Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree

Answers

Answer 1

The velocity of the ship = 22 ∠157° = (22 cos 157°) i+ (22 sin 157°) j

The velocity of current = 5 ∠213° = (5 cos 213°) i+ (5 sin 213°) j

So, the resultant velocity = 22 ∠157° + 5 ∠213°
= (22 cos 157°) i+ (22 sin 157°) j + (5 cos 213°) i+ (5 sin 213°) j
= (22 cos 157° + 5 cos 213°) i + (22 sin 157° + 5 sin 213°) j
= -24.444 i + 5.873 j
= 25.14 ∠166.5°

The correct answer is option (1)
1) 25 knots at 166.5 degree

Related Questions

What is the answer for this equation?

36^-x+3=(1/216)^x+1

Answers

x=-9
also photomath is a good app to use for math ☺️
hoped this helped

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!

Answers

I find short work can be made of many limit problems simply by graphing them. Your limits appear to be:
1. 1
2. -1
3. 0
4. 1
5. 1 (x has been replaced by 1/x and the limiting value of x changed to 0)

Simplify. x + 4.7 = −9.2 A. −13.9 B. 13.9 C. −12.9 D. 12.9

Answers

Note the equal sign. What you do to one side you do to the other.

Isolate the x, subtract 4.7 from both sides

x + 4.7 = - 9.2

x + 4.7 (-4.7) = - 9.2 (-4.7)

x = -9.2 - 4.7

x = -13.9

-13.9, or A, is your answer

hope this helps

Find the determinant of G

Answers

the determinant is found by the formula ad-cb

where the letters are: a and b is the top row and c and d is the bottom row
so ad = 12*2 and cb = -6*0

12x2 = 24
-6x0 =0

24-0 = 24
the determinant = 24

The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?

Answers

Hey there!

Let: 1st number = x
2nd number = x - 4
3rd number = 4x

x + (x-4) + 4x = 62
6x - 4 = 62
6x = 62 + 4
6x = 66

x = 11 ---> 1st number

x - 4 = 11 - 4
= 7 ---> 2nd number

4x = 4(11)
= 44 ---> 3rd number

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 160 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.

Answers

The Average rate of change of f(t) from t = 3 seconds to t = 5 seconds is - [tex]v_{avg} = -80\;ft/s[/tex]

We have a equation -

[tex]f(t) = -16t^{2} +48t+160[/tex]

that calculates the height of the ball from sea level in feet at different times.

We have to find the average rate of change of f(t) from t = 3 seconds to t = 5 seconds.

What is Average velocity?

The rate of change of displacement per unit time is called average velocity. Mathematically -

[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]

We have -

[tex]f(t) = -16t^{2} +48t+160[/tex]

For time t = 3 seconds, f(t) is -

[tex]f(3) = -16(3)^{2} + 48(3) + 160\\f(3) = -144 +144 +160\\f(3) = 160\; feets\\[/tex]

For time t = 5 seconds, f(t) is -

[tex]f(5) = -16(5)^{2} + 48(5) + 160\\f(5) = -400+240+160\\f(5) = -400 + 400\\f(5) = 0 feet[/tex]

The formula for average velocity is -

[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]

According to question -

[tex]t_{2} = 5s[/tex] and [tex]t_{1} = 3s[/tex]

[tex]d_{2} = f(5) = 0 feet[/tex] and [tex]d_{1} = f(3)=160[/tex]

Substituting the values in the formula of average velocity, we get -

[tex]v_{avg} = \frac{0 - 160}{5 - 3} \\v_{avg} = \frac{-160}{2\\} \\v_{avg} = -80\;ft/s[/tex]

Hence, average rate of change of f(t) from t = 3 seconds to t = 5 seconds is [tex]v_{avg} = -80\;ft/s[/tex].

To solve more questions on calculating the average rate of change of height with time, visit the following link -

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How do I convert 2.4 x 10^21 formula units of magnesium hydroxide to grams?

