A powerboat heads due northwest at 13 m/s with respect to the water

across a river that flows due north at 5.0 m/s.

What is the velocity (both magnitude and direction) of the motorboat with

respect to the shore?

Answers

Answer 1

9514 1404 393

Answer:

  16.9 m/s N 32.9° W

Step-by-step explanation:

The resultant magnitude can be found from the law of cosines. The internal angle between the boat's heading and the river flow is 135°, so the magnitude of the boat's net speed is ...

  v² = 5² +13² -2·5·13·cos(135°) ≈ 285.924

  v = 16.9093 . . . . m/s

The angle (α) between the boat's heading and the resultant velocity can be found from the law of sines.

  sin(α)/5 = sin(135°)/16.9093

  α = arcsin(5/16.9093×sin(135°)) ≈ 12.07°

The boat's actual heading will be this angle less than the 45° angle the heading makes with due North.

  45° -12.07° = 32.93°

The boat's velocity with respect to shore is about ...

  16.9 m/s N 32.9° W


Related Questions

Help pleaseeeeeeeeeeeeeeeee

Answers

Answer:  0.92 feet (choice B)

You're close but not quite there. To get the answer, you divide 29.44 over 32

If you had 32 feet of banner and 32 students, then each student would get 32/32 = 1 foot. Since the length of the banner is smaller than the number of students, this means each student only gets a fraction of a foot. This fraction value is fairly close to 1 because 29.44 is close to 32.

Answer:

B: 0.92

Step-by-step explanation:

Divide the banner length by the amount of students

[tex]\frac{29.44}{32}[/tex]

I need help again please help me with this question

Answers

Answer:

The size of a sundae and the amount of calories it contains.

Step-by-step explanation:

The answer choice is the only one with a positive correlation, because it is the only one that isn't depleting or going down in size. No matter if you eat the sundae or what size it becomes, the calories it contains will still be the same for the whole amount.

When a car travels, gas is used and it depletes. As a snowball does when it melts. And "the temperature on Tuesday" has no correlation involved at all

Who is the most powerful undertale character

Answers

Answer:

Asriel Dreemurr

Step-by-step explanation:

Answer:

clearly the gay robot

hes my favorite <3

solve 1,000x10 hint: use a strategy

Answers

Answer:

10000

Step-by-step explanation:

Answer:

10,000

Step-by-step explanation:

You just take the 0's and then you mutiply 1x1 and the answer you add the cero's you left  the one from the number 10 and allso the ones from 1000

The number of passengers in the bus double every minute. The bus was full of
passengers at 7.45am. When was it one quarter full?

Answers

Answer:

7:43 am.

Step-by-step explanation:

it was  1/2 full one minute ago then another 1/2 = 1/4 full 2 minutes ago.

Knowing how the bus fills, we want to find the time where the bus is one-quarter full.

The bus is one-quarter full at 7:43 am.

We know that at 7:45 am the bus is full. Let's say that the full bus has N people inside.

Each minute the population doubles, so if we go backwards, each minute the population is divided by 2.

One minute before, the bus must have half of the above population, meaning that at 7:44 am, the bus has N/2 people.

Another minuter before the people inside is halved again, then at 7:43 am we will have (N/2)/2 = N/4 people.

And if N is the people in a full bus, then N/4 represents the buss a quarter full.

Then we can answer the question as:

The bus is one-quarter full at 7:43 am.

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For a hypothesis test of the claim that the mean amount of sleep for adults is less than 6 hours, technology output shows that the hypothesis test has power of 0.4013 of supporting the claim that 6 hours of sloep when the actual population
mean is 4.5 hours of sleep. Interpret this value of the power, then identify the value of B and interpret that value
Interpret this value of the powers

Answers

Answer:

b

Step-by-step explanation:

Please help I need these quickly. Please answer sensibly! I will give brainliest to the correct answer.

Answers

Answer:

n+n= 2n

[tex](3n) ^{2} = 9n ^{2} [/tex]

5(n+2)=5n+10

2(n+1)=2n+1

[tex]n \div 4 = \frac{n}{4} [/tex]

[tex]n(n - 2 = n{2} - 2n[/tex]

Which direction am I going if I drive from Washington DC to Dallas texas

Answers

Answer:

north

Step-by-step explanation:

Sam wrote his bike 2/5 of a mile and walked another 3/4 of a mile how far did he travel?

Answers

Answer:

1.15 miles

Step-by-step explanation:

Answer:

24/20

Step-by-step explanation:

Changed denominator to 20 since 4 and 5  both go into 20. Got 8/20 and 15/20. Added and got 24/20. As a mixed number it is 1  1/5/ Hope this helps!

(Ill give brainliest if u help!)


Which equation has a value less than 54,811?


