California highway sign is not accurate.

3) Los Angeles

55 miles to kilometers:

(55\ mi)(\frac{1.609\ km}{1\ mi})=88.4\ km

The distance shown in that California highway sign is not accurate.

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Step-by-step explanation:

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ΔHGI  ≅ ΔUTH                by Angel Side Angle congruent

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Step-by-step explanation:


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Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1
defon
I'm guessing the series is supposed to be

\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}

By the ratio test, the series converges if the following limit is less than 1.

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|

The first n terms in the numerator's denominator cancel with the denominator's denominator:

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|

|x^n| also cancels out and the remaining factor of |x| can be pulled out of the limit (as it doesn't depend on n).

\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0

which means the series converges everywhere (independently of x), and so the radius of convergence is infinite.
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3 years ago
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