Answers

Are you taking chemistry at the same time? If not, this is a pretty hard question.

Facts

1. As a formula unit, Magnesium Hydroxide has a chemical formula of Mg(OH)2
2. That means for every Magnesium, there are 2 oxygens and 2 hydrogens
3. The weights of these components are found on a periodic table. Since every periodic table is different, I'm going to approximate the results.

Mg = 24
O = 16
H = 1

4. One mole of anything has 6.02 * 10^23 (in this case) formula units associated with it.

Step One
Find the number of grams in 1 formula unit using the numbers from the periodic table.

1 Mg = 1 * 24 = 24
2 O = 2 * 16 = 32
2 H = 2 * 1 = 2
Total = 58 grams

So
1 mole of Mg(OH)2 = 58 grams

1 mole / 6.02 * 10 ^23 formula units = x mole / 2.4 * 10 ^ 21 formula units
Cross multiply

1 mole * 2.4 * 10^21 formula units = x mole * 6.02 * 10^23 formula units.
Divide both sides by 6.02 * 10^23

1 * 2.4 * 10^21 / 6.02 * 10 ^ 23 = x
x = 0.003987 moles

Now do this again for grams
1 mole / 58 grams = 0.003987 mole / x grams Cross multiply
1 mole * x = 0.003987 * 58 grams
x = 0.2232 grams <<<<< Answer

A rectangular wall has a length of 12ft and a width of 8ft. The wall has two rectangular windows. Each window has a width of 3ft and a height of 5ft. Andrea chooses a point on the wall at random to test a new paint color. What is the probability she could choose a point on a window

Answers

The probability would be about 31%

A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^2+12 . What sock price should the company set to earn a maximum profit?

Answers

For this case we have the following function:
P (x) = - 3 (x-5) ^ 2 + 12
We derive the function to obtain the maximum.
We have then:
P (x) = - 6 (x-5)
We match zero:
-6 (x-5) = 0
We clear x:
x-5 = 0
x = 5
Answer:
the company should set a sock price of 5 $ to earn a maximum profit

Final answer:

To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.

Explanation:

The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.

In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.

This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.

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How many distinct permutations are there of the letters of the word BOOKKEEPER?
There are __[blank]__ distinct permutations of the letters of the word BOOKKEEPER.

A group of 3 English majors, 2 anthropology majors, and 5
history majors are going out to dinner, where they will sit at a circular table. If students with the same major need to sit together, how many different ways can the students be seated around the table?

Answers

The letters of the word BOOKKEEPER can be arranged in 151,200 ways.

The group can be arranged in 8640 ways with all students of the same major together.

Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
[tex]\frac{n!}{n_1!\times n_2!\times ... \times n_k!} \\ \\=\frac{10!}{1!2!2!3!1!1!} = \frac{10!}{2!2!3!} = 151,200[/tex]

Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.

Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.

This gives us 6(6*2*120) = 8640

Final answer:

The word BOOKKEEPER has 10 letters, but with repetitions. There are 30240 distinct permutations. On the circular table, with students of the same major sitting together, there are 1440 different ways to seat the students.

Explanation:

The word BOOKKEEPER has 10 letters, but the letter O appears twice, the letter K appears twice, and the letter E appears three times. To find the number of distinct permutations, we need to divide the total number of permutations by the repetitions. So, we have 10!/(2!2!3!) = 30240 distinct permutations.

In the second question, we need to consider the students with the same major sitting together as a single entity. We can treat the circular table as a linear arrangement by fixing one student in a position and arranging the rest. So, the total number of different ways the students can be seated around the table is (3!2!5!) × 2! = 1440.

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Find the domain of the function :

Can you show the steps

Answers

a rational function must not have a denominator of 0, since that means the divisor is a 0 and there's no number whatsoever you can multiply it with 0 to get the dividend, the short version of all that is, the fraction is "undefined".

a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.

so, what values "x" cannot take on safely? well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,

[tex]\bf 5x+2=0\implies 5x=-2\implies x=-\cfrac{2}{5}[/tex]

so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.

so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}

For a circle with a radius of 6 feet, find the arc length of a central angle of 45 degrees

Answers

The arc length formula is given below.

