1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pychu [463]
3 years ago
12

How do you solve his with working

Mathematics
1 answer:
AlexFokin [52]3 years ago
7 0
Check the picture below.

a)

so the perimeter will include "part" of the circumference of the green circle, and it will include "part" of the red encircled section, plus the endpoints where the pathway ends.

the endpoints, are just 2 meters long, as you can see 2+15+2 is 19, or the radius of the "outer radius".

let's find the circumference of the green circle, and then subtract the arc of that sector that's not part of the perimeter.

and then let's get the circumference of the red encircled section, and also subtract the arc of that sector, and then we add the endpoints and that's the perimeter.

\bf \begin{array}{cllll}
\textit{circumference of a circle}\\\\ 
2\pi r
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{arc's length}\\\\
s=\cfrac{\theta r\pi }{180}
\end{array}\\\\
-------------------------------

\bf \stackrel{\stackrel{green~circle}{perimeter}}{2\pi(7.5) }~-~\stackrel{\stackrel{green~circle}{arc}}{\cfrac{(135)(7.5)\pi }{180}}~+
\stackrel{\stackrel{red~section}{perimeter}}{2\pi(9.5) }~-~\stackrel{\stackrel{red~section}{arc}}{\cfrac{(135)(9.5)\pi }{180}}+\stackrel{endpoints}{2+2}
\\\\\\
15\pi -\cfrac{45\pi }{8}+19\pi -\cfrac{57\pi }{8}+4\implies \cfrac{85\pi }{4}+4\quad \approx \quad 70.7588438888



b)

we do about the same here as well, we get the full area of the red encircled area, and then subtract the sector with 135°, and then subtract the sector of the green circle that is 360° - 135°, or 225°, the part that wasn't included in the previous subtraction.


\bf \begin{array}{cllll}
\textit{area of a circle}\\\\ 
\pi r^2
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{area of a sector of a circle}\\\\
s=\cfrac{\theta r^2\pi }{360}
\end{array}\\\\
-------------------------------

\bf \stackrel{\stackrel{red~section}{area}}{\pi(9.5^2) }~-~\stackrel{\stackrel{red~section}{sector}}{\cfrac{(135)(9.5^2)\pi }{360}}-\stackrel{\stackrel{green~circle}{sector}}{\cfrac{(225)(7.5^2)\pi }{360}}
\\\\\\
90.25\pi -\cfrac{1083\pi }{32}-\cfrac{1125\pi }{32}\implies \cfrac{85\pi }{4}\quad \approx\quad 66.75884

You might be interested in
Which symbol replaces the box to make the statement true?
Karolina [17]

Answer:

0. toab1. The right answer for K12 is ( > ) I Took the test and is correct. 4×16-16 > 4× [24-2× (4+8)] heart outlined. Thanks 0. star outlined. star outlined. star outlined.

8 0
2 years ago
Which of the following relations is a function? A. (0, 4), (-2, 6), (0, 3), (-7, 2) B. (8, 1), (-2, 4), (0, 1), (8, 2) C. (0, 4)
fomenos

Answer: C

Step-by-step explanation:

C is a function because each of the inputs are distinct, meaning they only have one output each.

The other choices are not functions because at least one of the inputs corresponds to 2 or more outputs.

8 0
2 years ago
A green cross is formed by placing two rectangles of dimensions 8cm×4cm over
Goshia [24]

Answer:

<em>The perimeter of the green cross is 32 cm</em>

Step-by-step explanation:

<u>Perimeter</u>

It's the sum of all the external side lengths of a given shape.

The green cross formed by two rectangles is shown in the figure below.

We have outlined the dimensions of the external sides of the resulting cross.

Note there are four corners of 2 cm by 2 cm and four sides of 4 cm each.

The total perimeter is:

8 * 2 cm + 4 * 4 cm = 16 cm + 16 cm = 32 cm

The perimeter of the green cross is 32 cm

4 0
3 years ago
What is the answer to 0.55 divided by 100
ratelena [41]
The answer is 0.0055
7 0
3 years ago
Read 2 more answers
Simplify the following expression: (−4)(−2)(−3)
Hitman42 [59]

Answer:

-24

Step-by-step explanation:

-4*2*3= -24

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the trian
    10·1 answer
  • Plz Help
    13·1 answer
  • Which equation has the solution x = 5?
    10·2 answers
  • 1.) what do values a h and k tell about the graph
    5·2 answers
  • In the diagram, what is the measure of angle 1 to the nearest degree?
    13·1 answer
  • What is the rate of change of the following equation?<br> y = 5 X-3
    13·1 answer
  • Solve the system of linear equations using elimination. −7x + 3y = −6 −3x + 3y = 6
    7·2 answers
  • -8=-(x+4) what is the answer
    14·1 answer
  • Determine the x-intercept of the line whose equation is given:
    12·2 answers
  • Simplify the expression <br> -17.8a-2.4a+25-19.5
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!