A) 54,811 x 2 = ________

B) 54,811 x one and two fourths = ________

C) 54,811 x 1 = ________

D) 54,811 x two fourths = ________

Answers

Answer:

Answer is D

Step-by-step explanation:

Answer:

The answer would be D.

Step-by-step explanation:

8y-2x=-72 in slope form

Answers

Answer:

y=1/4x-9

Step-by-step explanation:

Slope-intercept form is y=mx+b.

8y-2x=-72

Add 2x to both sides

8y=2x-72

Divide both sides by 8.

y=1/4x-9

HTH :)

f(x) = 72-12x what is the domain and range

Answers

Answer:

The domain is x and the range is f(x)

Step-by-step explanation:

See attachment for answer:

Explanation:

Is undefined in other words “do not exist”



Consider a limousine that gets m(v)= (120 - 2v) / 5 miles per gallon at speed v , whose chauffeur is paid $15/hour, and gas costs $3.5/gallon.

a. Write the function that finds the cost per mile at speed v
b. What speed results in the most inexpensive driving speed?

Answers

Answer:

(17.5 / 120 - 2v) + (15 / v)

Step-by-step explanation:

Given : m(v)= (120 - 2v) / 5 miles per gallon at speed v ,

chauffeur is paid $15/hour

gas cost = $3.5/gallon.

Gasoline cost per mile :

Cost per gallon = $3.5

Cost per gallon * 1/(m(v))

$3.5 * 1 / (120 - 2v) / 5

$3.5 * 5 / 120 - 2 v

= 17.5 / 120 - 2v

Time = distance / speed

Chauffeur cost = 15 per hour / v

Hence ;

Total cost :

Cost of gasoline + Cost of chauffeur

(17.5 / 120 - 2v) + (15 / v)

Answer would be - (17.5 / 120 - 2v) + (15 / v)

First Given : m(v)= (120 - 2v) / 5 miles per gallon at speed v , The chauffeur is paid $15/hour. Then gas cost = $3.5/gallon. Gasoline cost per mile : Cost per gallon = $3.5 Cost per gallon * 1/(m(v)) When, $3.5 * 1 / (120 - 2v) / 5 $3.5 * 5 / 120 - 2 v

           Then result will be = 17.5 / 120 - 2v

        Time = distance / speed Chauffeur cost = 15 per hour / v

Hence ;

The total cost will be :  Cost of gasoline + Cost of chauffeur

(17.5 / 120 - 2v) + (15 / v)

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What is the measure of angle G? Type only the number:

Answers

Answer: 48

Step-by-step explanation:

total of all the degrees of the angles of the triangle is ALWAYS 180

let the measure of angle G be x

180 = 102+30+x

180 = 132+x

x = 48

helllppp meee please

Answers

Answer:

2, 3, 6, 7

Step-by-step explanation:

The selling price of a watch is rs 220. If 10% profit has been included in the marked price of the watch, what is the marked price??​

Answers

Answer:

22 is 10 of 220

Step-by-step explanation:

hope it help

If Paul’s savings are 25% more than Janet’s savings,
What percentage of Paul
savings are Janet’s savings

(A) 25 %
(B). 50%
(C) 75%
(D) 80%

Answers

How much is Janet saving tho?
how much savings does Janet have?

What is the x-coordinate of point B? Write a decimal coordinate.
(brainliest ) Edge 2020

Answers

The coordinate of point B is approximately (-1.5, 3.5).

FINANCE

2. Which of the following statements is FALSE?

A. Common stockholders have an upper limit on their dividends
B. Preferred stockholders are more protected from risk than common stockholders.
C. Common stockholders own the firm and are among the last to be paid in the event of bankruptcy.
D. Preferred stockholders are

Answers

Answer: I think its C

Step-by-step explanation:

why was mom now saying that Augie did not have to go to school​

Answers

Answer:

Is there suppose to be a picture?

Step-by-step explanation:

Answer:

Because she liked Augle more than the other child

Step-by-step explanation:

She didn't want him to go to school so that she could spend the day with her favorite child

A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively?

Answers

Answer: -81

Step-by-step explanation:

Let x = the car moving towards west = 30

Let y = truck moving towards north = 40

dx/dt = -55

dy/dt = -60

We the use Pythagoras theorem to solve further where,

s² = x² + y²

s² = 30² + 40²

s² = 900 + 1600

s² = 2500

s =✓2500

s = 50

We then differentiate with respect to t, then we will have:

s² = x² + y²

2s ds/dt = 2x ds/dt + 2y dy/dt

50 ds/dt = (30 × -55) + (40 × -60)

50 ds/dt = -1650 - 2400

50 ds/dt = - 4050

ds/dt = -4050/50

ds/dt = -81

Find the dimensions of a rectangle with area 729000 m2 whose perimeter is as small as possible. (Give your answers in increasing order, to the nearest meter.)

