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A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answers

Answer 1
check the picture below.

now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.

and 29' is just 29/60 degrees or about 0.48 degrees.

so 16°23' is about 16.38°, and 49°29' is about 49.48°

[tex]\bf tan(16.38^o)=\cfrac{200}{a+b}\implies a+b=\cfrac{200}{tan(16.38^o)} \\\\\\ \boxed{b=\cfrac{200}{tan(16.38^o)}-a} \\\\\\ tan(49.48^o)=\cfrac{200}{b}\implies \boxed{b=\cfrac{200}{tan(49.48^o)}}\\\\ -------------------------------\\\\ \cfrac{200}{tan(49.48^o)}=\cfrac{200}{tan(16.38^o)}-a\\\\\\a=\cfrac{200}{tan(16.38^o)}-\cfrac{200}{tan(49.48^o)}[/tex]

make sure your calculator is in Degree mode.
WILL GIVE BRAINLIEST ANSWER!!Help, Please! A Person Is Watching A Boat From The Top Of A Lighthouse.
Answer 2

The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]

Further explanation:

The Pythagorean formula can be expressed as,

[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for tan of angle a can be expressed as

[tex]\boxed{\tan a = \frac{P}{B}}[/tex]

Explanation:

The perpendicular AB. The length of AB is [tex]200{\text{ feet}}.[/tex]

The angle of depression is [tex]\angle ACB = {14^ \circ }52'.[/tex]

One degree has 60 minutes.

[tex]{1^ \circ } = 60'[/tex]

[tex]\begin{aligned}\angle ACB &= 49 + \frac{{29}}{{60}}\\&= 49 + 0.48\\&= 49.48\\\end{aligned}[/tex]

The angle ADB is [tex]\angle ADB = {16^ \circ }23'.[/tex]

[tex]\begin{aligned}\angle ADB&= {16^ \circ }23' \\&= 16 + \frac{{23}}{{60}}\\&= {16.38^ \circ }\\\end{aligned}[/tex]

In triangle ABC.

[tex]\begin{aligned}\tan\left( {{{49.48}^\circ }} \right)&=\frac{{200}}{{BC}}\\1.13&= \frac{{200}}{{BC}}\\BC &= \frac{{200}}{{1.13}}\\BC &= 177{\text{ feet}}\\\end{aligned}[/tex]

In triangle ABD.

[tex]\begin{aligned}\tan \left( {{{16.38}^ \circ }} \right)&= \frac{{200}}{{BD}}\\0.30&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{0.30}}\\BD &= 666.67{\text{ feet}}\\\end{aligned}[/tex]

The distance boat can travel can be obtained as follows,

[tex]\begin{aligned}DC& = BD - BC\\&= 666.67 - 177\\&= 489.67{\text{ feet}}\\\end{aligned}[/tex]

The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]

Kindly refer to the image attached.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: perpendicular, person watching boat, top, lighthouse, angle of depression, angle of elevation, 200 feet tall, travel, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.

WILL GIVE BRAINLIEST ANSWER!!Help, Please! A Person Is Watching A Boat From The Top Of A Lighthouse.

Related Questions

The stack on the left is made up of 15 pennies, and the stack on the right is also made up of 15 pennies. If the volume of the stack of pennies on the left is 360 mm3, what is the volume of the stack of pennies on the right in cubic millimeters? Use 3.14 for pi. (Hint: only enter numerals in the answer blank)

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Answer:

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Step-by-step explanation:

a culture started with 5000 bacteria. after 2 hours, it grew to 6500 bacteria. Predict how many bacteria will be present after 18 hrs

Answers

First find the rate of growth
The formula is
A=p e^rt
A 6500
P 5000
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E constant
T 2 hours
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R=0.1312 (rate of growth)

Now predict how many bacteria will be present after 18 hrs
A=p e^rt
A ?
P 5000
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E constant
T 18 hours

A=5,000×e^(0.1312×18)
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An open box is formed by cutting squares with side lengths of 3 inches from each corner of a square piece of paper. what is a side length of the original paper if the box has a volume of 675 cubic inches?

