Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?

Answers

Answer 1

The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.

How can the angle between the paths of the boats be found?

The given parameters are;

Direction of the first boat = Northeast

Speed of the first boat = 15 km/h

Direction of the second boat = Northwest

Speed of the second boat = 18 km/h

Distance between the boats after 45 minutes = 14.0 km.

45 minutes = 0.75 × 1 hour

Distance traveled by the first boat in 45 minutes, d1, is therefore;

d1 = 15 km/h × 0.75 hr = 11.25 km

For the second boat, we have;

d2 = 18 km/h × 0.75 hr = 13.5 km

Using cosine rule, we have;

14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)

Where A is the angle between the paths of the two boats.

Which gives;

[tex]cos(A) = \frac{361}{972} [/tex]

[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]

The angle between their paths to the nearest degree, A ≈ 68°

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Related Questions

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Answer:  6x+4x +13x+6 equal

Ethan is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
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Answer:

18

Step-by-step explanation:

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x = 0.5

Step-by-step explanation:

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Answer:

12x + 52

Step-by-step explanation:

Distribute.

(4 • 3x + 4 • 12) + 4

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Hangi sayının 10 eksiğinin 7 katı 70'tir ?​

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7*(x - 10) = 70
7x = 140. Wait if this is wrong I’m really sorry! Have a great day.

Fallon collected data for her favorite TV show. She recorded the number of viewers and the number of weeks since the show premiered. With the data in hand, she created this scatter plot and drew a line of best fit


What are the slope and the y-intercept of the line of best fit?

Answers

Answer:

On the best-fit line for the points {(2,3) (5,7) (1,2) (4,8)}, one point is (0.5,1.25) and another is the y-intercept (0,0.5). Use the formula for the slope of a line, m = (y2 - y1)/(x2 - x1), to find the slope

Step-by-step explanation:

Hope it help

Mark me as brainliest

Answer:

Slope is (6, 10) and (0, 12). The y-intercept is 12.

Step-by-step explanation:

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(2x+1)+(3x-5)=5x-4 you just have to try some of them out and see which ones work

Which expression can be used to find the volume of the sphere? A sphere with radius 9 inches. V = four-thirds pi r squared = four-thirds (3.14) (9) squared V = four-thirds pi r cubed = four-thirds (3.14) (9) cubed V = four-thirds pi r cubed = four-thirds (3.14) (18) cubed V = four-thirds pi r cubed = four-thirds (3.14) (18) cubed Mark this and retur

Answers

Answer:

V = four-thirds pi r cubed = four-thirds (3.14) (9) cubed

Step-by-step explanation:

if I have 100 baskets and I have 400 hundred apples how many apples will go into each basket

Answers

Answer: 4 apples will go into each basket if you want all the baskets to be filled with an equal amount.

Step-by-step explanation:

100x=400

dividing through by 100 we get

x=4

how can you tell the difference between circumcenter and incenter?

Answers

A circle inscribed inside a triangle is called the incenter, and has a center called the incenter. A circled drawn outside a triangle is called a circumcircle, and it's center is called the circumcenter. Drag around the vertices of the triangle to see where the centers lie.

8n + ? = 0
A.) - 8/n
B.) 8/n
C.) 1/8n
D.)-8n

Answers

D is the correct answer:)

can someone help me how to calculate 15% of R200​

Answers

Answer:

30

Step-by-step explanation:

formula :15÷100×200

Marco paid $12 for 3jump ropes. If each jump rope costs the same amount, how much does 1 jump rope cost? Write and solve an equation.

Answers

Answer:

each jump rope costs 4 dollars

12÷3=4

Answer:

$4

Step-by-step explanation:

Divide: 12 divided by 3=4

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

A home meal delivery business delivers 34.5 pounds of food each day. How many ounces of food will they deliver in 4 days? (1 lb.= 16 oz) fill in the blank they will deliver ______ ounces of food in 4 days.

Answers

Answer:

They will deliver 2208 ounces of food in 4 days.

Step-by-step explanation:

Multiply 34.5 by 16 to get the ounces and got 552. Then multiply 552 by 4 and you'll get the answer.

:))

What is the slope of the linear equation represented by the table.​ NEEDED PLSS

Answers

Answer:28/4

Step-by-step explanation:

Change of y over the change of x.

