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
What is the ratio Between 113 and165
Harlamova29_29 [7]
A ratio between is like 52
5 0
3 years ago
HELP ME I NEED HELP!!!!
eduard

Answer:

D

Step-by-step explanation:

Since they are the same variables

7 0
3 years ago
Mrs. Gray purchase a 15 pound turkey for $12.75 what was the price of the turkey per pound
Rus_ich [418]

Answer:

0.85 I believe

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Apopulation grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.a) Write a function to model the
solong [7]

Answer:

a) P(t) = 22000(1.071)^{t}

b) The population increases 7.1% each year.

Step-by-step explanation:

The continuous population growth model is given by:

P(t) = P_{0}(1+r)^{t}

In which P(t) is the population after t years, P_{0} is the initial population and r is the growth rate.

In this problem, we have that:

A population grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.

This means that P_{0} = 22000, r = 0.071

a) Write a function to model the population increase.

P(t) = 22000(1 + 0.071)~{t}

P(t) = 22000(1.071)^{t}

b) By what percent does the populaiion increase each year?

r = 0.071

So the population increases 7.1% each year.

6 0
3 years ago
Say if you drive 240 miles at a unit rate of 60 miles per hour, how many hours would it take to drive 240 miles? explain what yo
vichka [17]
4 hours. You divide 240 by 60 because you travel 240 total miles and you 60 mph and you will get 4 and it will be 4 hours
3 0
2 years ago
Other questions:
  • A study was designed to investigate the effects of two​ variables, (1) A​ student's level of mathematical anxiety and​ (2) teach
    13·1 answer
  • How do i do this problem?
    9·1 answer
  • What does 24 fluid ounces equal
    5·2 answers
  • A parallelogram with an area of 60 square units is formed by four lines in a coordinate plane. The parallelogram has one vertex
    8·1 answer
  • Which equation could be true ?
    15·1 answer
  • What is the expanded form of this number?<br><br> 18.029
    10·1 answer
  • PLSSSS HELP<br><br> Find the intersection of the circle x^2+ y^2 = 29 and y = x - 3 algebraically,
    14·1 answer
  • How do you find the slope and the y-intercept? its very confusing ​
    13·1 answer
  • Solve the right triangle.<br> Round your answers to the nearest tenth.
    8·1 answer
  • Which of the following is the best estimate of the circumference of a circle that has a diameter of 7 feet? 42 ft 21 ft 14 ft 11
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!