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
earnstyle [38]
3 years ago
9

each side of triangle xyz has length 9 .Find the area of the region inside the circumcircle of the triangle but outside the tria

ngle. PLEASE HELP QUICK!

Mathematics
1 answer:
mote1985 [20]3 years ago
6 0

Answer:

The area of the region inside the circumcircle of the triangle but outside the triangle is

A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of triangle

we have an equilateral triangle

Applying the law of sines

A_t=\frac{1}{2}(b^2)sin(60^o)

where b is the length side of the equilateral triangle

we have

b=9\ units

A_t=\frac{1}{2}(81)sin(60^o)

A_t=\frac{1}{2}(81)\frac{\sqrt{3}}{2}

A_t=81\frac{\sqrt{3}}{4}\ units^2

step 2

Find the area of circle

The area of the circle is equal to

A_c=\pi r^{2}

The formula to calculate the radius of the circumcircle of the triangle equilateral is equal to

r=b\frac{\sqrt{3}}{6}

where b is the length side of the equilateral triangle

we have

b=9\ units

substitute

r=(9)\frac{\sqrt{3}}{6}

r=3\frac{\sqrt{3}}{2}\ units

Find the area

A_c=\pi (3\frac{\sqrt{3}}{2})^{2}

A_c=\frac{27}{4} \pi\ units^2

step 3

Find the area of the shaded region

we know that

The area of the region inside the circumcircle of the triangle but outside the triangle is equal to the area pf the circle minus the area of triangle

so

A=(\frac{27}{4} \pi-81\frac{\sqrt{3}}{4})\ units^2

Simplify

A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2

You might be interested in
the sum of the measurement of two exterior angles of a triangle is 255. what is the measurement of the third exterior angle?
Sergio [31]

Answer:

The measurement of the third exterior angle is 105°.

Step-by-step explanation:

The sum of the measures of the exterior angles of a polygon is always 360° ( However it is triangle or rectangle or etc..)

Since, a triangle has three exterior angles,

Given,

The measurement of two exterior angles of a triangle is 255°,

Let x be the third exterior angle,

Then by the above statement,

x + 255° = 360°

x = 360° - 255° = 105°

Hence, the measurement of the third exterior angle is 105°.

3 0
2 years ago
Read 2 more answers
If you make 25 bookmarks and sell them each for 50 cents, if you sold all your bookmarks, how much money would you have?
olga55 [171]

Answer:

$12.50

Step-by-step explanation:

25 (bookmarks) x $0.50(price) = $12.50(profit)

3 0
3 years ago
Read 2 more answers
Using the order of operations , solve the value of the expression.
velikii [3]
Hello.

\frac{1}{6} (\sqrt{36} \div 3^{-2}) + 4^{3} \div |-8| = \\ \\ \frac{1}{6} (6 \div \frac{1}{9}) + 64 \div 8 \\ \\ \frac{1}{6} \times 54 + 8 \\ \\ \frac{54}{6} + 8 \\ \\ 9 + 8 = \\ \\ 17

Hope I helped!
8 0
3 years ago
Simplify: Square root of 8xy squared
SashulF [63]

Answer:

8xy

Step-by-step explanation:

\sqrt{(8xy)^{2}}=\sqrt{(8)^{2}x^{2}y^{2}} =8xy

6 0
3 years ago
Solve the following word problem by using a system of equations.
coldgirl [10]
For this problem, we can use systems of equations. I will use the variables <em>x </em> (for ice-cream) and <em>y</em> (for soda). We get the system:

2.25x+0.75y=30.00
x+y=18

Putting the second equation in terms of y, we get that y=-x+18. We can substitute this into our first equation.

2.25x+0.75y=30.00
becomes
2.25x+0.75(-x+18)=30

Solving for x, we get that x=11. This satisfies answer B.

However, if you want to check to see if this is correct, you could find y by plugging in your value of x into the first equation, then check to see if your found values satisfy BOTH equations.

2.25(11)+0.75y=30
24.75+0.75y=30
0.75y=5.25
y=7

Then we plug this into both equations to see if they are true.

2.25(11)+0.75(7)=30
24.75+5.25=30
30=30 (This is true)

x+y=18
11+7=18
18=18 (This is true).

Both equations are true, so the value for x and y are correct. We see that only answer B is supported through analyzing your work.

:)
4 0
3 years ago
Other questions:
  • One plane at 520 feet is ascending at a rate of 40 feet per minute. While another plane at 3800 feet is descending at a rate of
    11·1 answer
  • HELP PLZ ANSWER NEEDED
    8·2 answers
  • Please help fasttt!!
    9·1 answer
  • (2,-3) and (4, 8)<br> Slope = _
    6·2 answers
  • What is the measure of n?
    13·1 answer
  • The charity gala will cost $546 if it has 42 attendees. How many attendees can
    12·1 answer
  • GUYS HELP ME.. plEASEEEEE
    11·1 answer
  • How many milliliters of chocolate milk are in the container shown? Enter your answer in the box.
    5·1 answer
  • How do you factor x³-9?
    6·2 answers
  • Which is the product of 7/9 and 6?<br> A. 1 4/9<br> B. 3 7/9<br> C. 4 2/3<br> D. 7 5/7
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!