A sailboat leaves St. Thomas bound for an island in the British West Indies, 200 miles away. Maintaining a constant speed of 18 miles per hour, but encountering heavy crosswinds and strong currents, the crew finds after 4 hours that the sailboat is off course by 15°.
(a) How far is the sailboat from the island at this time?
(b) Through what angle should the sailboat turn to correct its course?
(c) How much time has been added to the trip because of this? (Assume that the speed remains at 18 miles per hour.)

Answers

Answer 1

The distance of the sailboat from the island at this time will be 131.78 miles.

How to calculate the distance?

The distance of the sailboat from the island will be calculated by using the law of cosines. This will be:

a² = (18 × 4) + 200² - (2 × 72 × 200 cos 15°)

a² = 72 + 200² - (144 × 200 cos 15°)

a = 131.78 miles.

The angle that should be used by the sailboat to correct its course will be:

= 180° - (sin 15°/131.78)

= 180° - 22.95°

= 157.05°

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Related Questions

help please
1.) Write in words the decimal 123.0047.



Write in fractional notation and simplify.

2.) 0.91 3.) 2.769



Write in decimal notation.

4.) 74 over 1000 5.) 37047 over 10000 6.) 756 9 over 100



Which decimal number is greater?

7.) 0.07 or 0.162 8.) 8.049 or 8.0094


Round the next decimal number, 5.6783, to the indicated decimal place.

9.) To the Unit 10.) To the Thousandth 11.) To the Tenth

Answers

1.) One hundred twenty-five and forty-seven thousandths

2.) 91/100.

3.) 2769/1000

4.) 0.074

5.) 3.705

6.) 75.69

7.) 0.162 is greater than 0.07

8.) 8.049 is greater than 8.0094

9.) 6

10.) 5.678

11.) 5.7



In two or more complete sentences, compare the number of x-intercepts in the graph of f(x)=x2 to the number of x-intercepts in the graph of g(x)= (x+2)2 -7

Answers

Because f(x)=x^2 is the parent function of a quadratic, it has one x-intercept at (0,0), no shifts up or down. But because g(x)=(x+2)^2-7 is a quadratic being shifted 2 units to the left and most importantly 7 units down, the function will cross the x-intercept 2 times.

I hope this is the answer you were looking for!

There is exactly 1 pair of parallel sides in the following shape.

Answers

The 7 unit side and the unit 10

since they are both perpendicular to the same 8 unit side

:)

How many subsets does the following set (4,5,6,7,8) have?​

Answers

Answer:Number of subsets will be given by 2^n, where n is the number of elements in the set.

Step-by-step explanation:

Number of elements is 5. Therefore, the number of subsets that can be formed from the given set is 2^5 = 32.

Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.

Use the drop-down menus to explain how to solve this problem.

First multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.

Answers

Answer:

$149 - skateboard price

$52 - carly's money

$20 × 5 cars = $100

$100 + $52 = $152

$152 - $149 = $3 left

I will give the brainiest if you get it right.

Answers

Answer:

  1 ≤ x < 7/4

Step-by-step explanation:

The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.

Inequality solutions

  f(4x -3) ≥ f(2 -x²)

  4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)

  x² +4x -5 ≥ 0 . . . . . subtract 2-x²

  (x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1

The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.

Domain restrictions

The domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values

Left side

  -8 < 4x -3 < 4

  -5 < 4x < 7

  -5/4 < x < 7/4

Right side

  -8 < 2 -x² < 4 . . . . . right side is always true

  x² < 10 . . . . . . . . . . . add x² +8

  |x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction

Solution

With the given domain restrictions on f(x), the inequality will be true on the interval ...

  1 ≤ x < 7/4

__

Additional comment

The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.

This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.

<95141404393>

Determine the type of symmetry of r=-7+ 2cos3ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) none of these
C)line /2
D) polar axis

Answers

well, hmmm to check for polar symmetry, hmmm say we simply replace the value for either "r" or "θ" or both in the original equation, if the equation rendered is the same as the original, there you have it, symmetry, so let's do that.

[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=-7+2cos(3\theta )\implies (-r)=-7+2cos[3(-\theta )]\implies -r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\implies r=7-2cos(3\theta )\impliedby \textit{woopsie, no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=-7+2cos(3\theta )\implies r=-7+2cos[3(-\theta )]\implies r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\impliedby \textit{low and behold\qquad \Large \checkmark}[/tex]

now, we could run a test for "the pole" or namely the origin by simply changin r = -r, however we already know where the symmetry is, so no need.

