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
vladimir1956 [14]
3 years ago
5

The figure above shows a right-angled triangle OAB. AOC is a minor sector enclosed in the triangle. If OA = 7 cm, AB = 6 cm, cal

culate the area and perimeternof the shaded region.​ PLEASE HELP!

Mathematics
1 answer:
dolphi86 [110]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\  \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = \frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = \frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

You might be interested in
Write the equation of a line that is perpendicular to y=5 and that passes through the point (−7,−5)
nordsb [41]

x =  - 7 \\  \\ hope \: it \: helps

6 0
2 years ago
Read 2 more answers
If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which
Inga [223]

Answer:

Step-by-step explanation:

the first ine make sense to me

if not right sorry

7 0
2 years ago
Use complete sentences to describe why √-1≠-√1
Salsk061 [2.6K]

Answer: because √-1 complex number ; and -√1 real number

Step-by-step explanation:

because √-1 complex number ; and -√1 real number or                                         \displaystyle\ (\sqrt{-1})^2 \neq(- \sqrt{1} )^2 \\\\-1\neq 1                                              

7 0
3 years ago
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer
choli [55]

Answer:

there is a 64% chance that the student got both problems wrong

a 32% chance that they got only 1 correct

and a 4% chance that they got both correct

Step-by-step explanation:

There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.

25-9=16

\frac{16}{25} =\frac{x}{100}

\frac{64}{100}

64%

\frac{8}{25} =\frac{y}{100}

\frac{32}{100}

32%

\frac{1}{25} =\frac{z}{100}

\frac{4}{100}

4%

3 0
3 years ago
Hello i need help with these questions asap!!
makvit [3.9K]

We use direct proportionality:

360⁰......Pi×R² (full circle)

120⁰.......x

x=120×pi×R²/360=pi×R²/3

x=pi×4²/3=16.76mi²

A=3×pi cm², for an angle of 2×pi/3=120⁰

In a similar way we compute the area of the full circle:

360.........x

120..........3×pi

x=3×pi×360/120=9×pi=3²×pi.

Thus the radius is 3cm.

3 0
3 years ago
Other questions:
  • I sphere has a diameter of 24 units what is the volume in cubic units
    5·1 answer
  • A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section)
    8·1 answer
  • Need help with this math problem
    11·1 answer
  • Need help on 6. 7. 8. 9. 10.
    14·1 answer
  • I need help with this ASAP, please thank you
    5·2 answers
  • Find the percent error of the measurement 4 cm.<br> 4%<br><br> 1%<br><br> 12.5%<br><br> 40%
    15·2 answers
  • Solve each equation algebraically using if–then statements to justify each step. 1. 5 + 4 = 19
    7·2 answers
  • 3^2 x 3^-5<br><br> and explain
    12·2 answers
  • Solve two sevenths times four sixths . (2 points) Group of answer choices six forty seconds eight forty seconds six thirteenths
    5·1 answer
  • Lidocaine (2 grams) was prescribed in 500 mL of fluid at 2 mg/ minute, to be administered via an infusion pump. What is the flow
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!