Y is +28

X is +4

Simplify: i^69
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Answers

Answer: it's just "i"

Step-by-step explanation:

Which equation correctly uses the law of cosines to solve for the length s?

Answers

Answer: Choice D

s^2 = 9^2 + 10^2 - 2(9)(10)cos(100)

==========================================================

Explanation:

Consider the pythaorean theorem

a^2 + b^2 = c^2

which is the same as saying

c^2 = a^2 + b^2

If we tack on "-2ab*cos(C)", then we end up with

c^2 = a^2 + b^2 - 2ab*cos(C)

which is one form of the law of cosines. The side c is opposite angle C, and the two are on opposite sides of the equation. The 'a's and 'b's are on the right side with the angle C.

Note if C = 90 degrees, then cos(C) = cos(90) = 0 which means the whole "-2ab*cos(C)" term goes to 0 and we'd be left with the pythagorean theorem again.

In this case, we replace c with s, replace 'a' with 9, replace b with 10, and C with 100.

Answer:

Option (4)

Step-by-step explanation:

Cosine rule states,

(UT)² = (SU)² + (ST)² - 2(SU)(ST)cos(∠UST)

Here, UT is the opposite side of angle UST and two sides SU and ST are the adjacent sides.

∠UST is the included angle between SU and ST.

By this formula,

s² = 9² + 10² - 2(9)(10)cos(100°)

Therefore, Option (4) will be the answer.

A jungle has 578 monkeys.
It also has 153 birds.
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Monkeys
X Х $ ?

Answers

Answer:

425 monkeys

Step-by-step explanation:

Subtract the number of birds from the number of monkeys to find the difference between the two.

578-153=425
Answer 425
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Answers

Answer:

<A≅<Z

Step-by-step explanation:

Hope This Helps!

Jack invested $7,600 in an account paying an interest rate of 6\tfrac{1}{4}6 4 1 ​ % compounded continuously. John invested $7,600 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 ​ % compounded quarterly. After 19 years, how much more money would John have in his account than Jack, to the nearest dollar?

Answers

Answer: John would have $1371.33 more in his account than Jack.

Step-by-step explanation:

Formula to calculate amount after t years if compounded continuously:

[tex]A=Pe^{rt}[/tex]

Formula to calculate amount after t years if compounded quarterly:

[tex]A=P(1+\dfrac{r}{4})^{4t}[/tex]

, where P= Principal amount, r= rate of interest.

Given: P= $7,600

t=19 years

For Jack, [tex]r=6\dfrac{1}{4}\%=\dfrac{25}{4}\%=\dfrac{25}{400}=0.0625[/tex]

For John, [tex]r=6\dfrac{3}{4}\%=\dfrac{27}{4}\%=\dfrac{27}{400}=0.0675[/tex]

Amount in Jack's account after 19 years= [tex]7600e^{0.0625(19)}[/tex]

[tex]=7600e^{1.1875}\\\\=7600(3.27887376794)\\\\\approx\$24,919.44[/tex]

Amount in John's account after 19 years= [tex]7600e^{0.0675(19)}[/tex]

[tex]=7600(1+0.0675)^{19}\\\\=7600(3.45931245291)\\\\\approx\$26,290.77[/tex]

Difference = 26290.77-24919.44 = $ 1,371.33

John would have $1371.33 more in his account than Jack.

Answer:668

Step-by-step explanation: I just did it.

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Answers

Answer:

y = 1/2x + 1

Step-by-step explanation:

To be perpendicular to a line is to have the product of the slopes be -1. First, we have to put 2x + y = 4 into slope-intercept form to find the slope of the line. We do this by subtracting 2x on both sides to get that y = -2x + 4. Now, the number that multiplied by -2 is equal to -1 is 1/2, so that is the slope of our line. We can substitute these values into the slope-point equation to find the equation. We would get that y - 1 = 1/2 * (x - 0). This simplifies to y = 1/2x + 1.