Check the picture below.


What is the area in polynomial form

Answers

Answer:

[tex] \orange{ \boxed{ \sf{ ( \: {x}^{2} + 11x + 18 \: ) \: sq. \: units}}}[/tex]

Solution :

Area = lenght x width

Lenght = x + 9

Width = x + 2

[tex] \sf \green{area \: = \: (x + 9)(x + 2)} \\ \sf \green{ = \: { {x}^{2} + 11x + 18}} [/tex]

Answer:

[tex]x^2+11x+18\: \sf(square\:units)[/tex]

Step-by-step explanation:

To use the area model of solving multiplication and division problems, calculate the area of each of the colored rectangles and add them together.

Area of a rectangle = Length × Width

Area of blue rectangle:  [tex]x \times x = x^2[/tex]

Area of pink rectangle:  [tex]x \times 9 = 9x[/tex]

Area of green rectangle:  [tex]2 \times x=2x[/tex]

Area of orange rectangle:  [tex]2 \times 9=18[/tex]

Area of entire rectangle = blue + pink + green + orange

                                        = [tex]x^2+9x+2x+18[/tex]

                                        = [tex]x^2+11x+18\: \sf(square\:units)[/tex]

If 1 penguin has a mass of 6 kg, what is the mass of 9 penguins?

Answers

Answer:

54 kg

Step-by-step explanation:

We need to multiply!!

6 x 9 = 54

Have an amazing day!!

Please rate and mark brainliest!!

A birthday cake weighs 7/8 pounds. If 2/3 of the cake is flour, how much is flour

Answers

Don’t know but you do have to subtract
5/24 is the amount for flour

-5 x + 10 -20 need help with this

Answers

Answer:

-5(x+2)

Step-by-step explanation:

Robin got home from school
at 3:45. She spent 2 hours
working on her homework, a
half an hour walking the dog,
and forty-five minutes eating
dinner with her family. Then
she began reading her book.
At what time was she finished
eating dinner?

Answers

Answer:

She was finished with dinner at 6:50

Step-by-step explanation:

3:45 + 2 = 5:45

5:45 + 30 = 6:05

6:05 + 45 = 6:50

3:45 + 2 = 5:45
5:45+ 30= 6:15
6:15 + 45 = 7:00
Hope this helped

can someone please help me with this

Answers

Answer:

"4 or less, let it rest. 5 or more, raise the score."

Step-by-step explanation:

1) 5.57, 5.62, 5.59

2) 2.349, 2.352, 2.346, 2.354

3)

0.7

0.3

1.5

3.4

4)

3.74

0.93

0.33

1.56

I hope this helps! Have a lovely day!! :)

(I would appreciate brainliest!!)

A Cyclist rides her bike of a rate of 18 Kilometers per hour. What is this rate in Kilometers per minute? How many Kilometers will the cyclist travel in 20 minutes? Do not Round your answers.

Answers

Step-by-step explanation:

18 ÷ 60 = 0.3

so 0.3 km per min.

0.3 × 20 = 6

so 6 km per hour

What is the answer for this question?

Answers

Answer:

is this from flvs?

Step-by-step explanation:

Solve | x + 6| - 7 = 8

A: x= -9 and x = -21

B: x = 9 and x = -9

C: x = -9 and x = 21

D: x = 9 and x = -21

Answers

Answer:

x = 9,-21

Step-by-step explanation:

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Cancel absolute sign and add plus-minus to 15:

[tex]\displaystyle \large{x+6=\pm 15}[/tex]

Transport 6 to subtract ±15:

[tex]\displaystyle \large{x=\pm 15-6}[/tex]

Consider:

[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Second Method

Given:

[tex]\displaystyle \large{|x+6|-7=8}[/tex]

Transport -7 to add 8:

[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]

Absolute Function Property:

[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]

Consider both intervals:

When x ≥ a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]

Transport 6 to subtract 15:

[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]

When x < a then:

[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]

Transport -6 to add 15:

[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]

Transport negative sign to 21:

[tex]\displaystyle \large{x=-21}[/tex]

Solution:

[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]

__________________________________________________________

Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!

A square pyramid has a base with a side length of 7.5 feet and lateral faces with heights of 16 feet. Write an expression that can be used to find the surface area, in square feet, of the square pyramid.

