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Luda [366]
3 years ago
8

14. At the library, Herb spent 1/6 hour looking for a book, 1/4 hour reading, and 1/2 hour doing research on the computer. How m

any
hours did Herb spend at the library?

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
5 0
Herb spent 55 minutes at the library
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Find the half range Fourier sine series of the function
worty [1.4K]
The full range is -\pi (length 2L=2\pi), so the half range is L=\pi. The half range sine series would then be given by

f(x)=\displaystyle\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L=\sum_{n\ge1}b_n\sin nx

where

b_n=\displaystyle\frac2L\int_0^Lf(x)\sin\dfrac{n\pi x}L\,\mathrm dx=\frac2\pi\int_0^\pi(\pi-x)\sin nx\,\mathrm dx

Essentially, this is the same as finding the Fourier series for the function

\begin{cases}g(x)=\begin{cases}\pi-x&\text{for }0

Integrating by parts yields

b_n=\dfrac2\pi\left(\dfrac\pi n-\dfrac{\sin n\pi}{n^2}\right)=\dfrac2n

So the half range sine series for this function is simply

f(x)=\displaystyle\sum_{n\ge1}\frac{2\sin nx}n
5 0
3 years ago
ABCD is a parallelogram. If mZCDA = 63, then mZABC = _?_ The diagram is not to scale.
nevsk [136]

Answer:

b. 63

Step-by-step explanation:

A Parallelogram is known to be a flat shape quadrilateral which has four opposite sides Each two opposite sides are parallel and are equal in length. The opposite angles are equal.

The above answer is correct because opposite angles of a parallelogram are equal:

m∠CDA = m∠ABC

where m∠CDA = 63

∴ m∠ABC = 63 (answer)

4 0
3 years ago
In DCAB, if ÐB = 380, What is ÐC?
Jobisdone [24]
What form is DCAB? and I do not see the point Đ
5 0
3 years ago
Find the volume of the<br> triangular prism.<br> 3.6 cm<br> 5.4 cm<br> 9 cm
MrMuchimi

Answer:

174.96cm2

Step-by-step explanation:

V=lbh

=3.6×5.4×9

=174.96cm2

I don't knowif you want it in milliliters or litres so here are both of them

milliliters = 174.96

litres = 0.17496

6 0
2 years ago
Janelle wants to learn to play the piano. Her friends recommended two different music schools. Make Music charges $525 for 10 ho
makvit [3.9K]

Answer:

Piano Play has the better deal

Step-by-step explanation:

Piano Play has the better deal because it has a lower unit rate

Make Music’s unit rate is 52.5 when you divide $525 by 10 hours

Piano Play’s unit rate is $45 when you divide $540 by 12 hours

3 0
3 years ago
Read 2 more answers
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