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3 years ago

The following table shows the number of fire hydrants in each neighborhood overseen by Fire District 9

Mathematics

1 answer:

Dafna11 [192]3 years ago

7 0

Answer:

Step-by-step explanation:

The median, is just the middle number in a set of numbers.

In this case, our set is: 17, 8, 15, 21, 12.

However, the set must be in increasing order, so the set becomes: 8, 12, 15, 17, 21.

This gives us the median, which is the middle number, to be: 15.

Let me know if this helps!

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Find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts. Use C for the constant o

umka2103 [35]

Answer:

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-1/2 ln⁡(1+x^2 )+C

Step-by-step explanation:

∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗

Let 1st=arctan⁡(x)

And 2nd=1

∫▒〖arctan⁡(x).1 dx=arctan⁡(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗

As we know that

derivative of arctan(x)=1/(1+x^2 )

∫▒〖1 dx〗=x

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1

Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now

Let 1+x^2=u

du=2xdx

Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get

1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)

1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)

1/2 ∫▒(2xdx/u) =1/2 ln⁡(u)+C

1/2 ∫▒(2xdx/u) =1/2 ln⁡(1+x^2 )+C

Putting values in Eq1 we get

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-1/2 ln⁡(1+x^2 )+C (required soultion)

3 0

3 years ago

Read 2 more answers

At Scott's Laundromat, the washing machines accept only quarters and

Y_Kistochka [10]

Answer:

8 quarters and 12 nickles

Step-by-step explanation:

8*25=2.00

12*.05=.60

4 0

3 years ago

Solve by using the measurements ∠PQR = 90°, ∠QRP = 80°, and r = 15. Round measures of sides to the nearest tenth and measures of

valkas [14]

Good evening ,

___________________

Step-by-step explanation:

Look at the photo below for the answer.

5 0

3 years ago

Read 2 more answers

At a wedding reception an equal number of guests were seated at each of three large tables, and 7 late arriving desks were seate

nikitadnepr [17]

Answer:

10 guests a table

Step-by-step explanation:

3 tables

7 late arrivals

37 total people

37 minus 7 is 30

30 divided by 3 is 10

answer is 10

8 0

3 years ago

What’s the answer?and how do you get it

Kay [80]

the solid is made up of 2 regular octagons, 8 sides, joined up by 8 rectangles, one on each side towards the other octagonal face.

from the figure, we can see that the apothem is 5 for the octagons, and since each side is 3 cm long, the perimeter of one octagon is 3*8 = 24.

the standing up sides are simply rectangles of 8x3.

if we can just get the area of all those ten figures, and sum them up, that'd be the area of the solid.

$\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=5\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(5)(24)\implies \stackrel{\textit{just for one octagon}}{A=60} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{two octagon's area}}{2(60)}~~+~~\stackrel{\textit{eight rectangle's area}}{8(3\cdot 8)}\implies 120+192\implies 312$

7 0

4 years ago