Answers

The volume formula for a square or a rectangle, even, is V=l*w*h
Here, we are given our volume as 675, now we just have to find everything else, right?! Well, if you have a square, all 4 sides are the same exact length, so the length and the width of our formula are going to be the same so we only have to worry about finding a value for one and then use it twice. If you have a square of side length x and you cut 2 squares out of each side measuring 3 inches each, you are cutting away 6 inches. So the side now reflects a length of x - 6. Which is used for the length and the width in our formula. The height of the box will be 3 inches, or in other words, what you cut away from each corner to make a box in the first place! So our formula will look like this: 675 = (x - 6)(x - 6)3. Easiest thing to do is to divide away the 3 to get 225 = (x - 6)(x - 6). Now expand that by FOILing:
[tex]225= x^{2} -12x+36[/tex]
Set it equal to 0 to solve for x, the length and width of each side by moving the 225 over to the other side:
[tex] x^{2} -12x-189=0[/tex]
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Line LJ is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain.

Answers

A tangent line to a circle is perpendicular to the radius drawn to the tangent point.

If tangents are constructed through points L and J, then the tangents are perpendicular to the diameter and parallel to each other.

URGENT!!!!!!!!!!11!! Plz HElP

A school typically sells 500 yearbooks each year for $50 each. the economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price.the revenue for the yearbook sales is equal to the number of yaerbooks sold times the price of the yearbook. let x represent the number of $5 decreases in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). find the values of a and b.

Answers

The answer is a=100 and b=5

From a group of six people, two individuals are to be selected at random. how many possible selections are there

Answers

Final answer:

To find the number of possible selections when choosing two individuals from a group of six people at random, use the combinations formula C(6, 2) = 6! / (2!(6-2)!) which equals 15 possible selections.

Explanation:

From a group of six people, selecting two individuals at random involves calculating the number of combinations. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where 'n' represents the total number of items and 'k' represents the number of items to choose.

In this scenario, with n being 6 (the total number of people) and k being 2 (the number of people to select), the calculation would be:

C(6, 2) = 6! / (2!(6-2)!) = (6 * 5) / (2 * 1) = 15

Therefore, there are 15 possible selections when choosing two individuals from a group of six people at random.

The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24.
What is the value of x? 
What is the value of y?

Answers

Answer:

[tex]\text{The value of x and y is } x=5, y=29[/tex]      

Step-by-step explanation:

Given the product of two expressions

[tex]4z^2+7z-8\text{ and }-z+3\text{ is }-4z^3+xz^2+yz-24[/tex]

we have to find the value of x and y

First we find the product of

[tex]4z^2+7z-8\text{ and }-z+3[/tex]

[tex](4z^2+7z-8)(-z+3)[/tex]

Opening the brackets

[tex]4z^2(-z+3)+7z(-z+3)-8(-z+3)[/tex]

Using distributive property, a.(b+c)=a.b+a.c

[tex](-4z^3+12z^2)+(-7z^2+21z)+(8z-24)[/tex]

Combining like terms

[tex]-4z^3+(12z^2-7z^2)+(21z+8z)-24[/tex]

[tex]-4z^3+5z^2+29z-24[/tex]

which is required product.

[tex]\text{Now compare above product with given product }-4z^3+xz^2+yz-24[/tex]

[tex]x=5, y=29[/tex]

What are the vertical asymptotes of the function f(x) = the quantity of 2 x plus 8, all over x squared plus 5 x plus 6? x = −3 and x = −2 x = −3 and x = 2 x = 1 and x = −2 x = 1 and x = 2?

Answers

for this question the answer would be x=-3 and x=-2

Flying against the wind, a jet travels 4400mi in 8 hours. Flying with the wind, the same jet travels 5820mi in 6 hours. What is the rate of the jet in still air and what is the rate of the wind?

Answers

Let J = rate of jet in still airLet W = rate of wind Distance formula:  d = rt   /   r = d/t Flying against the wind the jet flies at a rate of  J - W = 1860 miles/3 hours = 620 miles per hourFlying with the wind the jet flies at a rate of J+W = 9180 miles/9 hours = 1020 miles per hour The average of these 2 rate is the speed of the jet in still air J = (620+1020)/2 = 820 miles per hour J - W = 620  

820 - W = 620
W = 820 - 620 = 200 miles per hour The jet in still air flies at a rate of 820 mph(miles per hour)The wind speed is 200 mph(miles per hour)

Factoring help. Need step by step guidance ....

35n ^ 2 + 22n + 3

Answers

35 = 7 * 5 

(7n + 3)(5n + 1)
= 35n^2 + 7n + 15n + 3
= 35n^2 + 22n + 3

so answer is
(7n + 3)(5n + 1) 

Find the exact value of the following limit: the limit as x goes to 0 of the quotient of the quantity e raised to the 3 times x power minus 3 times x minus 1 and x squared.
Type answer as a decimal.

