If the tree is 25 feet tall , what is the angle of depression to his friend

Is 9.22222 a irrational number

jonny [76]

Answer:

No

Step-by-step explanation:

9.222222 is not a irrational number.

Hope this helps plz hit the crown :D

8 0

2 years ago

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Use a formula to find the monthly payment on a home mortgage of $84,400 at 4.884% interest for 15 years.

leonid [27]

The applicable formula is
A = P(r/12)/(1 -(1+r/12)^(-12n))
where P is the principal amount,
r is the annual interest rate (compounded monthly), and
n is the number of years.

Using the formula, we find
A = 84,400*(0.04884/12)/(1 -(1+0.04884/12)^(-12*15))
= 84,400*0.00407/(1 -1.00407^-180)
= 343.508/0.518627
≈ 662.34

The monthly payment on a mortgage of $84,400 for 15 years at 4.884% will be
$662.34

6 0

3 years ago

Solve using Fourier series.

Olin [163]

With $2L=\pi$ , the Fourier series expansion of $f(x)$ is

$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos\dfrac{n\pi x}L+\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L$
$\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos2nx+\sum_{n\ge1}b_n\sin2nx$

where the coefficients are obtained by computing

$\displaystyle a_0=\frac1L\int_0^{2L}f(x)\,\mathrm dx$
$\displaystyle a_0=\frac2\pi\int_0^\pi f(x)\,\mathrm dx$

$\displaystyle a_n=\frac1L\int_0^{2L}f(x)\cos\dfrac{n\pi x}L\,\mathrm dx$
$\displaystyle a_n=\frac2\pi\int_0^\pi f(x)\cos2nx\,\mathrm dx$

$\displaystyle b_n=\frac1L\int_0^{2L}f(x)\sin\dfrac{n\pi x}L\,\mathrm dx$
$\displaystyle b_n=\frac2\pi\int_0^\pi f(x)\sin2nx\,\mathrm dx$

You should end up with

$a_0=0$
$a_n=0$
(both due to the fact that $f(x)$ is odd)
$b_n=\dfrac1{3n}\left(2-\cos\dfrac{2n\pi}3-\cos\dfrac{4n\pi}3\right)$

Now the problem is that this expansion does not match the given one. As a matter of fact, since $f(x)$ is odd, there is no cosine series. So I'm starting to think this question is missing some initial details.

One possibility is that you're actually supposed to use the even extension of $f(x)$ , which is to say we're actually considering the function

$\varphi(x)=\begin{cases}\frac\pi3&\text{for }|x|\le\frac\pi3\\0&\text{for }\frac\pi3$

and enforcing a period of $2L=2\pi$ . Now, you should find that

$\varphi(x)\sim\dfrac2{\sqrt3}\left(\cos x-\dfrac{\cos5x}5+\dfrac{\cos7x}7-\dfrac{\cos11x}{11}+\cdots\right)$

The value of the sum can then be verified by choosing $x=0$ , which gives

$\varphi(0)=\dfrac\pi3=\dfrac2{\sqrt3}\left(1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots\right)$
$\implies\dfrac\pi{2\sqrt3}=1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots$

as required.

5 0

2 years ago

Which sentences contain two words that are related in the same way as the underlined words in the paragraph?

muminat

D is the correct answer

4 0

3 years ago

The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her

grigory [225]

Answer:

$12 per hour

Step-by-step explanation:

In order to find her hourly rate we have to find the amount of dollars billed per hour. To do this we can use this expression: $\frac{y2 - y1}{x2 - x1}$

Let's use the points (1, 27) and (2, 39) in the expression:

$\frac{39 - 27}{2 -1}$

Now let's simplify the expression:

39 - 27 = 12

2 - 1 = 1

The expression simplifies to 12/1, or 12. This means that Brenda is billed $12 every hour she uses her phone.

I hope this helps :)

6 0

3 years ago

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