Answer:
It is a fraction -5/9
Step-by-step explanation:
A ship leaves port at 10 miles per hour, with a heading of N 35° W. There is a warning buoy located 5 miles directly north of the port. What is the bearing of the warning buoy as seen from the ship after 7.5 hours?
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:
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simplify the quotient. Write the answer in sn.
Answer:
2.4*10^4
Step-by-step explanation:
write in scientific notation
first i would simplify the 3.6/1.5
=2.4
then you get (2.4*10^7)/10^3
formula: (m^x)/(m^y)= m^(x-y)
(2.4*10^7)/10^3
=2.4*10^(7-3)/1
=2.4*10^4
The coach for a basketball team wants to buy new shoes for her 12 players.
Super Sports is offering a 20\% discount on each pair of shoes, which were originally priced $72.50. A 6.5\% sales tax will be applied to the discounted price.
The same shoes are also available on Double Dribble's web site for $54.75. A 9\% processing fee will be applied to the cost of the shoes, plus a shipping fee of $5.99 for each pair.
What is the difference in the total costs of the 12 pairs of shoes between the two stores?
(please show ur work)
Answer:
$46.8
Step-by-step explanation:
Price for Super Sports:
$72.5*0.8=$58 (20% discount so price is 80% of original price)
$58+$58*0.065=$61.77 (6.5% sales tax added after discounted price)
$61.77*12=$741.24
Price for Double Dribble:
$54.75+$54.75*0.09=$59.6775≈$59.68 (9% processing fee added to cost; round to 2 decimal places)
$59.68+$5.99=$65.67 (shipping fee)
$65.67*12=$788.04
Difference in price:
$788.04-$741.24=$46.8
If you have questions please ask in the comments; also please give this answer brainliest if you found it useful!
Please solve this question
Answer:
K so we want to find angle EFC
Its a much longer process
AC is a line, so its 180 degrees
ED is 32 (This also makes AB 32 degrees)
Now we need DC
Find the other side angle length
180 - 32 - 87 = 61
theta is 61+32
Please help! With steps included :)
Answer:
Top question: -7°
Bottom question : 18°
Step-by-step explanation:
Top question:
The base angles of am isosceles triangle are congruent:
x + 46 = 39 because the base angles of an isosceles triangle are congruent
x + 46° = 39°
x = -7°
Bottom question
The missing angle is 3x because the base angles are congruent
To find the value of x, we must add all the angles inside the triangle, and find the value of x that makes it equal to 180°
3x + 3x + 4x = 180°
10x = 180°
x = 18°
Sorry for the late post!
-Chetan K
PT.2 OF MY HW IT IS UNIT RATE PLEASE HELP!
Answer:
Car 1
Step-by-step explanation:
Answer: Car 1
Step-by-step explanation:
Notice that the speed of each car is the slope of the line that represents its average speed.
Since the graph of the speed of Car 1 passes through (0,0) and (4,256), we get that its slope is:
256/4 = 64
Therefore the average speed of Car 1 is 64 mi/h.
Now, since the equation that represents the average speed of Car 2 is in slope-intercept form, we get that its slope is 55.
Therefore the average speed of Car 2 is 55 mi/h.
Answer: Car 1.
Anya purchased $124.35 worth of home improvement items at the hardware store. If the sales tax rate in her city is 6.75%, what is the total cost of her purchase?
Answer:
$132.74
Step-by-step explanation:
6.75% = 0.0675
Multiply 124.35 by 1.0675 because sales tax is added to original cost.
(124.35)(1.0675) = 132.74
The total cost of Anya's purchase of home improvement hardware is 132.74 dollars.
What is percentage?The percentage is the value per hundredth.
According to the given question, the sales tax is 6.75% which is not included in the home improvement hardware which cost Anya 124.35 dollars.
∴ The total cost of Anya's purchase including the sales tax is ( 100 + 6.75)% = 106.75% of 124.35 dollars which is,
= (106.75/100)×124.35 dollars.
= 1.0675×124.35 dollars.
= 132.74 dollars.
learn more about percentage here :
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Anyone please solve and explain part b
Answer:
f(2) = -6
f inverse of 1/2 is 17/2
Step-by-step explanation:
We are given a function [tex]\displaystyle \large{f(x) = \frac{6}{2x-5}}[/tex]
To solve for part (a), we have to substitute x = 2 in f(x).
