What is the arc length of the partial circle?

Answer:

1. The distance of the ship from the base of the lighthouse is approximately 1.24 miles

2. a)The horizontal distance the plane must start descending is approximately  190.81 km

b) The angle the plane's path will make with the horizontal is approximately 18.835°

3. The depth of the submarine is approximately 107.51 m

Step-by-step explanation:

The

1. From the question, we have;

The height of the observer above the water = 80 ft.

The angle of depression of the ship from the observer, θ = 0.7°

Let the position of the observer be 'O', let the location of the ship be 'S', let the point directly above the ship at the level of the observer be 'H', we have;

[tex]tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{HS}{OH}[/tex]

[tex]The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{HS}{tan(\theta) }[/tex]

HS = The height of the observer = 80 ft.

Therefore, we get;

[tex]The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{80 \, ft.}{tan(0.7^{\circ}) } \approx 6,547.763 \ ft.[/tex]

The distance of the ship from the base of the lighthouse ≈ 6,547.763 ft. ≈ 1.24 miles

2. The elevation of the plane, h = 10 km

The angle of the planes path with the ground, θ = 3°

Similar to question (1) above, the horizontal distance the plane must start descending, d = t/(tan(θ))

∴ d = 10 km/(tan(3°)) ≈ 190.81 km

The horizontal distance the plane must start descending, d = 190.81 km

b) If the pilot start descending 300 km from the airport, the angle the plane's path will make with the horizontal, θ, will be given as follows;

From trigonometry, we have;

[tex]tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}[/tex]

Where the opposite leg length = The elevation of the plane = 10 km

The adjacent leg length = The horizontal distance from the airport = 300 km

[tex]\therefore tan(\theta) = \dfrac{10 \, km}{300 \, km} = \dfrac{1}{3}[/tex]

[tex]\theta = arctan\left(\dfrac{1}{3} \right ) \approx 18.835^{\circ}[/tex]

The angle the plane's path will make with the horizontal, θ ≈ 18.835°

3. The angle at which the submarine makes the deep dive, θ = 21°

The distance the submarine travels along the inclined downward path, R = 300 m

By trigonometric ratios, we have;

The depth, of the submarine, 'd' is given as follows;

[tex]si(\theta)= \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{d}{R}[/tex]

∴ d = R × sin(θ)

d = 300 m × sin(21°) ≈ 107.51 m

The depth of the submarine ≈ 107.51 m

Answer:

the secound one

Step-by-step explanation:

hope it helped:3

Answer:

x = 4

Step-by-step explanation:

A trapezium is a quadrilateral (has four sides and four angles) with one pair of parallel sides. A trapezium is said to be isosceles if the bases are parallel, the two other sides known as the legs are equal and diagonals of the trapezium are equal to each other.

In trapezoid ABCD, BC and AD are the diagonals.

Hence BC = AD (property of isosceles trapezoid)

9x + 1 = 12x - 11

Simplifying:

12x - 9x = 1 + 11

3x = 12

Dividing both sides by 2:

x = 4

First, we have to simplify the first expression so we know what we're lookin' for.

-2-3n+3, -3n+1

We can scroll down the list of choices, and we can already see the answer.

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sorry if this doesn't help

Answer:

13,000

Step-by-step explanation:

10% of the original purchase price of $130,000.

130,000 x .10 = 13,000

Answer:

on the first one its 18 and the second one its 0 eighths

Step-by-step explanation:

i did it

The question was incomplete. The question should be like below :

Calculate 48×3/8 & choose which option is correct.

The options are :

1 ) 20

2 ) 18

3 ) 24

4 ) 16

The correct option is 2) 18

An expression is a mathematical sentence in which more than one number or variable is present with one or more mathematical operations.

The given expression is 48×3/8

Now, 48×3/8

       = 6×3

       = 18

The 2nd option is correct.

Learn more about expression here :

https://brainly.com/question/723406

#SPJ2

Answer:

Step-by-step explanation:

Answer:

19: 106

20: 79

21: 70

Step-by-step explanation:

Circle upper left

The central angles all add up to 360 degrees

BC + CD + 148 = 360

But CD = BC

2BC + 148 = 360            Subtract 148 from both sides

2BC = 360 - 148             Combine

2BC = 212                       Divide by 2

BC = 106

20

3 of the 5 arcs are marked as being equal.

Let each of them be called  = x

3x + 41 + 82 = 360          Combine

3x + 123  = 360                Subtract 123 from Both sides.

3x = 360 - 123

3x = 237

x = 237 / 3

x = 79

BC = 79

21

Unless DE and FC are diameters, this can't be solved. I will assume they are.

FB + 48 + 22 = 180.

