The answer would be 58 degrees. You have to add the measure of R and P, and since a triangle is a total of 180 degrees, you subtract the sum and R and P from 180 and get your answer. Hope this helps!

4 0

3 years ago

Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e

Bingel [31]

Assuming the series is

$\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}$

The series will converge if

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

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

So the series will certainly converge if $-1$ , but we also need to check the endpoints of the interval.

If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

$\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0$

and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

6 0

3 years ago

To hang lights up on his house.Garrett place is a 14 foot ladder 4 feet from the base of the house. How high up the house will t

Firlakuza [10]

This seems like a right triangle problem.

So assuming 14 feet is the hypotenuse and 4 feet is a leg of the right triangle, we can use the pythagorean theorem ( $a^{2} +b^{2} =c^{2}$ ) to solve for the height of the house, in which we shall name it x.

So, the equation is $4^{2} +x^{2} =14^{2}$ .

Solve for x:

16+x^{2}= 196

x^{2}= 196-16

x^{2}= 180

x = 6√5 feet

Hope this helps!

5 0

3 years ago

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