[tex]\displaystyle \large{f(2)=\frac{6}{2(2)-5} \\\displaystyle \large{f(2)=\frac{6}{4-5}=\frac{6}{-1}=-6[/tex]
Therefore, f(2) is -6.
Now we solve for part (b), we see the notation which is a minor different similar to f(x). We see that there is exponent of -1 between f and 1/2. The part (b) indicates that the function is an inverse of f(x).
[tex]\displaystyle \large{y=f^{-1}(x) \longrightarrow x=f(y)}[/tex]
To solve for part (b), first we solve for x in the function. Let f(x) = y.
[tex]\displaystyle \large{y=\frac{6}{2x-5}}[/tex]
Multiply both sides by 2x-5.
[tex]\displaystyle \large{y(2x-5)=\frac{6}{2x-5}(2x-5)}\\\displaystyle \large{y(2x-5)=6}[/tex]
Divide both sides by y-term.
[tex]\displaystyle \large{\frac{y(2x-5)}{y}=\frac{6}{y}}\\\displaystyle \large{2x-5=\frac{6}{y}}\\\displaystyle \large{2x=\frac{6}{y}+5}\\\displaystyle \large{x=\frac{6}{2y}+\frac{5}{2}}\\\displaystyle \large{x=\frac{3}{y}+\frac{5}{2}}[/tex]
Then swap x and y which we receive [tex]\displaystyle \large{y=\frac{3}{x}+\frac{5}{2}}[/tex]
Therefore, [tex]\displaystyle \large{f(x)=\frac{6}{2x-5} \longrightarrow f^{-1}(x)=\frac{3}{x}+\frac{5}{2}}[/tex]
Thus, [tex]\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{3}{\frac{1}{2}}+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=6+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{17}{2}}[/tex]
____________________
Let me know if you have any questions in comment.
Easy peace math problem
Answer:
225/10=441/l
cross multiply
225l=10*441
225l=4410
l=4410/225
l=19.6 liters of gas
Step-by-step explanation:
l=19.6 liters of gas
What is the percent of change from 46 to 69?
Answer:
percent of change =0.5
Step-by-step explanation:
x1=46 x2=69
(x2-x1) / x1
69-46 = 23 / 46 = 0.5
can someone please help me with this, thank you (picture attached)
Answer:
I can help you with it
Step-by-step explanation:
2. Sol went to the store to buy tomatoes. They were $1.89 per pound: Last week, the
price per pound was 30% lower. What was the price of tomatoes last week?
Answer:
1.323
Step-by-step explanation:
We can find 30% of 1.89 by multiplying: 1.89 x 0.3 = 0.567
Then, we must subtract: 1.89 - 0.567 = 1.323
M<2= x+49 (geometry)
Find the slope of the line (-3,-2),(1,-2)
Answer:
0
Step-by-step explanation:
The y-axis is the same so the slope has to be zero, since the line is not going vetrically anytime on the graph
A small van holds 8 students and a large van holds 12 students. There are a total of 48 students who plan to go on the field trip.
Look at triangle ABC. Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 2, and C at ordered pair 4, 2. What is the length of side AB of the triangle? (1 point) a 3 b 5 c Square root of 6 d Square root of 13
The length of side AB from the given coordinate grid is; √20
How to find the length of the side of a triangle?The formula for distance between two coordinates is;
d = √((y2 - y1)² + (x2 - x1)²)
From the graph attached in the given brainly link, we have;
A(4, 5) and B(2, 1)
Thus;
AB = √((1 - 5)² + (2 - 4)²)
AB = √(16 + 4)
AB = √20
In conclusion, the length of side AB is √20
Read more about Triangle side length at; https://brainly.com/question/3673178
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If correct Brainlyest
Answer:
c is the answer
Step-by-step explanation:
simplified on left-hand side is 2<5 and it is the same as -2<5
hope this helped :)
PLEASE ANSWER ASAP!! WORTH 20 POINTS
A cab company charges a $4 boarding rate in addition to its meter which is $1.50 for every mile. Write a linear equation which models this. Use the equation to determine the total fare for a trip that is 2 miles, 3 miles and 5 miles.
Answer:
y = 1.50x+4
if x = 2
y = 7
if x = 3
y = 8.5
if x = 5
y = 11.5
Step-by-step explanation:
every mile(x) add 1.50 dollars to 4 dollars
Describe how modern entertainment has begun to reflect the changing makeup of families in America.
It should be noted that modern entertainment has played a vital role in shaping African culture and homes.