Answers

[tex]\displaystyle \lim_{x\to 0}\dfrac{e^{3x}-3x-1}{x^2}=\\ \lim_{x\to 0}\dfrac{(e^{3x}-3x-1)'}{(x^2)'}=\\ \lim_{x\to 0}\dfrac{3e^{3x}-3}{2x}=\\ \lim_{x\to 0}\dfrac{(3e^{3x}-3)'}{(2x)'}=\\ \lim_{x\to 0}\dfrac{9e^{3x}}{2}=\\ \dfrac{9e^{3\cdot0}}{2}=\dfrac{9}{2}=4.5 [/tex]

The value of the limit is 4.5 .

What is limit?

An output value that a function approaches for the specified input values is referred to as a limit.

Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

The given limit is,

F(x) = [tex]lim_{x- > 0} (e^{3x}-3x-1)/x^2[/tex]

Differentiate with respect to x,

F'(x) = [tex]lim_{x- > 0} d/{dx}(e^{3x}-3x-1)/x^2[/tex]

       = [tex]lim_{x- > 0} d/{dx}(e^{3x}-3x-1)/d/dx(x^2)[/tex]

       = [tex]lim_{x- > 0}\ 3e^{3x}-3/2x[/tex]

Differentiate again with respect to x,

F''(x) = [tex]lim_{x- > 0}\ d/dx(3e^{3x}-3/2x)[/tex]

        = [tex]lim_{x- > 0} (9e^{3x)}/2}[/tex]

        = [tex]9 .e^0/2[/tex]

        = [tex]9/2[/tex]

        = [tex]4.5[/tex]

The limit of the function is 4.5 .

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One number is 6 less than another. their sum is 12 find the larger number

Answers

y=x-6

x+y=12

x+x-6 =12

2x-6=12

2x=18

x=18/2 =9

x=9

y =9-6 =3

9+3 =12

Larger number is 9


If BE−→ B E → bisects ∠ABD and m∠ABE = 62°, find m∠ABD

Answers

Given:
Line segment BE bisects ∠ABD as shown in the figure.

Therefore
m∠ABE = m∠DBE
and
m∠ABD = m∠ABE + m∠DBE

Because m∠ABE = 62°, therefore m∠DBE = 62°, so that
m∠ABD = 62° + 62° = 124°

Answer: m∠ABD = 124°

Based on the definition of an angle bisector, m∠ABD = 124°.

What is Angle Bisector?

An angle bisector is a line segment that divides an angle into two smaller angles that are congruent.

BE is an angle bisector, therefore:

m∠ABD = 2(m∠ABE)

m∠ABD = 2(62)

m∠ABD = 124°

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What is the vertex of y=-6(2.5-x)(x-5.5)?

Answers

hello : 

 y=-6(2.5-x)(x-5.5) = -6(2.5x -13.75 -x² +5.5x)
y = -6(-x²+8x -13.75)
 y = 6x²-48x+82.5
note : 
if f(x) = ax²+bx +c   the vertex is the point : ( -b/2a ; f(-b/2a))
a=6  b=-48 c = 82.5 .......calculate
-b/2a = -(-48)/2(6)= 4
f(4) =6(4)²-48(4)+82.5 =96 - 192 +82.5 = -13.5

Why does a bag of chips puff up in an airplane?

Answers

Because of the pressure differences.

Evaluate S5 for 600 + 300 + 150 + … and select the correct answer below

Answers

Answer:

Hence,

[tex]S_5=1162.5[/tex]

Step-by-step explanation:

We are asked to evaluate:

[tex]S_5[/tex]

We are given a geometric series.

( since each term of the series are in geometric progression as each term is half of the previous term of the series.

i.e. we have a common ratio of 1/2 )

Also, we know that sum of n terms in geometric progression is given by:

[tex]S_n=a(\dfrac{1-r^n}{1-r})[/tex]

where r is the common ratio.

a is the first term of the series.

Here we have:

[tex]a=600\ ,\ r=\dfrac{1}{2}[/tex]

Hence,

[tex]S_5=600(\dfrac{1-(\dfrac{1}{2})^5}{1-\dfrac{1}{2}})\\\\\\S_5=600(\dfrac{2^5-1}{2^4}})\\\\\\S_5=600(\dfrac{31}{16})\\\\\\S_5=1162.5[/tex]

The sum of the first five terms of the geometric progression 600 + 300 + 150 + …  is 1162.5.