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Answers

Answer:

[tex] \huge \boxed{ \boxed{x = 8}}[/tex]

Step-by-step explanation:

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[tex]step - 2 : solve[/tex]

[tex] \tt add \: 6 \: to \: both \: sides : \\ \tt12x - 6 + 6 = 90 + 6 \\ \tt 12x = 96[/tex][tex] \tt divide \: both \: sides \: by \: 12 : \\ \tt \frac{12x}{12} = \frac{96}{12} \\ \tt \therefore x = 8[/tex]

GIVING BRAINLIEST IM TIMEDDDD

Answers

Answer:its the 2nd one

Step-by-step explanation: i remeber because i took this quiz

Please help with this it is due today

Answers

Answer:

24

Step-by-step explanation:

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $35 each week for food, clothes and movie tickets. How many weeks can Keith withdraw money from his account?

Answers

8 weeks is the correct answer500 - 200 = 3008 x 35 = 280$280 is the closest you can get to $300 without going over.So, 8 weeks is the answer.Please let me know if I am wrong.

how many 1/5s are in 20?​

Answers

Answer:

There are 4

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

You have 49 dimes and quarters. You have 7 more quarters than dimes.How much money you have in quarters and dimes

Answers

Answer:

Step-by-step explanation:

Because you have seven more quarters than dimes, you have 28 quarters, and 21 dimes, which equals 49 dimes and quarters.

You have $9.10

I hope this helps!

Thanks!

[tex] \sqrt{ x} = \sqrt{2} + 1 \: then \: x = [/tex]
helpppp asap​
edit:help guys i have examm

Answers

Answer:

3+2√2

Step-by-step explanation:

Given the expression

√x = √2 + 1

To get x, we will have to square both sides

(√x)² = (√2 + 1)²

x = (√2 + 1)(√2 + 1)

x = √4+√2+√2+1

x = 2+2√2+1

x = 3+2√2

Hence the value of x is 3+2√2

7 The table below shows the population of
different regions in 1985 and in 2005.
Place
Entire world
China
Population in Population
1985
in 2005
4.9 X 109 6.4 X 109
1.1 X 109 1.3 X 109
7.6 x 108 1.1 x 10
2.4 x 108 3.0 X 108
8.9 X 106 7.2 X 106
India
United States
Bulgaria
a Determine the ratio of the population
of the entire world to that of China in
2005, giving your answer to the nearest
integer

Answers

Answer:

In this table the graphic shows that...

Step-by-step explanation:

...the population increased 5,9 x 10 6.

The ratio is 64:13

What is ratio?

Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b

Given data:

Population of china in 2005 =1.3*10^9

population of entire world in 2005 = 6.4*10^9

Now,

ratio= 6.4*10^9/ 1.3*10^9

ratio= 64/13 or 64:13

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Find the area of the shaded segment of the circle​

Answers

Answer:

≈ 0.8 m²

Step-by-step explanation:

________________________________________________

FORMULA FOR FINDING AREA OF SEGMENT :-

[tex]A = r^{2} [\frac{\alpha }{360} \times \pi - (\sin \frac{\alpha }{2} \times \cos \frac{\alpha }{2} )][/tex]

Where :-

A = Area of the segmentr = Radius of the circleα (alpha) = Angle subtended by arc at the center

________________________________________________

Angle subtended by the minor arc at the center = 360° - 300° = 60°

Radius of the circle = 3 m

Area of the segment =

[tex]3^{2} [ \frac{60}{360} \times \pi - (\sin \frac{60}{2} \times \cos \frac{60}{2})][/tex]

[tex]= 9[\frac{1}{6} \times \pi - (\sin 30 \times \cos 30)][/tex]

[tex]= 9[\frac{\pi }{6} - (\frac{1}{2} \times \frac{\sqrt{3} }{2} )][/tex]

[tex]= 9[\frac{\pi }{6} - \frac{\sqrt{3} }{4} ][/tex]

[tex]= 9[\frac{2\pi - 3\sqrt{3} }{12} ][/tex]

[tex]= \frac{9}{12} \times (2\pi - 3\sqrt{3})[/tex]

( Assuming √3 = 1.73 & π = 3.14 )

[tex]= \frac{3}{4} \times (6.28 - 5.19)[/tex]

[tex]= 0.75 \times 1.09[/tex]

[tex]= 0.8175[/tex]

∴ Area of the segment ≈ 0.8 m² (rounding to the nearest tenth)

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