Through modern entertainment, Africans views on marriages have changed. Most African men now marry one wife which was quite different in the olden days when it was believed that an increase in the number of wives one had was used to show superiority.
Also, entertainment has been impactful in the issue of child-bearing. Women now give birth to lesser children at an average of 3 per home.
Lastly, modern entertainment has also influenced the kind of movies and music that are listened to.
Learn more about entertainment on:
https://brainly.com/question/773944
Exit These two right cylinders have the same height, 25 centimeters. The radius of the smaller cylinder is 5 centimeters and the radius of the larger cylinder is 3 times greater than that of the smaller cylinder. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder? A. 6:1 B. 12:1 C. 9:1 D. 25:1
ANSWER:
The ratio of the volume of the larger cylinder to the volume of the smaller cylinder is B. 12:1
What is the value of x?
70°
35°
30
Answer:
75 degrees
Step-by-step explanation:
all added up is 180 on every triangle. 70+35=105. 180-105=75
A printer is printing photos. For every 8 photos, the printer takes 2 minutes. Complete the table below showing the number of photos and the time it takes to print them.
if f(x)=2x^2+1 and g(x)= x^2-7 find (f-g)(x)
Answer:
x² + 8
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 2x² + 1 - (x² - 7)
= 2x² + 1 - x² + 7 ← collect like terms
= x² + 8
There are 34 carpenters in a crew. On a certain day, 29 were present. What percent showed up for work? (round to the nearest tenth)
Answer:
About 85.29 percent
Step-by-step explanation:
Recall that a percentage can also be represented as a proportion under 1; for example, 30 percent is .30 as a proportion of 1. So here we have 29 carpenters out of 34 that showed up, a ratio of .8529 showed up to work, and .8529 balance translates to 85.29 percent.
So 85.29 percent of the carpenters showed up to work.
-3x + 4y = -15 and 4x - y = -19
Answer:
x=-7, y=-9. (-7, -9).
Step-by-step explanation:
-3x+4y=-15
4x-y=-19
---------------
y=4x-(-19)
y=4x+19
-3x+4(4x+19)=-15
-3x+16x+76=-15
13x=-15-76
13x=-91
x=-91/13
x=-7
4(-7)-y=-19
-28-y=-19
y=-28-(-19)
y=-28+19
y=-9
What's the y-intercept?
Answer:
-9 would be your y-intercept
Step-by-step explanation:
Have a great rest of your day
#Nova
What is 6n+5=17
WHAT DOES N EQUAL TOOOOO HELPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEE
Step-by-step explanation:
Let's solve your equation step-by-step.
6n+5=17
Step 1: Subtract 5 from both sides.
6n+5−5=17−5
6n=12
Step 2: Divide both sides by 6.
[tex]\frac{6n}{6} =\frac{12}{6}[/tex]
[tex]n=2\\[/tex]
I hope this help's :)
Answer:
n = 2
Step-by-step explanation:
[tex]6n + 5 = 17 \\ \: \: \: \: \: \: \ - 5 \: \: \: \: - 5 \\ - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \frac{6n}{6} = \frac{12}{6} \: \: \: \: \: \: \: \: \: \: \\ n = 2[/tex]
Hope this helps! Brainliest would be really appreciated!
Line a goes through the points (- 3, 4) and (1, 2) . Line b goes through the point (6, 2) and (8, 1) . Are lines a and b parallel, perpendicular, or neither?
Answer:
They are parallel
Step-by-step explanation:
Find slope of point A
(-3,4), (1,2)
2-4=-2 1-(-3)=4
slope of a= -2/4 or -1/2
Find slope of point B
(6,2), (8,1)
1-2=-1, 8-6=2
slope of b= -1/2
Both have different slopes, and it can't be perpendicular because they have different denominator values.
Answer:
Step-by-step explanation:
(-3,4) (1,2)
difference is (y2 - y1) /( x2 - x1)
-2 / -4
-1/2 is the slope
(6,2) (8,1)
same as the last
-1 / 2
these lines have the same slope so they are parallel, if their slopes were reciprocals (-1/2 and 2) they would be perpendicular.
What theorem can be used to prove that the two triangles are congruent?
SAS
AAS
SSS
ASA
What is (f+g) (x) f(x) = -3x g(x)=-2x^2+x as a polynomial or rational function in simplest form?
Answer:
56xy23
Step-by-step explanation:
56 x 12 bhi 56 xy23