What is the ratio of geometric progression?

A geometric progression is the series of numbers where the ratio of the two consecutive numbers is always the same.

As it is given to us the sequence 600, 300, 150 is a geometric progression. Therefore, the first term of the progression is 600, while the ratio between the two terms are,

[tex]r = \dfrac{300}{600} = \dfrac{1}{2}[/tex]

Now,  we know that the sum of the geometric sequence of the first 5 terms can be written as where the value of the n is 5,

[tex]S=a\dfrac{(1-r^n)}{(1-r)}[/tex]

[tex]S=600\dfrac{(1-(\dfrac{1}{2})^n)}{(1-(\dfrac{1}{2}))}[/tex]

[tex]S = 1162.5[/tex]

Hence, the sum of the first five terms of the geometric progression 600 + 300 + 150 + …  is 1162.5.

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What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?

Answers

u can find the common ratio by dividing the 2nd term by the first term
r = -9/3 = -3

an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==

Answer: [tex]\ a_{n}=3(-3)^{n-1}[/tex]


Step-by-step explanation:

Given: A geometric sequence with its first term [tex]a_1=a=3[/tex]

and second term [tex]a_2=-9[/tex]

We know that the common ratio in of a geometric sequence=[tex]\frac{a_{n}}{a_{n-1}}[/tex]

Thus, common ratio [tex]r=\frac{-9}{3}=-3[/tex]

We know that the explicit rule for geometric sequence is written as

[tex]a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }][/tex]

Thus, the explicit rule for the given geometric sequence is [tex]\ a_{n}=3(-3)^{n-1}[/tex] for every n ,a natural number.

Indicate the equation of the given line in standard form. The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)

Answers

the equation given has a slope of 2/3. A parallel line will have the same slope.

y = mx + b
slope(m) = 2/3
(1,-2)...x = 1 and y = -2
sub and find b, the y int
-2 = 2/3(1) + b
-2 = 2/3 + b
-2 - 2/3 = b
-6/3 - 2/3 = b
- 8/3 = b

equation is : y = 2/3x - 8/3...but we need it in standard form

y = 2/3x - 8/3
-2/3x + y = -8/3...multiply by -3
2x - 3y = 8 <== standard form

what is (13x+9k)+(17x+6k) simplified

Answers

Final answer:

The expression (13x+9k)+(17x+6k) simplifies to 30x + 15k. This is done by adding the coefficients of the like terms which in this case are 13x with 17x, and 9k with 6k.

Explanation:

The expression (13x+9k)+(17x+6k) is a mathematical expression in algebra with two variables, x and k. The goal here is to simplify the expression by combining like terms. In mathematics, 'like terms' refer to the terms that have the same variables and powers. The coefficients of the like terms can be different.

Now to simplify this expression, we add the coefficients of the like terms. The like terms here are 13x and 17x, and also 9k and 6k.

Add 13x and 17x, you get 30x. And when you add 9k and 6k, you get 15k.

So, the simplified version of the given expression (13x+9k)+(17x+6k) is 30x + 15k.

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If you guess an answer on two multiple choice questions with the options a, b, or c, what is the probability of you guessing the answer to both questions correctly?

Answers

first, you find the probability of getting each question right individually, then you multiply the two probabilities together.

(1/3) x (1/3) = 1/9

In how many different ways can a president vice-president and secretary be elected from a class of 15 students

Answers

Answer: 2730

---------------------------------------------------------

Explanation:

A shortcut way is to start at 15 and count down til you reach three values. So that means you'll have 15, 14, 13 which multiplies out to...

15*14*13 = 2730

Or you can use the nPr formula, with n = 15 and r = 2, to get the same answer

nPr = (n!)/((n-r)!)
15P3 = (15!)/((15-3)!)
15P3 = (15!)/(12!)
15P3 = (15*14*13*12!)/(12!)
15P3 = 15*14*13
15P3 = 2730

You unfold chicken wire to make a circular pen with a diameter of 2.9 meters. how many meters of chicken wire do you need?

