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The value of the angle subtended by the distance of the buoy from the

port is given by sine and cosine rule.

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:

https://brainly.com/question/23427938

Answer:the answer is that if thruster b is going the opposite way it will stay in 1 place as thruster a is firing up to make the rocket fly if thruster b is going the opposite way it will just hover with that being said that's the answer

Step-by-step explanation:

Answer:.35,38% 3/5

Step-by-step explanation:Hope this helped

Answer: 0.35, 38% , 3/5

Step-by-step explanation:

3/5= 0.6= 0.60

38%= 0.38

0.35

Answer:

15/2

Step-by-step explanation:

y varies directly as x can be written as:

y & x

y = Kx

K = y/x

But from the question, we were told that:

y = 10

X = 20

K = y/x

K = 10/20

K = 1/2

The formula for the expression is:

y = Kx

y = 1/2 x

Now let us solve for y, when:

x = 15

y = 1/2 x

y = 1/2 x 15

y = 15/2

Answer:

When x = 15, y = 15/2

Step-by-step explanation:

Formula:  "y varies directly with x" comes out to y = kx symbolically.

Find the value of the constant of proportionality, k:  If y = 10 when x = 20, then this relationship becomes 10 = 20k, and k = 1/2.

Then the formula is y = (1/2)x.

When x = 15, y = 15/2

Answer:

B.zero

#carryonlearning

Answer:

D

Step-by-step explanation:

A vertical line parallel to the y- axis has an undefined slope

Answer:

D.

Step-by-step explanation:

It's not linear but it is decreasing.

Answer: Firstly, we take a look at the Y numbers to figure out if we're increasing or decreasing. Obviously, the numbers are going into the negatives so we know it's decreasing. After plotting the graph you'll see it's constant and in a straight line making it linear. So, your answer would be decreasing; linear.

The simplified form of the given expression is [tex]5\sqrt{2}[/tex].

Given expression,

[tex]5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex].

We have to simplify the above expression.

So, [tex]5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\\[/tex]

First solve for the square root,

[tex]5\sqrt{2\times2\times2} -\sqrt{3\times3\times2} -2\sqrt{2} \\\\10\sqrt{2} -3\sqrt{2}-2\sqrt{2} \\[/tex]

[tex]7\sqrt{2} -2\sqrt{2}[/tex]

[tex]5\sqrt{2}[/tex]

Hence the simplified form of the given expression is [tex]5\sqrt{2}[/tex].

For more details follow the link:

https://brainly.com/question/2719671

Given that

Money of a man = Rs. X

Money given to his wife = half of the money

= Rs. X/2

Money given to his son = 1/4th of the money

⇛Rs. X/4

Money given to his daughter = Rs. 1200

Total money

⇛ (X/2)+(X/4)+1200 = X

⇛ (2X+X+4800/4 = X

⇛ (3X+4800)/4 = X

⇛ (3X+4800) = 4X

⇛4X=3X+4800

⇛4X-3X = 4800

⇛X = 4800

⇛X-4800 = 0 is the required equation

⇛X = 4800

The money of the man = Rs. 4800 Ans.

also read similar questions: what if a man has 19 cows and he wants to give Half of them to his brother 1/4th to Son and 1/5th to daughter?

https://brainly.com/question/23613815?referrer

Following the proportions given in the table, it is found that in the 7th arrangement, there will be:

From the table, it can be seen that for the nth arrangement, the number of daisies and tulips follows a proportional relationship, that is:

Hence, in the 7th arrangement, there will be:

You can learn more about proportions at https://brainly.com/question/24372153

[tex] \sf \: I = P(1 + \frac{r}{n} {)}^{nt} - P \\ \sf = 5774(1 + \frac{13}{100} ) ^{1 \times 5} - 5774 \\ \sf= 5774 \times ( \frac{113}{100} ) ^{5} - 5774 \\ \sf= 10638.22 - 5774 \\ \sf = 4864.22[/tex]

Answer:

$4864.22 (approximate value)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

91 & 92

Step-by-step explanation:

Answer:

9.5671*9.5671=91.52940241

between 91 and 92

Hope This Helps!!!

Answer:

849,400

Step-by-step explanation:

hi

Answer:

I thinks it 849,400 bc you would round it up because it over half

Answer:

x=-3

Step-by-step explanation:

x^2+6x+9=0

Factor

(x+3)(x+3) =0

Using the zero product property

x+3 =0  x+3=0

x=-3   x=-3

Solution

x=-3

Answer:

$10.60

Step-by-step explanation:

Sarawong ends with $11.40, and we need to find his weekly allowance by working backward. First, we learn that he earned $6.10 of that total amount of money by washing the dog, so we can subtract the two values:

11.4 - 6.1 = 5.3

So, before washing the dog, Sarawong had $5.30. But he only received this after spending half of his weekly allowance, so $5.30 must be half of his weekly allowance. If we multiply $5.30 by 2, we should be able to find his weekly allownce.

5.3 × 2 = 10.6

Now, we can check our work. First, he spends half of his weekly allowance on candy. Half of 10.6 is 5.3, so he now has $5.30. Then, he earns $6.10 more by washing the dog. 5.3 + 6.1 = 11.4, which is the ending value. So, our work was correct! Hopefully that's helpful. :)

Answer:

Step-by-step explanation:

slope is 4    y is 3

Answer:

slope is 4 y = 3

Step-by-step explanation:

Plz mark as brainliest

Answer:2k

Step-by-step explanation:

-k+3k

-1k+3k

(-1+3)k

2k

Answer:

2k

Step-by-step explanation:

-k is the same as -1k so you can just solve it like that. Also, when adding terms with variables you just add the number in front (if they have the same variable). So -1k + 3k = 2k. Pretty much the same as -1 + 3, you just add a variable..

Work Shown:

sin(angle) = opposite/hypotenuse

sin(B) = AC/AB

sin(B) = 2/3

B = arcsin(2/3)

B = 41.8103 approximately

B = 41.81

Note: The arcsine function is the same as the inverse sine function, and that's denoted as [tex]\sin^{-1}[/tex] on many graphing calculators. Your calculator needs to be in degree mode.

Answer:

B) x^3-x^2-8x-2

Step-by-step explanation:

Expand the equation of g(x) to standard form

f(x) = x^3-4x+2

g(x) = x^2-4x+4

Subtract like terms in the equation and solve for the answer.

f(x) - g(x) = x^3-x^2-4x-4x+2-4

x^3-x^2-8x-2

Answer:

54 minutes

Step-by-step explanation:

4 Dozen is 48

So we will need to know how many 18 minutes it takes to back 144 donuts

So divide 144 by 48

Which is 3

So you will need 3, 18 minutes to make 144 donuts

Now multiply 18 by 3 which is 54

So it takes 54 minutes to bake 144 donuts

Hope this helps!

Step-by-step explanation:

4 Dozen = 4 x 12 = 48 every 18 minutes

144/48 = 3

3 x 18 = 54 minutes

Answer:

perimeter= 3.9+2.5+4.6+3.5+1.2= 15.7cm

Answer:

3

Step-by-step explanation:

18/6=3

Answer:

y = 4/7x

Step-by-step explanation:

(0,0)

(7,4)

up 4 right 7

4/7

y = 4/7x

Answer:

y = 4/7 x

Step-by-step explanation:

using rise/run = slope

rise = 4

run= 7

4/7 = slope

The x-values that will make the output values of the floor and ceiling functions equal are;

Option A: -8

Option D: 0

The complete question is;

At which x-values are the output values of the floor function g(x) = ⌊x⌋ and the ceiling function h(x) = ⌈x⌉ equal? Check all that apply.

A) –8

B) –5.2

C) –1.7

D) 0

E) 2.4

When it comes to floor functions and ceiling functions, they are always equal to each other when the x value is an integer.

Now, looking at the giving options the only integers we have are -8 and 0.

Thus, the only values in the options that would make the output values of the floor function and ceiling function equal are -8 and 0.

Read more on floor function and ceiling function at; https://brainly.com/question/7321190

Step-by-step explanation:

11 = 8(3q - 1)

11 = 24q - 8

11 + 8 = 24q

19 = 24q

19/24 = q

q = 0.791666666666666

q = 0.8 to 1 decimal place

Answer:

Question:which polynomial function in factored form represents the given graph below?

Answer:If a polynomial of lowest degree p has zeros at x=x1,x2,…,xn x = x 1 , x 2 , … , x n , then the polynomial can be written in the factored form: f(x)=a(x−x1)p1(x−x2)p2⋯(x−xn)pn f ( x ) = a ( x − x 1 ) p 1 ( x − x 2 ) p 2 ⋯ ( x − x n ) p n where the powers pi on each factor can be determined by the behavior of the graph

Step-by-step explanation:

CARRY ON LEARNING

BRAINLILEST NA LANG KUNG TAMA SALAMAT

[tex] \frac{8 - \sqrt{ - 36} }{2} \\ = \frac{8 - \sqrt{ 2 \times \: 2 \times 3 \times - 3} }{2} \\ = \frac{8 -2 \sqrt{ - 9} }{2} \\ = \frac{2(4 - \sqrt{ - 9} )}{2} \\ = 4 - \sqrt{ - 9} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

Unfortunately, the problem could not be solved because there is a minus in √36. This basically means that this problem has no answer. Remember, if there is a minus in a root system, that basically means that the answer is Un-defined.

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]