FB + 70 = 180

FB = 110

===========

FC = FB + BD + DC

180 = 110 + 22 + DC

180 = 132 + DC

DC = 180 - 132

DC = 48

===========

BC = BD + DC

BC = 22 + 48

BC = 70

Answer:

117

Step-by-step explanation:

Answer:

help me first on this question

Step-by-step explanation:

Answer:

I think it’s H

Step-by-step explanation:

Answer:

The answer is H bacause it has the most number of colours

Answer:

4g+8m

Step-by-step explanation:

7m+m=8m 11g-7g=4g

Answer:

12 53,9

Step-by-step explanation:

Answer:

12,53,9

Step-by-step explanation:

:PPP

Answer:

Assuming what you meant was [tex]\frac{1}{2}x + 3 = -x +7[/tex], the answer would be x = 8

Answer:

Step-by-step explanation:

Given function:

The complete video games can be expressed as positive integers or whole numbers, so the domain is whole numbers.

Correct choice is (4)

Answer:

Whole Number

Explanation:

Domain : The set of all the input values (i.e. the value of x ) in the function is called domain

The daily cost of production in a video game factory is calculated using c(x) = 400 + 25x

Cost expression : C(x) = 400 + 25x

Cost expression : C(x) = 400 + 25x

As x defines the number of complete video, since number of video cannot be negative.

1) Integers : integers are the numbers which can be positive, negative or zero, but cannot be a fraction

As, number of videos cannot be negative

so, x cannot be any integers

So, Integers is not the domain

2) Positive real numbers : Real numbers are the numbers which include both rational and irrational numbers.

As the x represent the complete number of video games, thus, x cannot be irrational

Hence, Positive real numbers is not the domain

3) Positive Rational Number : a number is expressed in the form of p/q then it is a rational number

The number of videos are in the complete number, so a fraction cannot be a complete number, thus, rational number cannot be a domain.

4) Whole Number : Whole numbers include natural numbers that begin from 1 onwards

As Numbers of videos are the complete number, and they are always positive, which is the defination of whole number, Domain is whole number

Answer: u multiply them all together

Step-by-step explanation:nugggybi8ybggg8yiubgy8iibgu777777777b8u

Answer:

13

Step-by-step explanation:

Answer:

c=13

Step-by-step explanation:

Hey There!

c+11=24

When looking at this problem you want to get the variable on one side (c) and the constant on the other ( any whole number)

as you can see we need to get rid of the 11 on the left side

to do that we subtract 11 but whatever you do to one side you have to do to the other side

11-11 cancels out

24-11=13

so we can conclude that

c=13

Answer:

12m^2+14m

Step-by-step explanation:

The "^means exponet" Hope I made your day

:)

9514 1404 393

Answer:

  Vertex: (-1, 4)

  Maximum: f(-1) = 4

  Increasing: (-∞, -1)

  Decreasing: (-1, ∞)

Step-by-step explanation:

The equation can be written in vertex form by "completing the square."

First factor out the leading coefficient from the x-terms.

  f(x) = -(x² +2x) +3

Then add the square of half the x-coefficient inside parentheses. Add the opposite of that amount outside parentheses.

  f(x) = -(x² +2x +1) +3 +1

Write in vertex form.

  f(x) = -(x +1)² +4 . . . . . . . compare to a(x -h)² +k

You can see that the vertex is (h, k) = (-1, 4), and that the vertical scale factor 'a' is negative. This means the vertex is the maximum and the parabola opens downward.

The function will be increasing to the left of the maximum, decreasing to its right.

__

Vertex: (-1, 4)

Maximum: f(-1) = 4

Increasing: (-∞, -1)

Decreasing: (-1, ∞)

Graph: see attached

Answer:

katelyn

Step-by-step explanation:

you divide distance by time to get rate, and katelyn has a faster rate because 210/3 is more than 540/8

Answer:

Katelyn drove faster

t=d/s

s=d/t

d=s*t

Step-by-step explanation:

s=d/t is what we are using to find the speed

Katelyn- 210/3=70

Samantha-540/8=67.5

70>67.5

Katelyn drove faster

Answer:

$625

Step-by-step explanation:

to find the original divide the sale price by the decreased percentage. 125/%20(or .20)

Answer:

78

Step-by-step explanation:

probability of getting a 5 which is 78.

Another way to look at this is that if we know the probability of the result being 5, then the probability of it not being 5 is just one minus that probability. We know that 5 is just one out of the 8 possibilities, so

P5=18

So the probability of not 5 is

Pnot5=1−P5=1−18=78

I have big brain

Answer:

139 e7

Step-by-step explanation:

I'm not good at scientific notation but I think I'm getting better....

Answer:

1.39 x 10^9

Step-by-step explanation:

Answer:

56÷x+8

Step-by-step explanation:

Answer:

B: z*=1.645

Step-by-step explanation:

Khan academy step by step

Answer: z*=1.645

Step-by-step explanation: