A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 980 meters from the base of the cliff. The angle of elevation from sea level to the base of
the lighthouse is 47.3. The angle of elevation from sea level to top of the lighthouse is 51.3°. Find the height of the lighthouse from the top of the cliff.
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.
Answers
The height of the lighthouse from the top of the cliff is 161.2 cm
The situation forms two right angle triangle.
Right angle triangleRight angle triangle has one of its angles as 90 degree. Therefore, the sides and angles can be found using trigonometric ratios as follows;
tan 51.3 = opposite / adjacent
where
opposite = height of cliff and light house = x
adjacent = distance of the ship from the base of the cliff
Therefore,
tan 51.3 = x / 980
cross multiply
x = 980 tan 51.3
x = 1223.23995563 meters
tan 47.3 = opposite / adjacent
where
opposite = height of cliff = y
adjacent = distance of the ship from the base of the cliff
tan 47.3 = y / 980
y = 980 tan 47.3
y = 1062.01582791 meters
The height of the lighthouse from the top of the cliff = 1223.23995563 - 1062.01582791 = 161.224127725 = 161.2 cm
learn more on trigonometric ratio here: https://brainly.com/question/26299702
Related Questions
y+2=-3(x-1)in slope intercept form
Answers
First you distribute the -3. So -3 times x which is -3x and -3 times -1 which is positive 3. Therefore you get y+2=-3x+3.
Then you subtract the 2 from both sides. 2-2=0, so you have just y. Now subtract 2 from the 3 on the right and you get 1. Therefore you get y=-3x+1.
a song has 540 beats. if the song is 3 minutes long, how many beats per minute does the song have? ( PLEASE AWNSER UNTIL 10 MINUTES AND I WILL DELETE)
Answers
Answer:
180
Step-by-step explanation:
Divide 540 by 3 to get 180 which is your answer!
Have a good day!
Please mark brainliest!
Solution:
Note that:
540 beats = 3 min.Simplify the equation to know how much beats in 1 minute.
540 beats = 3 min.=> 1 minute = 540/3 beats=> 1 minute = 180 beatsThe beats per minute in this song is 180 beats per minute.
You enter an online Esports tournament. The entry fee is $17, and the top 3 finishers win money. First place wins $325. Second place wins $276. Third place wins $106. You give yourself an X chance of finishing in the top 3, and if you finish top 3, then you have an equal chance of finishing first, second, or third. What is X such that entering this tournament is a fair gamble for you. A fair gamble is one where the expected value of entering the tournament is $0.
Answers
Using the expected value of a discrete distribution, it is found that X = 0.0673.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, we have that the distribution is:
P(X = -17) = 1 - X.
P(X = 325) = X/3.
P(X = 276) = X/3.
P(X = 106) = X/3.
Hence, since the expected value is 0:
[tex]-17(1 - X) + 325\frac{X}{3} + 276\frac{X}{3} + 106\frac{X}{3} = 0[/tex]
[tex]-17 + 17X + 235.67X = 0[/tex]
[tex]252.67X = 17[/tex]
[tex]X = \frac{17}{252.67}[/tex]
[tex]X = 0.0673[/tex]
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/24855677
Despite booming new car sales with their cha-ching
sounds, the average age of vehicles on roads is not
going down. The bar graph shows the average price of
new cars in Country A and the average age of cars o
roads for two selected years. In 2014, the average price
of a new car was $37,600. For the period shown, new-
car prices increased by approximately $1250 per year.
If this trend continues, how many years after 2014 will
the price of a new car average $47,600? In which year
will this occur?
How many Years after 2014 will the average price of new cars average $47,00?
I provided a Picture for the graph! Thanks a ton!
Answers
Answer to the 1st question: 8 years
Answer to the 2nd question: The year 2022
=======================================================
Further explanation:
x = number of years after 2008
y = average price of a new car
The prices are going up by $1250 per year on average. This is the slope because the slope is the rate of change. So m = 1250.
The y intercept is b = 30100 as this is the price in 2008.
This leads us to go from y = mx+b to y = 1250x+30100
Plug in x = 0 and you should get y = 30100.
Also, plugging x = 6 into the equation leads to y = 37600 to help confirm things.
-----------------
Next, we plug in y = 47600 and solve for x.
y = 1250x+30100
47600 = 1250x+30100
47600-30100 = 1250x
17500 = 1250x
1250x = 17500
x = 17500/1250
x = 14
This means 14 years after the year 2008 is when the average new car price will be $47,600.
2008+14 = 2022
2022-2014 = 8
Therefore, 8 years after 2014 (aka the the year 2022) is when the new car average price will be $47,600.
14 students have volunteered for a committee. Eight of them are seniors and six of them are juniors. (a) How many ways are there to select a committee of 5 students
Answers
======================================================
Explanation:
We have five slots to fill, which I'll label A through E.
There are,
14 choices for slot A13 choices for slot B12 choices for slot C11 choices for slot D10 choices for slot EEach time we fill up a slot, we count down by 1.
This gives 14*13*12*11*10 = 240,240 different permutations. If order mattered, then this would be the answer.
However, order doesn't matter on a committee without rankings. Each member has the same rank as any other.
Within any group of 5 people, there are 5! = 5*4*3*2*1 = 120 ways to arrange them. This means we divide that 240,240 figure by 120 to find the number of combinations.
There are (240,240)/(120) = 2002 different combinations.
---------------------------------------
Here's how we could have done the problem using the nCr combination formula.
Plug in n = 14 and r = 5.
n C r = (n!)/(r!(n-r)!)
14 C 5 = (14!)/(5!*(14-5)!)
14 C 5 = (14!)/(5!*9!)
14 C 5 = (14*13*12*11*10*9!)/(5!*9!)
14 C 5 = (14*13*12*11*10)/(5!)
14 C 5 = (14*13*12*11*10)/(5*4*3*2*1)
14 C 5 = (240240)/(120)
14 C 5 = 2002
The value of q is:
A. 42.
B. 39.
C. 40.
Answers
Answer:
40
Step-by-step explanation:
Its pretty easy i did that on a test and got a 100
Do this problem 3 2/3x-4/5(x-3 3/4)
Answers
-4x^2+15x+10/ 5x
Answer if the X is next to the 2/3 (multiplying 2/3):
(43/15) x +3
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a 3 or 5?
Answers
Answer:
3
Step-by-step explanation:
you should divide 52 by a number to get 3
i’ll give brainliest!
Answers
Answer:
-6
Step-by-step explanation:
just keep the same slope and just pretend to move the line up 8 which would decrease the x value by 14 equaling -6
Which of the following numbers is the smallest
Answers
The smallest number from the folowing option is A . 0.0082.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
The given numbers are;
0.0082
1/3
0.048
0.36
1/9
thus, The smallest number from the folowing option is A . 0.0082.
Learn more about a number pattern:
brainly.com/question/14471389
#SPJ2
Ahmad has $112 in his checking account and earns $75 per weeks
working part-time. Assume he has no expenses currently.
Calculate how much will Ahmad save in his account at the end of 4
weeks 2
Answers
Answer:
your is.... 2212
Step-by-step explanation:
7 days in a week, right?
7 * 4 = 28
75 x 28 + the additional 112
What is the length of ONE side in a square if the perimeter is 4x + 25
Answers
Answer:
Hi, you already asked this question, the answer is 6...
Step-by-step explanation:
help needed brainliest will be given for attempt
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Answers
Answer:
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Step-by-step explanation:
Area of a circle D=10
a.62.80
b.78.50
c.314
d.15.70
e.31.40
Answers
Area of circle= 5*5*3.14
Area of circle= 78.54
Fatima is painting this cardboard cut out for her class play. the cutout is a trapezoid 3 m tall. it has a square opening. what is the area that Fatima needs to paint?