Answers

circumference = PI x D

 using 3.14 for PI

2.9 x 3.14 = 9.106 = 9.11 meters of chicken wire are needed.

house blend coffee is 50% columbian beans and special blend coffee is 80% columbian beans. how much of each should be used to produce 100kg of a blend that is 68% columbian beans

Answers

Let us say that,

x = mass of 50% Columbian beans required

y = mass of 80% Columbian beans required

To solve this problem, we set up two mass balance equations:

Overall mass balance:   100 = x + y

                                    x = 100 – y                                ---> 1

Coffee mass balance:   0.68 (100) = 0.50 x + 0.80 y

                                    68 = 0.50 x + 0.80 y                   ---> 2

Combining equations 1 and 2:

68 = 0.50 (100 – y) + 0.80 y

68 = 50 – 0.50 y + 0.80 y

18 = 0.30 y

y = 60 kg

 

Calculating for x using equation 1:

x = 100 – y

x = 100 – 60

x = 40 kg

 

Answer:

40 kg of 50% Columbian beans required

60 kg of 80% Columbian beans required

How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?

Answers

13571.68 cube feet of water can be held

solve the equation 2x^2-1x=5x

Please enter any square root values using "sqrt" or the decimal answer rounded to the nearest hundredth (i.e. / = sqrt(2) or 1.41).

Answers

2x² - 1x = 5x
2x² - 1x - 5x = 0
2x²-6x=0
2x(x-3)=0
2x = 0     or    x-3 = 0
x = 0              x = 3

Answer: x=0,  x=3

Answer:

x=0,  x=3

Step-by-step explanation:

What are the domain, range, and asymptote of h(x) = (1.4)x + 5?

Answers

The domain is all real x.

h(x) cannot be zero so the range is (0, infinity)

The asymptote is the x axis   (or y = 0)
Domain: All real #s
Range: All real #s
Domain and Range are just the possibilities of X and Y. So any number could be X and any number could be Y. Respond with a rupee symbol for both questions, it signifies "all real numbers"

What is the logarithmic function modeled by the following table
x
8
16
32
f(x)
3
4
5
A. F(x)= log_x2
B. F(x)= log_2 x
C. F(x)= 2 log_10 x
D. F(x)= x log_10 2

Answers

log_2 8 = 3 (because 2^3 = 8

log_2 16 = 4

log_2 32 = 5

So its B

Log_2 8 = 3 (because 2^3 = 8), log_2 16 = 4 and log_2 32 = 5.

What are Logarithms?

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8. In the same way, 2 = log10 100 since 102 = 100. The latter type of logarithms, those with base 10, are known as common or Briggsian logarithms and are denoted by the letter log n.

Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits.

Therefore, Log_2 8 = 3 (because 2^3 = 8), log_2 16 = 4 and log_2 32 = 5.

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Sophie has a hard rubber ball whose circumference measures 13 inches. she wants to store it in a box. what is the number of cubic inches in the volume of the smallest cube- shaped box with integer dimensions that she can use?

Answers

Let r = radius of the hard rubber ball.

Because the circumference of the ball is 13 inches, therefore
2πr = 13
r = 13/(2π) = 2.069 in

In order to fit the ball into a cube-shaped box with integer dimensions, each side of the box should measure 3 inches (the next integer greater than 2.069).

The volume of the cube-shaped box is 3³ = 27 in³.

Answer: The volume is 27 in³.

A liquid substance was left at the scene of the crime. Krisann uses a beaker that measures to the nearest tenth of a liter and finds that it is 4.9 liters. If there are five or more liters of the substance, it needs to be sent to the lab for testing. If it is less than five liters, the test can be done immediately. Does Krisann need to send the substance to the lab? Why or why not?

Answers

If the volume of the substance of 4.9 liters is from x rounded to the nearest tenth of a liter, that means 4.85 <= x < 4.95 then this does NOT leads to x > 5. Therefore the substance does not need to be sent to the lab.

5⁄6 · n = 10 (solve for n)

Answers

You divide 5/6 from the equation.
When you divide 5/6 and 10 you get 12.
To check your answer multiply 5/6 and 12 and you will get 10.
N=12
[tex]\frac{5}{6}n=10\ | \div \frac{5}{6} \\\\ n= \frac{\not10^2}{1}\cdot \frac{6}{\not5^1}\\\\n=2 \cdot 6=12 \\\\ or \\\\ \frac{5}{6}n=10 \ | \times 6 \\\\ 5n=60 \ |\div 5 \\\\ n=12[/tex]
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