Arc Length, s = radius*theta where theta is in radians. First we need to convert theta from degrees to radians.

theta (radians) = 45 degrees * π radians / 180 degrees = 0.785 radians

radius = 6 ft
theta = 0.785 radians

s = arc length = 6 ft * 0.785 radians = 4.712 ft

PLEASE SOMEONE I AM SO DESPERATE like actually crying
1. The equation of a parabola is given. y=−1/6x2+7x−80 What is the equation of the directrix of the parabola?
2. (y+2)^2= 129X-5)
What is the equation of the directrix of the parabola?

Answers

Part 1)
we have that
y=−1/6x2+7x−80

y= (−1/6)x^2+7x−80 multiply both sides by -6

-6y = x^2 - 42x + 480 subtract 480 from both sides

-6y - 480 = x^2 - 42x take (1/2) of 42 = 21.....square this = 441 and add to both sides

-6y - 480 + 441 = x^2 - 42x + 441 simplify the left, factor the right

-6y - 39 = (x - 21)^2 factor the left side as

-6 (y + 39/6) = ( x - 21)^2 (1)

Using the form

4p (y - k) = ( x - h)^2 we can write (1) as

4 (-3/2)(y - (-39/6) ) = ( x - 21)^2

The vertex = ( h, k) = ( 21, -39/6) and p = -3/2

And the directrix is given by

y = k - p → y = -39/6 - (-3/2) = -39/6 + 3/2 = -39/6 + 9/6 =

-30/6 = - 5-------> y=-5

the answer Part 1) is

y=-5

Part 2) (y+2)^2= 129X-5

What is the equation of the directrix of the parabola?
(y+2)²= 129X-5 -----> 129*(x-5/129)=(y+2)² (1)

Using the form

4p (x - h) = ( y - k)^2 we can write (1) as

4*(129/4)*(x-5/129)=(y+2)²

The vertex = ( h, k) = ( 5/129, -2) and p = 129/4

And the directrix is given by

x = h - p → x = 5/129 - (129/4) = (20-16641)/516-----> -16621/516

x=-32.21

the answer part 2) is

x=-32.21

Please answer ASAP!!! How many vertical asymptotes does the graph of this function have ?

Answers

Answer:

The answer is 1.

Got it from Apex

Step-by-step explanation:

I need to answer three questions about y = x^(-2) on the interval [-4, -1/2]. I have attached my questions and my answers as screenshots:

Part 1 - ANSWER C
Part 2 - ANSWER A
Part 3 - ANSWER B

I am referring to each part in the order that I uploaded the screenshots. You will see that my answers are highlighted in blue. I like second opinions!

Answers

I wasn't sure how to order things, so I decided to write directly on top of your screenshots. Have a look at the three attachments. Two of which are correct. There is one incorrect answer though you're fairly close.

Write a quadratic equation whose solutions are 2i and -2i.

Answers

are there any answer choices

Answer:

answer= 2i

Step-by-step explanation:

Please help with geometry

Answers

[tex]A=240\\\\A=a\cdot h\\\\New:a'=\dfrac{1}{4}a\ and\ h'=2h\\\\A'=a'h'=\dfrac{1}{4}a\cdot2h=\dfrac{1}{2}ah=\dfrac{1}{2}A=\dfrac{1}{2}\cdot240=\boxed{120}[/tex]

What is the area of the parallelogram?

Answers

Area of the parallelogram is given by:

Area = Base x Height

Base = 8 cm

Height is the perpendicular distance between the base. 6 cm is not the height, but we can use 6 cm and the angle 60 to find the height. See the picture attached with.

The height x is the perpendicular side of the triangle as shown in figure and 6 is the hypotenuse.

