From the top of a 200 foot lighthouse, the angle of depression to a ship on the ocean is 23 degrees.
How far is the ship from the base of the lighthouse?

I know I did it right by the key says its wrong. Please provide steps

Answer:

ln (1 + sin^2(x)) + C

Step-by-step explanation:

Note that sin(2x) = 2 sin(x) cos(x).

So, the integrand is rewritten as:

(2 sin(x) cos(x)) / (1 + sin^2(x) ).

Now, make the substitution u = sin(x), so that du = cos(x) dx.  Thus, in terms of the variable u, the integrand is

(2 u )/(1 + u^2).

Make another substitution v = 1 + u^2, so that dv = 2 u du, and the integrand in terms of v is

1 / v

Now, we integrate, and then back substitute to write that the indefinite integral is

ln |v| + C = ln |1 + u^2| + C = ln |1 + sin^2(x)| + C + ln (1 + sin^2(x)) +C, since 1 + sin^2(x) + 1 is positive for all real x.

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

We have to evaluate the given integral.

[tex] \displaystyle \rm = \int \dfrac{ \sin(2x) }{1 + \sin^{2} (x) } \: dx[/tex]

[tex] \displaystyle \rm = \int \dfrac{2 \sin(x) \cos(x) }{1 + \sin^{2} (x) } \: dx[/tex]

Now let us assume that:

[tex] \rm \longmapsto u = 1 + { \sin}^{2}(x)[/tex]

[tex] \rm \longmapsto \dfrac{du}{dx} = 2 \sin(x) \cos(x) [/tex]

[tex] \rm \longmapsto dx = \dfrac{1}{2 \sin(x) \cos(x) } \: du[/tex]

Therefore, the integral becomes:

[tex] \displaystyle \rm = \int \dfrac{1}{u} \: du[/tex]

[tex] \displaystyle \rm = \ln(u) + C[/tex]

[tex] \displaystyle \rm = \ln(1 + sin^{2}x ) + C[/tex]

Therefore:

[tex] \displaystyle \rm \longmapsto \int \dfrac{ \sin(2x) }{1 + \sin^{2} (x) } \: dx = \ln(1 + sin^{2}x ) + C[/tex]

Answer:

Not if you want it to be a positive number. You can but it will be a negative.

Step-by-step explanation:

Answer:

type b balls

Step-by-step explanation:

Answer:

b balls

Step-by-step explanation:

your mom

Answer:

Can you ask again with a picture? it's not clear with only text

Answer:

y=-5/4x+1

Step-by-step explanation:

y- y-coordinate= slope(x- x-coordinate)

y- (-4)= -5/4 (x - 4)

y - (-4)= -5/4x +5

move (-4) to the other side of the equal sign, the sign changes to +4

y= -5/4x +5 +4

y=-5/4x+1

Answer:D

Step-by-step explanation:the exterior angle of a triangle is equal to the sun of the opposite interior angles

120 =11x-6+10x

21x= 126

x=6

Answer:

8/12-1/5=7/15 reduce 8/12 to 2/3

Answer:

Slope: 2/3

Step-by-step explanation:

Take the first point (2,1) as (x1, y1), and,

the second point (5,3) as (x2, y2).

Using the slope formula to calculate the slope:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

= (3-1)/(5-2)

= 2/3

Hence, the slope is 2/3

Hope this helps and be sure to have a wonderful time ahead at Brainly! :D

Answer:

x[f]=at^2/2+v[i]t+x[i]

Brackets dennote a subscript.

You're given x[f], a, t,and v[i]. You can just plug in their values into the formula and solve for x[i]. The horizontal velocity is irrelevant, the height of the tower is the initial position of the arrow, and final position is gonna be when it reaches the ground,or 0.

Answer:

36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]= 36-[18-{14-(15-4)}]= 36-[18-{14-9}]=36-[18-5]=36-13=23

Step-by-step explanation:

36 - [18 - {14 - (15 - 4 ÷2 ×2)}]

= 36 - [18 - {14 - (15 - 2 ×2)}]

= 36 - [18 - {14 - (15 - 4)}]

= 36 - [18 - {14 - 11}]

= 36 - [18 - 3]

= 36 - 15

= 21

21

Answer:

1....... range...............

Answer:

they include Quartile ,Inter-quatile , range......................

Step-by-step explanation:

#1

[tex]\\ \sf\longmapsto (1+cosx)(1-cosx)[/tex]

[tex]\\ \sf\longmapsto 1-cos^2x[/tex]

[tex]\\ \sf\longmapsto sin^2x[/tex]

#2

[tex]\\ \sf\longmapsto \dfrac{1}{cot^2x}-\dfrac{1}{cos^2x}[/tex]

[tex]\\ \sf\longmapsto tan^2x-sec^2x[/tex]

[tex]\\ \sf\longmapsto 1[/tex]

Answer:

-0.5 is the larger average rate

Step-by-step explanation:

-3.142 is less than -0.5

Answer:

you're supposed to distribute the 4 to whatever "n" is

Answer: A

Step-by-step explanation:since the dot on -3 is solid that means it is included or equal to. since the dot on 2 is not filled in that means not equal to that number but everything up to it, including everything from -3 up to but not including 2

Step-by-step explanation:

(n-2xb)(4n-xb)

= 4n^2 - 8xbn - xbn + 2(xb)^2

= 4n^2 - 9xbn + 2(xb)^2

Answer:

Step-by-step explanation:

The ratio given:

Toni receives $160, which is 5 portions.

Each portion is:

Shai gets:

Mara receives:

Step-by-step explanation:

It is given

4x+3y=24

We can also write it as

3y=24−4x

 y=324−4x

Substituting x=0 in the given equation

 y=324−4(0)

 So we get 

 y=324

 By division 

 y=8 

 Substituting x=3 in the given equation 

 y=324−4(3)

 So we get

 y=312

 BY division 

 y=4

Answer:

(1 + x)(1 - x)

Step-by-step explanation:

Step 1: Rewrite 1 as 1^2

Step 2: Apply difference of two squares formula [tex]x^2 - y^2 = (x+y)(x-y)[/tex]

Therefore, the answer is (1 + x)(1 - x).

Answer: 9^4 is 6561 and 3^8 is 6561 so yes it is equivalent.

Brainliest if you liked answer

Answer:

Correct answer is 0.67

Step-by-step explanation:

Answer:

s(t)=200(1/2)^t/13

Step-by-step explanation:

Here's answer:

https://www.nysedregents.org/algebratwo/619/algtwo62019-mrs.pdf

The number of years it will take for  1/10 of this substance to remain is; 50 years

The half life formula is;

N(t) = N₀(¹/₂)^(t/t_1/2)

where;

N(t) is quantity of the substance remaining

N₀ is initial amount of substance

t is time elapsed

t_1/2 is half life

Thus;

S(t) = 200(¹/₂)^(t/15)

We want to find the time it will take 1/10 of the substance to remain. Thus;

1/10 = (200/200)(¹/₂)^(t/15)

1/10 = (¹/₂)^(t/15)

t/15 = In(1/10)/In(¹/₂)

t/15 = 3.32193

t = 49.88 ≈ 50 years

Read more about Half Life at; https://brainly.com/question/26689704

Answer:

B = 3.31662479

rounded to 3.32

Step-by-step explanation:

Pythagorean theorem: [tex]a^{2} + b^{2} = c^{2}[/tex]

A & B = the base and height

C = The diagonal line.

A & B can be base or height. ( base = 2 Height = 3. It can be [tex]2^{2} + 3^{2}[/tex] or [tex]3^{2} + 2^{2}[/tex] )

Because when you add it doesn't matter where each number is put.

I like doing b for the base, because there's a b in base, to make it easier for me. But you can do whatever.

A = 5

B = ?

C = 6

[tex]5^{2} + b^{2} + 6^{2}[/tex]

From here you will solve to get b.

[tex]5*5 + b^{2} = 6 * 6[/tex]

[tex]25 + b^{2} = 36[/tex]

25 - 25 + [tex]b^{2}[/tex] = 36 - 25

[tex]b^{2}[/tex] = 11

To under the exponent you have to [tex]\sqrt[/tex] it.

[tex]\sqrt{b_{2}}[/tex] = [tex]\sqrt{11}[/tex]

[tex]5^{2} + 3.32^{2} = 6^{2}[/tex]

B = 3.31662479

rounded to 3.32

Check your work :

[tex]5^{2} + 3.32^{2} = 6^{2}[/tex]

________

[tex] \: [/tex]

a² = c² - b²

a² = 6² - 5²

a² = 36 - 25

a² = 11

a = √11

a ≈ 3.316...

Answer:

By eating plants or other animals that contain nitrogen

Answer:

Step-by-step explanation:

the answer is (4 x 4)+2

Answer:

o (4+2) x4   is the expression that means 4 batches of 4+2 teaspoons of vanilla.

Step-by-step explanation:

1c = t(4 + 2) is created as t = tspoon but any letter cna represent and maybe the o means teaspoons so lets compare

we see the brackets on (4+2) x4 and use this. And if you must put a 0 in front then I would also convert to show without 0 and show both

As long as brackets separate the (4x 2) to the 4 batches it becomes a workable expression.

When algebra becomes understandable for multiplying we show 4(4 +2)

because in brackets its always add or subtract, but we recognise mainly as the question is worked out first for one part being  1 cupcake = 1c

so 1c = 4t+2t

then;  4c = 4t+2t

we need to multiply the set as a reverse to usual equations that try to make you find what t or c means.

so as we are not subtracting the numbers either side of the = we can just demonstrate a multiplication

4( 4+2)t = 0(4+2) x 4

equation in bold = expression given and chosen

they both mean the same so we know the first one in bold is an equation and the 2nd one as asked is an expression

Answer: Never(!) [assuming I understand/interpret the question properly]

Step-by-step explanation: The question wants to know how many months it will take for your neighbor's total cost be the same as yours, with three televisions. One has to interpret "total cost." I deem it to be the total accumulated costs, including installation. If you interpret it as the cost per month, then they charges are the same after the month the installation cast was paid. That's because the satellite provider charges per television, and 3*(13.32) is equal to the same 39.96/month charged by the cable provider. It the questions means total cumulative costs, the satellite customer will never exceed the cable customer's total bill, because of the installation fee ($75 for cable and free for satellite)

Step-by-step explanation:

imjteiuddjddjjdjjdjsh

usudtdbiemsihdhhdud yeh dhejuehhee

Hope's this helps

Answer:

Example Problem

1,234 ÷ 4 = 308 r 2

Step-by-step explanation:

I wasn't able to find a long division symbol so im sorry for any confusion!

         0308

4 Γ1234

       −0      

         12    

       −12    

         03  

       −0  

         34

       −32

         2

Answer:

see explanation

Step-by-step explanation:

Given

5y + 4 = 10 ( subtract 4 from both sides )

5y = 10 - 4 , that is

5y = 6

Thus 5y + 4 = 10 is equivalent to 5y = 6

Answer: y=  9x+6y=15

Step-by-step explanation: