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blsea [12.9K]
3 years ago
6

Find the area of a circle with the radius of 10.

Mathematics
1 answer:
BARSIC [14]3 years ago
7 0

Answer:

about 314.16 units squared

Step-by-step explanation:

The formula for area is A = πr^2. Plugging in r, the radius, we get A = π10^2. Evaluating π*10, we get A = [about] 314.16^2.

If the problem asks you to plug in 3.14 for pi, the answer is 314 units squared.

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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.
3 0
3 years ago
The locations, given in polar coordinates, for two ships are (8 mi, 63º) and (8 mi, 123º). Find the distance between the two shi
PolarNik [594]
The arrangement forms an isosceles triangle with equal legs of 8 mi. The angle between the legs is,

123-63 = 60°. Therefore, the other two angles ares:

Angles = (180-60)/2 = 120/2 = 60°

It can therefore be noted that all angles are equal and thus the resulting triangle is actual an equilateral triangle and thus all the sides are equal.

It can be concluded that the ships are 8 miles apart.
8 0
3 years ago
Read 2 more answers
What combination of transformations is shown below ?
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Answer:

Translation then Reflection

Step-by-step explanation:

Step 1 to 2 is Translation

Step 2 to 3 is Reflection

6 0
3 years ago
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If f(x) = 5x − 3, which expression represents its inverse function?
Drupady [299]

Answer:

B.

\frac{x+3}{5}

Step-by-step explanation:

5x - 3 = y then 5x = y + 3 then  x = (y + 3)/5

then the inverse function of f is : (x+3)/5

6 0
3 years ago
Renata ganó una rifa y se le entregaron 7832 pesos. Ella decidió repartirlos de la siguiente manera: a su mamá 3/8 del total, a
gogolik [260]

Answer:

A su mamá

= 2937 pesos

A su hermano

= 1566.4 pesos

El resto para ella

= 3328.6 pesos

Step-by-step explanation:

El número total de pesos que cada uno consiguió se calcula como:

Su madre

= 3/8 del total

= 3/8 × 7832

= 2937 pesos

Su hermano

= 1/5 del total

= 1/5 × 7832

= 1566.4 pesos

Sí misma

= El resto

= 7832 - (2937 + 1566,4)

= 7832 - 4503.4

= 3328.6 pesos

5 0
3 years ago
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