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
diamong [38]
1 year ago
9

Find the area of the segment (unshaded area) of Circle G with radius 4in. Round to the nearest tenth.

Mathematics
2 answers:
frez [133]1 year ago
5 0

Answer:

4.6 in²  (nearest tenth)

Step-by-step explanation:

To find the <u>area of the unshaded region</u>, subtract the <u>area of ΔAGB</u> from the <u>area of sector AGB</u>.

The measure of an arc is equal to its corresponding central angle measure.  Therefore, the <u>central angle of sector</u> AGB is 90°.

As the two sides of ΔAGB adjacent the central angle are the radii of the circle they are therefore equal in length ⇒ ∠GAB = ∠GBA.  

Therefore, ΔAGB is an isosceles triangle.

<u>Area of triangle (using the Sine Rule):</u>

\sf A=\dfrac{1}{2}ab \sin C

(where a and b are the side lengths and C is the included angle)

Given:

  • a = b = radius = 4 in
  • C = 90°

\implies \sf Area\:of\:triangle=\dfrac{1}{2}(4)(4)\sin 90^{\circ}=8\:in^2

<u>Area of a sector of a circle</u>

\textsf{A}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2

\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}

Substituting the given angle and radius:

\implies \textsf{A}=\left(\dfrac{90^{\circ}}{360^{\circ}}\right) \pi (4)^2=4\pi\:\: \sf in^2

<u>Area of the unshaded region:</u>

\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\& = 4 \pi - 8\\& = 4.566370614...\\ & = 4.6\:\sf in^2\:\:(nearest\:tenth)\end{aligned}

Romashka [77]1 year ago
4 0

Angle is 90°

The sector is 1/4 th of circle

Area of sector

  • πr²/4
  • π(4)²/4
  • 4πin²

Triangle is right angled

Area

  • 1/2(4)²
  • 16/2
  • 8in²

Area of unshaded region

  • 4π-8
  • 4(π-2)
  • 4(3.14-2)
  • 4(1.14)
  • 4.56in²
You might be interested in
See the attachment below for the question.
tangare [24]

Answer:

The correct answer is third option

x = 3

Step-by-step explanation:

It is given that,

4ˣ = 8⁽ˣ ⁻ ¹⁾

<u>To find the value of x</u>

4ˣ  = (2²)ˣ

8⁽ˣ ⁻ ¹⁾ = (2³)⁽ˣ ⁻ ¹⁾

4ˣ = 8⁽ˣ ⁻ ¹⁾

(2²)ˣ =  (2³)⁽ˣ ⁻ ¹⁾

2²ˣ = 2⁽³ˣ ⁻ ³⁾

2x = 3x - 3

3x - 2x = 3

x = 3

The correct answer is third option

x = 3

5 0
3 years ago
Read 2 more answers
Find the range of values of p if the median is 3
faltersainse [42]

If we deal with Natural numbers then the range is

1 ≤ p ≤ 5

4 0
3 years ago
Given h(x)=-x+2, find h(2)
Bingel [31]

Answer:

0

Step-by-step explanation:

Replace x with 2.

-(2)+2=0

6 0
2 years ago
Read 2 more answers
Can someone please help me with this
lana [24]

Answer:

3x-10+70°=180°(Supplementary angles)

3x+60°=180°

3x=180°-60°

3x=120°

3x/3 =120°/3

x=40°

Step-by-step explanation:

Hope that this is helpful.

Have a wonderful day.

6 0
3 years ago
ericas mother saved her quarters and dimes .she counted 48 coins with a value of $7.50.how many quarters and dimes were there?
katrin2010 [14]
28 Quarters and 5 dimes
8 0
3 years ago
Read 2 more answers
Other questions:
  • Simone has 32 erasers. She arranges the erasers into 5
    11·1 answer
  • I need help with that question please
    14·2 answers
  • Which is a possible expression for the series<br> –7 + 12 –17 +22 –27
    15·1 answer
  • He park trail is 10x^2+4x+2 miles long. The hiker has traveled 5x-1 miles. How much farther does the hiker need to travel to get
    11·1 answer
  • 0.19444444444 as a fraction
    5·1 answer
  • 18 over 4= I need help I been trying to find out what the answer is please help
    7·1 answer
  • Task 1 Nonlinear Systems of Equations Create a system of equations that includes one linear equation and one quadratic equation.
    6·1 answer
  • 4250cm ........... m?​
    9·2 answers
  • Use the properties of equality to solve the equation 3x+2-x=11x+9. State which property justifies your first step and why you ch
    15·1 answer
  • Katrina had $138.72 in her checking account. she wrote checks to take out $45.23 and $18.00, and then made a deposit of $75.85 i
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!