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
How many pennies are on the nth square? 2n 2n â€"" 1 2n 1 2n â€"" 1 2n 1.
The number of pennies is an illustration of pattern and sequence.
The number of pennies in the nth square is [tex]2^{n-1[/tex]
From the complete question, we have the following parameters
[tex]f(1) =1[/tex]
[tex]f(2) =2[/tex]
[tex]f(3) =4[/tex]
[tex]f(4) =8[/tex]
Rewrite the functions as follows:
[tex]f(1) = 2^0[/tex]
[tex]f(2) = 2^1[/tex]
[tex]f(3) = 2^2[/tex]
[tex]f(4) = 2^3[/tex]
Express 3 as 4 - 1
[tex]f(4) = 2^{4-1[/tex]
Replace 4 with n
[tex]f(n) = 2^{n-1[/tex]
Hence, the number of pennies in the nth square is [tex]2^{n-1[/tex]
Read more about pattern and sequence at:
https://brainly.com/question/24655254
If F(x) = x - 7 and G(x) = x^3, what is G(F(x))?
=
A. x^3+ x - 7
B. X^3-7
C. (x-7)^3
D. x^3(x - 7)
Answer:
C
Step-by-step explanation:
Evaluate P(3, 3)
A. 1
B. 9
C. 6
Answer:
6
Step-by-Step explanation:
P (n,k) where n=k is equal to n!
So, P (3,3) = 3! = 6
Generally, P (n,k) = n!/(n-k)!
how many cases does he hear per hour?
Answer:
13
Step-by-step explanation:
5 x 2 2/3
= 5 x 8/3 = 40/3 =13 1/3
So it's basically 13 1/3, but its 13.
What is the slope of the line that passes through the points (-5, -5 ?(−5,5)?
Answer:
undefined
Step-by-step explanation:
I'm assuming the points are (-5,-5) and (-5,5)
The formula to do slope is: (y2-y1)/x2-x1)
2 points: (x1, y1) (x2, y2)
So then:
(5-(-5))/(-5-(-5))=10/0
This shows that the line is vertical, which means that slope is undefined.
Answer:5/65/6
The slope of the line passing through the point (5,5) is 5/6.
Step-by-step explanation:
can yallll help pls . ………
Step-by-step explanation:
so, what is the problem with the first one ?
you only need to put the specified values into the places of the variables and then simply calculate :
2×-5 + 8×6 = -10 + 48 = 38
that is how expressions, equations and functions work.
for the second, I am counting only the squares with their clear "majority" inside the line. any small parts of squares I ignore.
so,
first row : 3
second row : 5
third row : 5
fourth row : 6
fifth row : 7
sixth row : 7
seventh row : 4
eighth row : 2
total : 39
What is the full length of the segment?
Answer:
2
Step-by-step explanation:
if the angle of the two triangles are the same,
6 is 2/3 of nine
Therefore,
2/3x3=2
What is 1 4/5 times 2 1/3
Answer:
4.2
Step-by-step explanation:
4 1/2
Explanation:1 4/5 = 9/5
2 1/3 = 7/3
---------------------------
9/5 · 7/3 = 21/5 OR 4 1/2
Please find the surface area of the pyramid... I will mark you brainliest
Answer:
S.A. = 704 in²
Step-by-step explanation:
Surface area (S.A. ) = 1/2 lp + B where l is the slant height , p is the perimeter of the base, and B is the area of the base .
Given l = 14; The Base figure is a square so the p = 4· side = 4 · 16 = 64 and the area of the Base = s² = 256
S.A = 1/2 · 14 · 64 + 256
S.A. = 448 + 256
S.A. = 704 in²
HELP PLZZ! DUE IN 15 MIN!! plz explain your answer to
Therefore, the chance of getting a 5 or 6 in the next turn is about 40%.
Hoped this helped
[tex]BrainiacUser1357[/tex]
Two shops, Waitroze and Budgins sell the same brand of cans of soup but with different offers.
Calculate the price for 24 tins at each shop.
Waitroze = 8 for £3.35
Budgins = 6 for £2.89
Answer:
24 cans at Waitrose would be £10.05.
24 cans at Budgins would be £11.56.
Step-by-step explanation:
Times the waitrose offer by 3
Times the budgins offer by 4
Hope that helped. x
What is the probability for a bowler to score over 136? The mean for the set is 130, and the standard deviation is 3. So I know that it is Mean + 2(Standard Deviation), so is it 2.35% or 2.5%?
Answer:
135%
Step-by-step explanation:
Can someone help me with this please
Answer:
C) The difference between the 75th and 25th percentiles is 12 inches.
Step-by-step explanation:
The interquartile range is the length of the "box" in a "box and whisker" plot. One end is the 25th percentile, and the other end is the 75th percentile. It is the difference between the maximum and minimum of the middle 50% of the data.
For the baker's loaf-length data set, the interquartile range being 12 inches means the loaves in the 75th percentile are 12 inches longer than the loaves in the 25th percentile. This could be described by choice C.
The square root of a certain number is 9.5671 . The certain number is between which 2 integers?
Answer:
91 & 92
Step-by-step explanation:
Answer:
9.5671*9.5671=91.52940241
between 91 and 92
Hope This Helps!!!
The standard configuration for a Colorado license plate is 3 letters followed by 3 digits. How many different license plates are possible if letters and digits can be repeated?
Answer:
17,576,000 different combinations possible.
Step-by-step explanation:
Please Help Quickly I Need Help ASAP
Answer:
the first question is 2,0 and the second answer is 2,5
Step-by-step explanation:
The Wilson family invited 100 relatives to their Christmas party. 90 guests had Dutch heritage, 80 had German heritage and 75 had English heritage. What is the minimum number of people who claimed ancestry from all three heritages? What is the formula i use to find out the answer of the question? and how do i find out the answer?
Answer:
Out off 100
Step-by-step explanation:
10 don't have dutch heritage.
20 don't have German heritage.
25 don't have English heritage.
100 - 55
At minimum, 45 people have all three heritages.
6- 1/3 = decimal maths
Answer:
To get 6 1/3 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction. Here are the detailed math steps we use to convert 6 1/3 mixed number to decimal form: Step 1:Multiply the whole number by the denominator: 6 × 3 = 18
Step-by-step explanation:
The value of the expression 6 - 1/3 will be 17 / 3.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The numbers are given below.
6 and 1/3
Then the difference between the numbers 6 and 1/3 will be given by putting a minus sign between them. Then we have
⇒ 6 - 1/3
⇒ (18 - 1) / 3
⇒ 17 / 3
The value of the expression 6 - 1/3 will be 17 / 3.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
How many screeches are equal to 20 meows? 20 meows = 12 laughs 3 laughs = 2 purrs 40 purrs = 120 screeches Explain how you got there.
Answer:
24 screeches = 20 meows.
Step-by-step explanation:
Calculate purrs:
12/3 = 4
4*2= 8
Use purrs to calculate screeches:
Set up a proportion: [tex]\frac{8}{x} = \frac{40}{120}[/tex]Solve proportion by cross-multiplying8*120 = 960960/40 = 24 screechesHow to derive Universal Law of Gravitation ?
Answer:
These are the answers
Step-by-step explanation:
The orbit of a planet is an ellipse, with the Sun at one of the two foci.
A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
Hope it helped !
Answer:
The universal law of gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the ...
Bernoulli formula: define focal length
Si unit of thrust: newton's third law of motion examples
A. Joshua puts $8,765 in a
10-year 5.28% savings
certificate in which interest is
compounded quarterly. How
much total interest has he
earned at the end of the ...
a) second year?
b) fourth year?
c) seventh year?
d) tenth year?
The amount at the end of the second year is $9,734.49.
The amount at the end of the fourth year is $10,811.22.
The amount at the end of the seventh year is $12,653.68.
The amount at the end of the tenth year is $14,810.14.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $8765
r = 5.28%
n = 4 (quarterly)
Amount after 2 years.
A = 8765 [tex](1 + 0.0131)^2[/tex]
A = $9,734.49
Amount after 4 years.
A = 8765 [tex](1 + 0.0131)^4[/tex]
A = $10,811.22
Amount after 7 years.
A = 8765 [tex](1 + 0.0131)^7[/tex]
A = $12,653.68
Amount after 10 years.
A = 8765 [tex](1 + 0.0131)^{10}[/tex]
A = $14,810.14
Thus,
The amount at the end of the second, fourth, seventh, and tenth year is given above.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ2
Describe how total job benefits and total employee compensation differ
Answer:
in my opinion they do not.
Step-by-step explanation:
Answer: Total compensation is everything the company provides an employee in exchange for working. It includes base salary, bonuses, benefits, perks and on-site amenities.Total compensation indicates that an employee is making two or three times his base salary.
Andrew is painting a wall on the side of his house. He has a 20 foot ladder wich makes a 79 degree angle with the ground. Standing on the second to past rung of the ladder, Andrew can reach 5 feet above the point where the ladder rests against the wall. How high up the wall can Andrew paint
Andrew can reach a maximum of [tex]24.6ft[/tex] high up the wall.
The right-angled triangle formed can be solved using the [tex]sine[/tex] ratio. that is
[tex]sin(72^\circ})=\dfrac{h}{20}[/tex]
where [tex]h[/tex] is the distance from the foot of the wall to the tip of the ladder where it rests on the wall. Substituting, and solving for [tex]h[/tex], we get
[tex]0.9816=\dfrac{h}{20}\\\\h=20\times0.9816\\\\h=19.632ft[/tex]
Since Andrew can reach an extra [tex]5ft[/tex] above the point where the ladder rests against the wall, the maximum height Andrew can paint is
[tex](19.632+5)ft=24.632ft\\\\\approx24.6ft[/tex]
Another solved word problem on trigonometry can be found here: https://brainly.com/question/12146092
Write an equation for a line that passes through (2,5)
and (6, 7).
Answer:
y=2x-9
Step-by-step explanation:
Use the table from a random survey about the preferred service for streaming movies. Out of 750 people, how many would you expect to prefer Company B?
Answer:
The correct answer option is 192
Step-by-step explanation:
We are given the results of a random survey about the preferred service for streaming movies.
We are to find the number of people we would expect to prefer Company B.
Number of people using service B = 32
Total number of people = 125
Number of people expected to prefer Company B =32/125 x 750 = 192
What is the equation please
Answer:
y = -2/5x - 2
Step-by-step explanation:
Answer:
y = 2/5x -2 or y = 0.4x -2
Explanation:
Step 1: Calculating Slope (m).
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{0-(-2)}{5-0}[/tex]
m = [tex]\frac{2}{5}[/tex]
m = 0.4
Now putting value of m in equation (i)
y = 0.4x + b -----(ii)
Step 2: Calculating Y-intercept (b).
Lets choose the first point, (0,-2) for calculating y-intercept:
y = mx + b
-2 = 0.4(0) + b
-2 = 0 + b
-2 = b
b = -2
Now put the value of b in equation (ii)
y = 0.4x + -2
Find the square of (a+b+c)
Answer:
a^2 + b^2 + c^2 +2ab + 2ac + 2bc
A)14.3
B)11
C)7.4
Plz help
Answer:
c
Step-by-step explanation:
Write the following expression as a sum and/or difference of logarithms. Express powers as factors.
log_b (u^9v^4) u>0, v> 0
Answer:
9log_b(u)+4log_b(v)
should be like that. let me know if iam wrong
A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as long
the banner and the poster have perimeters 24 inches. What are the lengths and of widths of the poster and the banner?
Rectangular Poster:
Length = 9
Width = 3
Rectangular Banner:
Length = 10
Width = 2
Hope this is helpful!