So,we can write

cos 60 = x/6
⇒
x = 6 * cos 60 = 3 cm

So, now we can write:

Area of parallelogram = 8 x 3 = 24 cm²

The area of a parallelogram is base*height

or A = base*lateral side /cos(theta)

A = 8 * 6 / cos(60) = 96cm^2

The area of the parallelogram is 96 sq.cm

brainly The point (−4, 2) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work. (10 points)

Answers

The tangent = -2/4 = -1/2
The length of the hypotenuse = sqrt20 = 2 sqrt5
sine = 2 / 2 sqrt5 = 1 / sqrt5
cosine = -4 / 2 sqrt5 = -2/sqrt5

help me 15p for an answer and brainliest
help mme please
the true it is 20p

Answers

Option 4.
______________

Answer:

Option 4.

Step-by-step explanation:

The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year.

An exponential function comes down from the positive infinity and passes through the points zero comma eighty-seven thousand. The graph is approaching the x-axis.

What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?

$90,000, and the graph would have a y-intercept at 20,000
$87,000, and the graph would have a y-intercept at 67,000
$87,000, and the graph would fall at a slower rate to the right
$87,000, and the graph would fall at a faster rate to the right

Answers

The initial value of the truck is the value of y when x = 0. Since the graph passes (0, 87000), this means that the value of the truck initially was $87,000. If the initial value was only $67,000, then the y-intercept would have been (0, 67000). This is the second choice.

Answer:

I just took the test the answer is

Step-by-step explanation:

B. 87,000, and the graph would have a y-intercept at 67,000.

quando o Ângulo de elevação do sol e de 70 a sombra de um edifício medes 20 cm calcule a altura do edifício
dados : sen 70=0,93 cos 70=0,3 e tg70=2,74?

Answers

Use x para a altura.

tg 70 = x/(20 cm)

x = 20 cm * tg 70

x = 20 cm * 2,74

x = 54,8 cm

Resposta: A altura do edifício é 54,8 cm.

PLEASE ANSWER QUICKLY! Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?

A. n may cause p.

B. p must cause n.

C. n must cause p.

D. n must not cause p.

Answers

The correct answer will be option A.

Correlation does not imply Causation.
This means if two variables are strongly related, it is not a must thing that one is causing any occurrence or change in the other variable. For example, before and during an occasion or an event people buy new clothes and celebrate by having different drinks. So there will be a strong correlation between buying new clothes and having drinks.
Thus this mean, having different drinks is causing people to buy new clothes? The answer is NO.

However, it is possible that if two variables are correlated on might be causing the other. For example, more hours of work will help the worker to earn more. So more work is causing the salary to grow. So more work is Causing an increase in salary? The answer is YES

Therefore, the answer to this question will be option A

Three added to eight times a number is the same as three times the value of two times the number minus one

Answers

im sorry do not now i will try and help

Choose the example that correctly shows the mean population density of a region.

A. 678 people per cubic meter

B. 678 cubic meter per number of people

C. 678 people per square mile

D. 678 square mile per people

Answers

678 people per cubic meter - lol!! That would be a SQUash!!!

The answer is C

- 678 per square mile

Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $14 per hour at her job, and Jack is paid $7 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $770 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?

Answers

By setting up a system of equations we can easily solve this problem. Let's denote Jane's working hours with x and Jack's working hours with y. Since they don't want to work more than 65 hours, the first equation is x+y=65. The second equation is 14x+7y=770. By solving this system of equation [tex] \left \{ {{x+y=65} \atop {14x+7y=770}} \right. [/tex], we find that y=20 hours, which is Jack's maximum working hours.

Answer:

Step-by-step explanation:

the equation 3sinx+cos^2x=2 is solved below
Please help! Thanks!

Answers

we have that
3sin x+cos²x=2
3sin x+(1-sin²x)=2
-sin²x +3sin x=1
sin²x -3 sin x+1=0---------> up to here the procedure is correct
let
A=sin x
then
A²-3A+1=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(A²-3A)=-1

Complete the square. Remember to balance the equation by adding the same constants to each side.

