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4 years ago

If y varies inversely as x and x = 9 when y = 45 , find x when y = 9 .

Mathematics

1 answer:

Harman [31]4 years ago

6 0

I believe it's 1.8, but correct me if I'm wrong.

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Calculate the unit rate: write your answer as a decimal 1/2 mile in ever 1/3 hour

Alexandra [31]

Answer:

$unit \: rate = \frac{distance}{time}$

unit rate is similar to speed / velocity:

$unit \: rate = \frac{ (\frac{1}{2} )}{ (\frac{1}{3})} \\ \\ = \frac{1}{2} \div \frac{1}{3} \\ \\ = \frac{1}{2} \times \frac{3}{1} \\ \\ = > { \boxed{ \boxed{unit \: rate = \frac{3}{2} \: miles \: per \: hour}}}$

[unit rate must have units including per <time> ]

7 0

3 years ago

Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

Tess needs to buy sand for her children’s playground. The sand costs $8 per ton, and there is a delivery cost of $50 with each o

Butoxors [25]

Answer:

All positive rational numbers greater than 50

Step-by-step explanation:

Since the delivery cost is fixed per trip, the cost incurred can be represented by the equation

y(x)=8x+50 so in case Tess wants only 1 tone, the cost will be y(x)=8(1)+50=58

Therefore, it's proper to conclude that all numbers in the possible range are positive rational numbers greater than 50

6 0

3 years ago

What is the volume of the cone with height of 6 m and diameter of 8 m rounded to the nearest cubic meter

yawa3891 [41]

Answer:

101 m^3

Step-by-step explanation:

v = π * r^2 * h/3

= π * 4^2 * 6/3

v= 100.53 m^3

v= 101 m^3 to the nearest cubic meter

5 0

3 years ago

PLEASE HELP MEEE

kicyunya [14]

Answer:

Step-by-step explanation:

Example: Based on Week starting on Monday

Odie works M-W-F-Sun-Tues-Thur-Sat

Mary Thur- M-Thurs

Carlos Fri-Wed-M

3 0

3 years ago