Please provide an expression, not just the surface area please :)

Answers

Check the picture below.

so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]

please help I'm so stuck on this​

Answers

Answer:

divide the anser in the pasage

Step-by-step explanation:

divide the two numbers

What is the value of [5] – 1 – 5] - ( – 5)?

Answers

Value is -1 , Hope this helps.

Roderick has a dog that has a mass of 9 kilograms what is the mass of the dog in grams

Answers

Answer:

9000 grams

Step-by-step explanation:

multiply the mass value by 1000

Factor completely 4a^2-b^2-2a+b GUYS HELP THERE ARENT ANY CORRECT ANSWERS ON BRAINLY URGENT

Answers

Answer:

(2a-b)(2a+b-1)

Step-by-step explanation:

6.
Part I: Suppose a prism has a square base with each side of length 3.75 cm and a height
of 5.65 cm. Use the formula below to find the volume. Show your work and round your
answer to the nearest hundredth. (5 points)

Answers

Answer:

79.45401²

Step-by-step explanation:

[tex]1)\ V=B\ Sh[/tex]

[tex]\therefore\ V=3.15\times 3.75\times 5.65[/tex]

[tex]=79.403125[/tex]

[tex]\approx 79,45\ cm^3[/tex]

I hope this helps you

:)

Rounded to the nearest hundredth, the volume of the prism is approximately 79.50 cm^3.

To find the volume of a prism, we use the formula:

Volume = Base Area * Height

In this case, the prism has a square base with each side of length 3.75 cm and a height of 5.65 cm. The formula for the area of a square is:

Base Area = Side Length^2

So, the base area can be calculated as:

Base Area = 3.75 cm * 3.75 cm = 14.0625 cm^2

Now, we can find the volume using the formula:

Volume = Base Area * Height

Volume = 14.0625 cm^2 * 5.65 cm

Volume ≈ 79.5025 cm^3

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how many positive integers are between 28/3 and 83/5

Answers

Answer: ur dad

Step-by-step explanation:

lol

There are 7 positive integers in between 28/3 and 83/5.

What is an integer?

An integer is a whole number (not a fractional number) that can be positive, negative or zero.

Given that;

Two fractions are;

28/3 and 83/5.

Now, Write fraction into decimal form as;

28/3 = 9.33

83/5 = 16.6

So, All Integers in between 9.33 and 16.6 are;

⇒ 10, 11, 12, 13, 14, 15, 16

Thus, There are 7 positive integers in between 28/3 and 83/5.

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Khairi has only 20¢ and 50¢ coins in his coin bank. There are twice as
many 20¢ coins as 50¢ coins. How many 20¢ coins are there in the coin
bank if all the coins add up to $17.10?

Answers

Answer:

There is 43 20¢ in the coin bank.

what is 5b^-2/b^-3? I need to know

Answers

Answer:

5b

Step-by-step explanation:

Hope this helps <3

What is the least common multiple of 324 and 245?

Answers

the lcm would be 79380

Step-by-step explanation:

5×7×7

2×2

×3×3×3×3

muliply all the 3 numbers and then you get 79380

simplify and tell the function

Answers

Answer:

2x - 5

Step-by-step explanation:

I just know and am positive with my answer. Hope this helped and have a good one!

Can i have help on #3 and #2? Thanks<3

Answers

Answer:

I don't know if these are right

2.756

3. 1,426.42

For a ride on a rental scooter, Goran paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Goran's ride was $23.79. For how many minutes did Goran ride the scooter?

Answers

Answer:

Step-by-step explanation:

he paid a 3 dollar fee so we can remove that 23.79-3 = 20,79

now we devide 20,79 by 11 or 189 minutes.

solve please. find volume

Answers

The figure given in the image is a cuboid which have 3 sides, with Length, breadth and height, it's basically a 3-D shape, so here for volume of the cuboid, we can just multiply all the sides and we will be just done then after writing the SI unit of volume against it

[tex]{:\implies \quad \sf So,\:\: Volume=4\dfrac{2}{5}\times 10\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=\bigg(\dfrac{20+2}{5}\bigg)\times 10\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=\dfrac{22}{5}\times 10\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=22\times 2\times 3}[/tex]

[tex]{:\implies \quad \sf Volume=44\times 3=\boxed{\bf{132\:\: m^{3}}}}[/tex]

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