Answers

Step-by-step explanation:

Area of a rectangle = Length * Width

A = LW

729000 =  LW .... 1

Perimeter of a rectangle P = 2L+2W

P = 2L+2W

From 1;

W = 729000/L

P = 2L + 2(729000/L)

P = 2L + 1458000/L

To minimize the perimeter, dP/dL = 0

dP/dL = 2 -  1458000/L²

2 -  1458000/L² = 0

2L² - 1458000 = 0

2L² = 1458000

L² = 729000

L = √729000

Length = 853.8m

W = A/L

Width = 729000/853.8

Width = 853.8

Hence the dimension to the nearest meter is 854m by 854m

Michael buys pants from a clothing company for $70 dollars. He then sells each pair of pants in his clothing shop at a 40% markup. How much is the markup on the pants?

Answers

Answer:

$98

Step-by-step explanation:

70 is the original price, but the mark up is 40%. So, 40% of 70 is 28

$70 + $28 = $98

Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 15 based on earlier studies.

Answers

Answer:

67

Step-by-step explanation:

You have to use fractions to show your work and I'm not going to do that but just know that it is the answer.

Geometry: Express the area of each figure as a monomial. I need help with this, anyone? ​

Answers

Answer:

answer 28ab³ I think maybe

The area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].

Here,

The formula to calculate the area of a right-angled triangle is:

Area = (1/2) * base * height

In this case, the right-angled triangle has a height of [tex]6ab^3[/tex] and a base of [tex]4a^2b[/tex].

Now, let's substitute these values into the formula:

Area = [tex](1/2) * 4a^2b * 6ab^3[/tex]

Now, simplify the expression:

Area = [tex]2 * a^2b * 6ab^3[/tex]

To find the monomial representation, multiply the coefficients and add the exponents of like terms:

Area = [tex]12a^{(2+1)}b^{(1+3)[/tex]

Finally, simplify the exponents:

Area = [tex]12a^3b^4[/tex]

So, the area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].

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what is the correct evaluation of 3x-x+2,when x is equal to -4?

14

-6

6

-14​

Answers

Answer:

The answer is -6.

Step-by-step explanation:

You have to substitute x = -4 into the expressions :

3x - x + 2

= 3(-4) - (-4) + 2

= -12 + 4 + 2

= -6

The measure of the angle is 44 times greater than its supplement.
What is the measure of the​ supplement?

Answers

Answer: The measure of it's supplement is 4°

Step-by-step explanation:

If an angle is 44 times is supplement, then we can represent it by the equation   x = 44y    where  x is the angle and y is it's supplement.

Supplementary angles add up to 180 degrees, meaning that  x + y = 180.

  x = 44y  

x + y = 180  

Using both equations substitute the value for x in the first equation, into the second equation and solve for y.

 

44y + y = 180           Combine like terms on the left side

   45y = 180        Divide both sides   45

 y = 4  

This means the measure of it's supplement is 4 degrees.

Now input 4 into one of the equations for  y and solve for x to find the main angle.

x = 44(4)

x = 176  

This also means that the angle itself is 176 degrees.

The measure of the supplementary angle is 4°.

It is given that the measure of the angle is 44 times greater than its supplement.

We have to find out the measure of the supplement.

What are supplementary angles ?

Two angles are said to be supplementary angles if the sum of two angles is 180°.

As per the question ;

The measure of the angle is 44 times greater than its supplement.

Let's assume the supplementary angle is x .

So,

The other angle will be 44 × x .

We know that sum of two angles if they are supplementary is 180°.

x + 44 x = 180 °

⇒ 45 x = 180°

⇒ x = 180 ÷ 45

x = 4°

And the other angle will be ;

= 44 × 4

= 176°

Thus , the measure of the supplementary angle is 4°.

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what is the solution to this equation: 5x to the 2 power - 36x - 81 = ?

Answers

Answer:

5x² - 36x - 81

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Combining Like TermsStandard Form: ax² + bx + c = 0

Step-by-step explanation:

Step 1: Define expression

5x² - 36x - 81

Step 2: Simplify

We cannot simplify the expression down further.

An apple tree can grow about 400 apples. Jake says that 13 apple trees can grow about​ 6,000 apples. Do you​ agree? Explain.

Answer: No. Since 13×400=5,200​, 13 apple trees can grow about 5,200 apples.​ Jake's estimate of​ 6,000 is much higher than 5,200.

Answers

Answer:

you answered it

Step-by-step explanation:

you put no blah blah blah

The subset of the sample space probability experiment

Answers

Step-by-step explanation:

The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1.

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