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
WINSTONCH [101]
3 years ago
9

Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa

rd Edmonds at 9 mph. Edmonds is 6 miles due east of Kingston. After 20 minutes, the ferry turns, heading due south. Ballard is 8 miles south and 1 mile west of Edmonds. Impose coordinates with Ballard as the origin. (Let one unit equal one mile.) (a) Find the equations for the lines along which the ferry is moving. eastward ? southward x=−2 Correct: Your answer is correct. (b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat. Looking down from above, as in the picture, the radar region looks like a circular disc. The boundary is the "edge" or circle around this disc, the interior is the inside of the disc, and the exterior is everything outside of the disc (i.e., outside of the circle). Give a mathematical description of the boundary, interior, and exterior of the radar zone. (Express your answers as equations and/or inequalities using the variables x and y.) boundary 9=(x−(−2))2+(y−10)2 Correct: Your answer is correct. interior ? exterior ? (c) When does the ferry enter the radar zone? (Round your answer to one decimal place.) (d) Where does the ferry exit the radar zone? (Round your answers to one decimal place as needed.) (x, y) = −2,7 Correct: Your answer is correct. When does the ferry exit the radar zone? (Round your answer to one decimal place.) (e) How long does the ferry spend inside the radar zone? (Round your answer to one decimal place.)
Mathematics
1 answer:
sergij07 [2.7K]3 years ago
8 0

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

You might be interested in
Is the answer a gauze?
Zinaida [17]
I think so.. If not i am super sorry!!
8 0
3 years ago
Three friends are dividing the cost of a kite equally the Kite
Tomtit [17]
Each person will pay $5.25.
7 0
3 years ago
Read 2 more answers
What is the output of the function f(x) = x + 21 if the input is 4? When the input is 4, the output of f(x) = x + 21 is
notka56 [123]
To find the output when you know the input, just plug the input into the function.

x+21=4+21=25

The output is 25.

Hope this helps!
8 0
3 years ago
Read 2 more answers
$75, $97, $360, $84, $119, $100 Find the median<br> a. 45<br> b. 98.5<br> C. 97<br> d. 100
mafiozo [28]

Answer:

C.97

Step-by-step explanation:

5 0
3 years ago
R2+2r-33=0 solve by completing the square
-BARSIC- [3]
R^2+2r-33=0  move constant to other side by adding 33 to both sides

r^2+2r=33   halve the linear coefficient, square it and add to both sides, in this case it is just one

r^2+2r+1=34  now the left side is a perfect square...

(r+1)^2=34  take the square root of both sides...

r+1=34^(1/2)  subtract 1 from both sides

r=-1+34^(1/2) and -1-34^(1/2)
8 0
3 years ago
Other questions:
  • Which relationship describes angles 1 and 2?
    7·1 answer
  • Lolo type 1125 words in 15 minutes. w represent the number of words typed each minute. if lolo type the same number of words eac
    7·1 answer
  • Kyle incorrectly says that the product of - ( - 6 ) # ( - 1 ) is 6 . 11. After a recycling awareness program, the number of tons
    8·1 answer
  • A bus can hold 56 children. If 140 children from St. Mary’s
    14·2 answers
  • Please help brainliest if correct
    12·2 answers
  • Which of the following statements about UK and UL is true?
    5·1 answer
  • Each year, the number of students taught by Mr. Wright increases by 2. The first year, he taught 18 students. The total number o
    12·2 answers
  • A rectangular field is 1/3 as wide as it is long and is enclosed by x yards of fencing. What is the area of the field in terms o
    11·1 answer
  • The diagram shows two campsites on opposite ends of a lake and two triangles formed by intersecting segments from the campsites.
    8·1 answer
  • Suppose that the times it takes adult women to run a mile are normally distributed with an unknown mean and standard deviation.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!