The value of the angle subtended by the distance of the buoy from the
port is given by sine and cosine rule.
The bearing of the buoy from the is approximately 307.35°Reasons:
Location from which the ship sails = Port
The speed of the ship = 10 mph
Direction of the ship = N35°W
Location of the warning buoy = 5 miles north of the port
Required: The bearing of the warning buoy from the ship after 7.5 hours.
Solution:
The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
Where;
a = The distance between the ship and the buoy
b = The distance between the ship and the port = 75 miles
c = The distance between the buoy and the port = 5 miles
Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°
Which gives;
a = √(75² + 5² - 2 × 75 × 5 × cos(35°))
By sine rule, we have;
[tex]\displaystyle \frac{a}{sin(A)} = \mathbf{ \frac{b}{sin(B)}}[/tex]
Therefore;
[tex]\displaystyle sin(B)= \frac{b \cdot sin(A)}{a}[/tex]
Which gives;
[tex]\displaystyle sin(B) = \mathbf{\frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }}[/tex]
[tex]\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx 37.32^{\circ}[/tex]
Similarly, we can get;
[tex]\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx \mathbf{ 142.68^{\circ}}[/tex]
The angle subtended by the distance of the buoy from the port, C is therefore;
C ≈ 180° - 142.68° - 35° ≈ 2.32°
By alternate interior angles, we have;
The bearing of the warning buoy as seen from the ship is therefore;
Bearing of buoy ≈ 270° + 35° + 2.32° ≈ 307.35°
Learn more about bearing in mathematics here:
https://brainly.com/question/23427938
A local volunteer group has 150 raffle tickets to sell. They sell them in packs of three tickets per customer. Determine which graph and which equation represent the number of tickets, T, the group has left after selling tickets to c customers.
The equation that represents the number of tickets T, the group has left after selling tickets to c customers is:
T = 150 - 3c
The graph representing the equation is plotted below
The total number of tickets that the volunteer group has = 150
They sell the tickets in packs of three tickets per customer
The number of customers is c
Number of tickets sold to c customers = 3c
The number of tickets left after selling tickets to c customers is:
T = 150 - 3c
Learn more here: https://brainly.com/question/25912293
Answer:
I HAVE COME TO SAVE THE DAY!
ok the equation is t= -3c + 150
the graph is the one that is the same as the equation the y intercept is 150 the slope is -3 over 1 (up three over one) on y test the answers were the top right for both boxes but it might be different for you
it takes a swimmer 72.54 seconds to swim the 100 meter length of the pool going west what was his velocity.
(MUST show work and formula)
Step-by-step explanation:
Solution
(s) = 100m
(t) = 72.54s
(v) = ??
We have,
v = s÷t
v = 100 ÷ 72.54
v = 1.37 m/s
Hence, the velocity of the swimmer is 1.37 m/s
[this is how I personally have to do it but not sure about you]
High school Geometry
Answer:
the answer is b. sss is not possible
how much is 3 liters in 50 bottles
Answer : 0.06 liters per bottle
Step - by - step explanation :
3 liters divided by 50 bottles = 0.06 liters per bottle
[ Sorry if this wasn't what you meant when you asked the question ]
Happy holidays ! :3
can someone tell me if i did this right lol
Answer:
Your calculation is correct, but I'd answer 33.0 in.
Step-by-step explanation:
You are correct. Good job.
Answer:
I'm 96% sure its right, and those are pretty good odds ^^
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST THANKS
Answer:
the third answer, y= (1/3) x
Answer:y=(1/3)x
Step-by-step explanation:
the functions below show the amount of money bella and sweet t had saved after earning money for doing chores
Answer:
Hello your answer should be: Bella saved more per chore than Sweet T.
Step-by-step explanation:
Hope this helped! :)
Have a great rest of your day!
What is 7(x-3) Equal to
Answer:
7x-21
---------------------
Write (5/3)³ as a quotient of powers.
Answer:
The number (5/3)³ written as a quotient of powers is; 5³/3³
According to the question;
We are required to determine write the number, (5/3)³ as a quotient of powers
The number (5/3)³ can be evaluated as;
= 125/27
= 5³/3³
Step-by-step explanation:
Plz help. Find the value of each variable. 1. 95° 120° 4120° 125° x + 840° .
Answer:
Step-by-step explanation:
Solve the expression then name the polynomial
If f(x) = 2x – 3 and g(x) = 3x2
– 2x + 6 then what is (f + g)(x)?
How many terms are in the expression 3xy+2x+1
Answer:
4
Step-by-step explanation:
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X
ASAP HELP PLEASE SHOW ALL WORK AND PLEASE NO LINKS
Answer:
the triangle always equals 180.
so divide it right?
Refer to the attachment
What property was used in step 1 to arrive at step 2?
Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.
Answer:
Distributive Property
Step-by-step explanation:
5(x - 7) = 55 ⇒ 5x - 35 = 55
The 5 was distributed in 5(x-7) to get 5x - 35.
Can you plsssssssssssssssssssssssssssss help me with this.
Answer: (-1, 7) should be the answer
Step-by-step explanation:
why did you copy my profile picture hello......
Square of the difference of two terms
Answer:
123-23=100
100^2=100*100=10^4=10000
Identify the slope represented in the graph below.
Use the information given to answer the question. An office supply store has 1,508cases of paper and
736
boxes of pens. Each case of paper contains
24
packs of paper, and each box of pens contains
50 pens.
Part A
How many packs of paper does the office supply store have?
36,192 packs of paper
36 , 192 packs of paper
36,432 packs of paper
36 , 432 packs of paper
37,700 packs of paper
37 , 700 packs of paper
37,750 packs of paper
2+2+9+9+9+9+7+7+6-8-6+7+8+9+8+9+0+9+8+9
Answer:
The answer is 113.
Answer:
141
Step-by-step explanation:
There are 8 nines: 9×8=72
There are 3 sevens: 7×3=21
There are 4 eights: 8×4=32
6×2=12
2×2=4
All together you get
Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers.
Answer:
y = - 3x + 7
Step-by-step explanation:
( 2 , 1 )
( 5 , - 8 )
m = ( - 8 - 1 ) / ( 5 - 2 ) = - 3
y - 1 = - 3 ( x - 2 )
y = - 3x + 7
HELP ASAP!!!!hgghfuygkjb,
Answer:
120$
Step-by-step explanation:
Find the value of x?
Answer:
145°
Step-by-step explanation:
See the attachment. Angles A, B, and C all belong to the triangle.
We know that A + B + C = 180° since the angles of a triangle always add to 180°. We also know that when two lines meet that their sum is also equal to 180°. So we can write for each interior angle the following:
Result
<A = (180 - 88) 72
<B = (180-x) 180-x
<C = (180 - 127) 53
The sum of angles A, B, and C is equal to 180:
72 + (180-x) + 53 = 180
x = 145if x and x/4 are a pair of supplementary angles find angles
[tex]\text{Supplementary angles adds up to 180 degree.}\\\text{Given that the angles are x and x/4. As they are supplementary}\\\text{ they add up to 180 degrees}\\\\\\ x+\dfrac{x}{4}=180\\\\\\\dfrac{4x+x}{4}=180\\\\\\5x=720\\\\\\x=\dfrac{720}{5}\\\\\\\boxed{x=144}[/tex]
The logarithmic expression [tex]log_{b}(\frac{1}{b^{-b}} )[/tex] where b > 0, is equal to
a) [tex]b^{-b}[/tex]
b) [tex]b^{b}[/tex]
c) [tex]-b[/tex]
d) [tex]b[/tex]
[tex]\log_b \left(\dfrac 1{b^{-b}}\right)\\\\=\log_b (b^{-b})^{-1}\\\\=\log_b b^b\\\\=b \log_b b\\\\=b \cdot 1\\\\=b[/tex]
The least common multiple of two whole numbers is 28 the ratio of the greater number to the lesser number is 7:2 what are the two numbers
Answer:
14, 4
Step-by-step explanation:
First things first, we can name out pairs with the ratio of 7:2.
7, 2
14, 4
21, 6
We can then test these pairs out with the first condition and find the answer.
The least common multiple has to be 28:
LCM(7, 2) = 14
LCM(14, 4) = 28
Ah, ha! We can see that the least common multiple of 14 and 4 is 28.
What is an equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1)
y= 3x + 1
y=x-3
y=2x+5
y= 2x – 5
5y+12>62 solve for y
Answer:
y>10
Step-by-step explanation:
5y+12>62
Subtract 12 on both sides
5y > 50
Divide 5 on both sides
y > 10
Answer:
y>10
Step-by-step explanation:
First, let's subtract 12 from both sides:
5y+12-12>62-12
Then let's simplify:
5y>50
Now let's divide both sides by 5:
5y/5>50/5
And then simplify to get our answer y>10
Hope this helped
Solve the inequality.
D
— < -4
-5
Write the fraction 35/42 simplest form
Answer:
5/6
Step-by-step explanation:
For every 20 emails that Greg sent in a month, he received 50 emails. What is the ratio in simplest form of the number of emails sent to the number of emails received by Greg that month?
A. 5:2
B. 3:5
C. 2:5
D. 5:3
Answer:
C. 2:5
Step-by-step explanation:
You can divide both side of the ratio 20:50 by 5 which leaves you with 4:10. You can simplify it again by dividing it by 2 and get 2:5