(A²-3A+2.25)=-1+2.25

Rewrite as perfect squares

(A-1.5)²=1.25

(+/-)(A-1.5)=1.12

first solution

(A-1.5)=1.12--------> A=1.12+1.5-----> A=2.62-----> sin x=2.62

second solution

-(A-1.5)=1.12----> -A+1.5=1.12----> A=1.5-1.12----> A=0.38---> sin x=0.38

the answer is

the equation was factored incorrectly

Its is b. hope this halps

If an airplane travels 15 miles in 2 minutes what is the speed in miles per hour

Answers

15 miles = 2 minutes

1 hour = 60 minutes

60 ÷ 2 = 30

30 × 15 = 450

Answer = 450 miles in 1 hour

Hope this helped :)

Rachel enjoys exercising outdoors. Today she walked5 2/3 miles in2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile

Answers

the answer to your question is

Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.

Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile

Answer:

Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles or 5.67 miles in 2 2/3 hours or 2.67 hours.

Rachel’s unit walking rate in miles per hour is = [tex]\frac{5.67}{2.67}[/tex] = 2.125 miles per hour or 2 1/8 miles per hour.

Rachel’s unit walking rate in hours per mile = [tex]\frac{2.67}{5.67}[/tex] = 0.47 hours per mile.

Anyone know the answer?

Answers

i think it is 3=4 i could be wrong though

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In what type of law is the government always the plaintiff? a. civil law b. criminal law c. tort law d. public law e. common law What impact did the social security act of 1935 have on america? Please help very urgent 4.5< b Jenna is 14 months old and uses only "bottle," "no," "up," "bye-bye," "mama," and "dada" when she talks. however, when the family is on their way to visit jenna's grandmother, and her father tells jenna to get her blue bunny from the bedroom and bring it with her, jenna quickly runs to get the bunny. this episode demonstrates that One light-hour is the distance light travels in one hour. the speed of light is about 300,000 km/s (3 10^5km/s). if jupiter is 0.72 light hours from the sun, how far is this? Someone who brags about his physical health and vitality in front of a friend going through chemotherapy exhibits a symptom of which personality disorder 14) Jillian has $50 that she plans on investing in an account that will double her money every week. This can be represented by the equation M = 50(2)x where M represents the amount of money she has and x represents the number of weeks that have passed. Her uncle Charlie gives her a gift of $400 so she decides to start her investement with that money plus the $50 she already had. What should be changed in the equation M = 50(2)x to represent the new situation? When a person has fever, the temperature of the body needs to be cooled down. a person (about 50 kg 50 kg ) with a high temperature of 104 f 104f (~ 40 c 40c ) needs to be placed in a tub of cool water to reduce her body temperature. 1) what could be a more effective way to reduce the temperature of the person? to place her in a 30 c 30c tub of water for 10 10 minutes. to place her in a 25 c 25c tub of water for 5 5 minutes. to place her in a 20 c 20c tub of water for 1 1 minute? Can you solve 5a please greatly appreciated. Which of the following is not one of the "5Rs"? A. Recycle B. Rethink C. Reduce D. Reinvent What is the equation of the line whose y-intercept is 3 and slope is 1?y=x-3y=x+3y=3x+1 After the supreme court's decision in miranda v. arizona, a few states and the federal government tried to void the decision with legislation. in 2000, the supreme court later revisited miranda and ruled that 2/5x = -3/15 + 1/x x=0x=15x=5x=3 Which statement best summarizes the relationship between the enlightenment and the abolition movement What value of y makes the equation true? When the united states entered the war in europe where did it attack first apex? A wheel spins at 300 revolutions per minute. What is the angular velocity of the wheel, in radians per second? Round the answer to the nearest hundredth. ____ disorder is a major psychological disorder that involves a sudden loss of memory or change of identity. personality dissociative factitious somatic symptom How do Australians in hot dry climates get water Preguntas choose the answer that best completes each sentence los ciclistas (cyclists) viajan a taxco porque hay __. un maratn (marathon) un festival una carrera de bicicleta