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
Artyom0805 [142]
3 years ago
15

The course for a boat race starts at point A and proceeds in the direction of S52'E for 1 hour at 8 knots to point B and then in

the direction S50°W for 1 hour at 4.5 knots to point C and finally back to A. Find the total distance of the race and find the compass bearing from point A to point to the nearest whole degree.

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
8 0

Answer:

20.823 nautical miles

S20°E

Step-by-step explanation:

I assume you mean ° (degrees), not ' (minutes).  There are 60 minutes in 1 degree.

S52°E means "south, 52° east", or 52° east of south.

S50°W means "south, 50° west", or 50° west of south.

1 knots = 1 nautical mile / hour, so the boat first travels 8 nautical miles from A to B, then 4.5 nautical miles from B to C, then finally back to A.

If we say A is at the origin, then the coordinates of B are:

(8 sin 52°, -8 cos 52°)

And the coordinates of C are:

(8 sin 52° − 4.5 sin 50°, -8 cos 52° − 4.5 cos 50°)

(2.857, -7.818)

So the distance from A to C is:

x = √(2.857² + (-7.818)²)

x ≈ 8.323

And the total distance of the race is:

d = 8 + 4.5 + 8.323

d = 20.823

The compass bearing from A to C is:

θ = atan(2.857 / 7.818)

θ ≈ S20°E

You might be interested in
What is the mean (average) of these five numbers?
IRINA_888 [86]

Answer:

C. 5

Step-by-step explanation:

Mean: Numbers over amount of numbers

(2 + 4 + 5 + 6 + 8)/5

25/5

5

4 0
2 years ago
find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0​
Citrus2011 [14]

Answer:

Radius: r =\frac{\sqrt {21}}{6}

Center = (-\frac{3}{2}, -\frac{2}{3})

Step-by-step explanation:

Given

9x^2 + 9y^2 + 27x + 12y + 19 = 0

Solving (a): The radius of the circle

First, we express the equation as:

(x - h)^2 + (y - k)^2 = r^2

Where

r = radius

(h,k) =center

So, we have:

9x^2 + 9y^2 + 27x + 12y + 19 = 0

Divide through by 9

x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0

Rewrite as:

x^2  + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}

Group the expression into 2

[x^2  + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}

[x^2  + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}

Next, we complete the square on each group.

For [x^2  + 3x]

1: Divide the coefficient\ of\ x\ by\ 2

2: Take the square\ of\ the\ division

3: Add this square\ to\ both\ sides\ of\ the\ equation.

So, we have:

[x^2  + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}

[x^2  + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2

Factorize

[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2

Apply the same to y

[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2

[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2

[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}

Add the fractions

[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}

[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}

[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}

[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}

Recall that:

(x - h)^2 + (y - k)^2 = r^2

By comparison:

r^2 =\frac{7}{12}

Take square roots of both sides

r =\sqrt{\frac{7}{12}}

Split

r =\frac{\sqrt 7}{\sqrt 12}

Rationalize

r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}

r =\frac{\sqrt {84}}{12}

r =\frac{\sqrt {4*21}}{12}

r =\frac{2\sqrt {21}}{12}

r =\frac{\sqrt {21}}{6}

Solving (b): The center

Recall that:

(x - h)^2 + (y - k)^2 = r^2

Where

r = radius

(h,k) =center

From:

[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}

-h = \frac{3}{2} and -k = \frac{2}{3}

Solve for h and k

h = -\frac{3}{2} and k = -\frac{2}{3}

Hence, the center is:

Center = (-\frac{3}{2}, -\frac{2}{3})

6 0
2 years ago
Someone help me asap math 10
Ghella [55]

Answer:

x ≈ 25.4 Km

Step-by-step explanation:

Using the tangent ratio in the right triangle on the right

tan54° = \frac{opposite}{adjacent} = \frac{opp}{17} ( multiply both sides by 17 )

17 × tan54° = opp , thus

opp ≈ 23.4

-------------------------------------------

Using the cosine ratio in the right triangle on the left

cos23° = \frac{adjacent}{hypotenuse} = \frac{23.4}{x} ( multiply both sides by x )

x × cos23° = 23.4 ( divide both sides by cos23° )

x = \frac{23.4}{cos23} ≈ 25. 4 Km ( to the nearest tenth )

6 0
3 years ago
When solved for x, which inequality represents the number line?
ikadub [295]

Answer:

x<-3

The value of x is found in all the numbers that are less than - 3 or all the numbers from - 3 to negative infinity

Please note: - 3 is not included in those numbers

4 0
2 years ago
What is the area of rectangle ABCD?
lina2011 [118]
Multiply the length by the width and your answer will be there.
8 0
2 years ago
Read 2 more answers
Other questions:
  • Beth runs a catering business and needs 64 pints of water every day. She gets water in 2-gallon jugs. So, she gets jugs of water
    8·1 answer
  • A school day starts at 07:15. There are three periods of 40 minutes, four periods of 35 minutes and two periods of 50 minutes. T
    11·1 answer
  • In a lab, scientists are growing a culture of bacteria. It is known that the
    12·1 answer
  • Find the output, k, when the input, t, is -7−7minus, 7.<br> k = 10t-19k=10t−19
    7·1 answer
  • A cell phone company charges $120 for the phone, and then $35 a month for phone service. Another cell phone company charges $55
    13·1 answer
  • Non example of a ratio tables
    15·1 answer
  • Leila writes 6 pages per day starting on Sunday. She wants to know how many pages she will write by the end of the day on Saturd
    11·1 answer
  • 70. Dominic buys a new suit that is on sale for 20% off
    15·1 answer
  • What two numbers multiply to 6 but add up to -1?
    5·2 answers
  • Help people please i have like 3 minutes left
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!