PLS SHOW WORK.
Answers
Answer:
8 square meters
Step-by-step explanation:
Area of the trapezoid is (1/2)(3)(2+4)=9
Area of the trapezoid is (1)(1)=1
So the area she needs to paint is 9 - 1 = 8
Simplify the expression.
2.4 - 4.3n - 3n + 6
Answers
Answer:
-7.3n+8.4
Step-by-step explanation:
combine like terms
Hope this helps! Have a great day!!
Answer:
8.4 - 7.3n
Step-by-step explanation:
1. Rearrange
2.4 - 4.3n - 3n + 6 = 2.4 + 6 - 4.3n - 3n
2. Combine like terms
2.4 + 6 - 4.3n - 3n = 8.4 - 7.3n
The answer is 8.4 - 7.3n
Hope this helps :)
Have a great day!
13.333...% as a fraction
Answers
Answer:
[tex]13 \frac{333}{1000}[/tex]
Step-by-step explanation:
The amount of numbers after the decimal point tell you the amount of zeros to put after the 1 in the denominator.
Just rewrite the whole number infront of the decimal point into the fraction
Answer:
[tex]\frac{2}{15}[/tex]
Step-by-step explanation:
[tex]13.333...\%=\frac{13.333...}{100}=\frac{10+3.333...}{100}=\frac{10}{100}+\frac{3.333...}{100}[/tex]
[tex]=\frac{1}{10}+\frac{\frac{10}{3}}{100}=\frac{1}{10}+\frac{1}{30}=\frac{4}{30}=\frac{2}{15}[/tex]
Find the circumference of the circle below:
15.7 cm
31.4 cm
100 cm
314 cm
help me
Answers
Answer:
31.4 cm
Step-by-step explanation:
[tex]C=2\pi r[/tex]
[tex]=2*\pi *5[/tex]
[tex]\neq 31.41593[/tex]
≈ 31.4
. A jeweler has 100 necklaces and bracelets to sell at a flea market. Bracelets are selling for $5.75 each, and necklaces are $8.50 each. If the jeweler makes $685.00 after selling all of the items, how many of each type of jewelry did the jeweler sell?
Answers
Answer:
there are total 60 bracelets and 40 necklaces.
Explanation:
let necklaces be x
let bracelets be y
make two equations from the given values:
x + y → 1005.75y + 8.50x → $685solving steps:
x + y → 100
x → 100 - y
using substitution method:
5.75y + 8.5x → 685
5.75y + 8.5(100 - y) → 685
5.75y - 8.5y + 850 → 685
-2.75y → 685 - 850
-2.75y → -165
y → 60
Find x:
x + y → 100
x → 100 - 60
x → 40
Answer:
60 bracelets
40 necklaces
Step-by-step explanation:
Let n = number of necklaces sold
Let b = number of bracelets sold
Given:
Total number of items sold = 100⇒ n + b = 100
Given:
Sale price of bracelet = $5.75Sale price of necklace = $8.50Total sales = $685⇒ 5.75b + 8.5n = 685
Rewrite n + b = 100 to make b the subject, substitute into 5.75b + 8.5n = 685 and solve for n:
⇒ b = 100 - n
⇒ 5.75(100 - n) + 8.5n = 685
⇒ 575 - 5.75n + 8.5n = 685
⇒ 575 + 2.75n = 685
⇒ 2.75n = 110
⇒ n = 40
Substitute found value for n into n + b = 100 and solve for b:
⇒ 40 + b = 100
⇒ b = 60
can I have help pls
Answers
The average size of a human cell is one-ten-thousandths (0.0001) of a meter. Write it in scientific notation. ( Follow this format without spaces: _.___x10^__ )
Answers
Answer:
The average size of a human cell is one-ten-thousandths (0.0001) of a meter. Write it in scientific notation. ( Follow this format without spaces: 1769 ma 20
3. Over the next two days, Job.net Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of 2. On the second day, the agency will interview clients in groups of 4. If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day?
Answers
Here is my answer. Good luck.
Brainliest if correct
Answers
Answer:
y = 3
Step-by-step explanation:
Since x = 4
4 + y = 7
Subtract 4 from both sides of the equation
y + 4-4 = 7 -4
Simplify
y =3
[RevyBreeze]
A new movie theater opens at the local mall. During the first month, the owner collected information
on how many customers they had throughout each day. The owner concluded that the number of
customers the theater has at any given moment can be represented by C(x) = -x2 + 11x where x
represents the number of hours that the movie theater has been open on a given day. The theater
opens at 12:00 PM.
At what time does the theater have no customers?
a.
11:00 PM
b. 5:30 PM
c. 2:00 PM
d. 8:30 PM
Answers
The time at which the theatre does not have any customers is; Choice A: 11:00 PM
Functions and variableFrom the task content;
The function which represents the number of customers the theater has at each point in time is;C(x) = -x² + 11xHence, when C(x) = 0, the theater has no customers.
0 = -x² +11xDivide through by x;
0 = -x +11x = 11.
Read more on functions and variables;
https://brainly.com/question/24253401
Equations of the form cosθ=k where -1 ≤ k ≤ 1 has/have ______________ solution(s).
A. two
B. infinitely many
C. one
D. none
Answers
The supplement of a 60∘ angle is an angle that measures how many degrees?
Answers
Answer:
120 Degrees
Step-by-step explanation:
Supplementary means angles that add up to 180 Degrees, so 180 - 60
Hope it helps
Rewrite the quadratic function below in standard form. y = 3(x+9)(x+1)
Answers
Answer:
y = 3x² + 30x + 27
Step-by-step explanation:
Formula: Ax + By = C
y = 3 (x + 9) (x + 1)
y = 3x + 27x + 3x + 7
y = 3x² + 30x + 27
(2x-3)(3x+4) expand and simplify?
Answers
Answer:
6x2-x-12
Step-by-step explanation:
The given expression:
(
2
x
−
3
)
(
3
x
+
4
)
Simplify by using the FOIL method:
(
2
x
−
3
)
(
3
x
+
4
)
=
2
x
⋅
3
x
+
2
x
⋅
4
−
3
⋅
3
x
−
3
⋅
4
=
6
x
2
−
x
−
12
Therefore, the simplest form of the given expression is
6
x
2
−
x
−
12
.
Which of the following is true about the line that passes through the points (-5, 8) and (1,8
Answers
Answer: there is a horizontal line on the bottom side to each point.
Step-by-step explanation: -5 x 8y, 1x 8y so from each position they are on the bottom. negative on the right, positive on the left (x axis)
Help bell math math math
Answers
y = ax + b
The coefficient of x is the slope of the line in this form of the linear equations.
=====================================
The perpendicular line have negative and inverse slope which means the product of their slope must equals to - 1 .
Thus if we suppose that the line we want to find it's equation has a slope of m ; we have :
4 × m = - 1
Divide both sides by 4
4m ÷ 4 = - 1 ÷ 4
m = - 1/4
Thus we know the coefficient of x now :
y = - 1/4 x + b
======================================To find the value of b we need one of the point that the line passed through it which is the point ( 4 , - 11 ) .
All we have to is put the coordinates in the equation and find the value of b.
Let's gooo....
y = - 1/4 x + b
put the coordinates in the equation
- 11 = (- 1/4)×4 + b
- 11 = - 1 + b
Add both sides 1
- 11 + 1 = -1 + 1 + b
b = - 10
======================================
Thus :[tex]y = - \frac{1}{4} x + ( - 10) \\ [/tex]
[tex]y = - \frac{1}{4} x - 10 \\ [/tex]
Answer:
y = ax + b
Step-by-step explanation: