A boat is heading towards a lighthouse, whose beacon-light is 102 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 7 , before they draw closer. They measure the angle of elevation a second time from point b at some later time to be 12. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Answer:
351 ft (nearest foot)
Step-by-step explanation:
Model the problem as a right triangle, where the horizontal leg is the water (where the boat is at the vertex with the hypotenuse), and the vertical leg is the lighthouse. The angle of elevation is between the boat and the top of the lighthouse. (see attached diagram)
Horizontal distance from point A to the lighthouse
Using the trig ratio tan(x) = O/A where x is the angle, O is the side opposite to the angle and A is the side adjacent to the angle:
Given:
x = 7O = 102 A = ?⇒ tan(7) = 102/A
⇒ A = 102/tan(7)
⇒ A = 830.7233357... ft
Horizontal distance from point B to the lighthouse
Given:
x = 12O = 102 B = ?⇒ tan(12) = 102/B
⇒ B = 102/tan(12)
⇒ B = 479.8722712... ft
Therefore, distance from A to B:
⇒ distance = A - B
⇒ distance = 830.7233357... - 479.8722712...
⇒ distance = 350.8510645...
⇒ distance = 351 ft (nearest foot)
Related Questions
Solve the following systems of equations by substitution method.
1) y = -2 and 4x - 3y = 18
IF YOU WANT TO ANSWER MORE: HERE IS THE REST PART OF THE QUESTION—
2) y = 6x - 11 and 2x + 3y = 7
3) x = -3y - 5 and 4x - 5y = -3
4) x = 5y - 7 and -2x - 3y = -12
5) 5x - 3y - 8 = 0 and 2x - 3y - 6 = 0
6) x - 3y - 11 = 0 and 5x + y - 7 = 0
7) 2x - 3y = -1 and y = x - 1
8) -4x + y = 6 and -5x - y = 21
Answers
Answer:
1) x = 3 and y = -2
2) x = 2 and y = 1
3) x = -2 and y = -1
4) x = 3 and y = 2
5) x = 2
6) x = 2 and y = -3
7) x = 4 and y = 3
8) x = -3 and y = -6
Step-by-step explanation:
1. Answer :
y = -2
4x - 3y = 18 ----(1)
Substitute y = -2 in (1).
4x - 3(-2) = 18
4x + 6 = 18
Subtract 6 from both sides.
4x = 12
Divide both sides by 4.
x = 3
So,
x = 3 and y = -2
2. Answer :
y = 6x - 11 ----(1)
2x + 3y = 7 ----(2)
Substitute y = 6x - 11 in (2).
2x + 3(6x - 11) = 7
2x + 18x - 33 = 7
20x - 33 = 7
Add 33 to both sides.
20x = 40
Divide both sides by 20.
x = 2
Substitute x = 2 in (1).
y = 6(2) - 11
= 12 - 11
= 1
So,
x = 2 and y = 1
3. Answer :
x = -3y - 5 ----(1)
4x - 5y = -3 ----(2)
Substitute x = -3y + 5 in (2).
4(-3y - 5) - 5y = -3
-12y - 20 - 5y = -3
-17y - 20 = -3
Add 20 to both sides.
17y = -17
Divide both sides by 17.
y = -1
Substitute y = -1 in (1).
x = -3(-1) - 5
= 3 - 5
= -2
So,
x = -2 and y = -1
4. Answer :
x = 5y - 7 ----(1)
-2x - 3y = -12 ----(2)
Substitute x = 5y - 7 in (2).
-2(5y - 7) - 3y = -12
-10y + 14 - 3y = -12
-13y + 14 = -12
Subtract 14 from both sides.
-13y = -26
Divide both sides by -13.
y = 2
Substitute y = 2 in (1).
x = 5(2) - 7
= 10 - 7
= 3
So,
x = 3 and y = 2
5. Answer :
5x + 3y - 8 = 0 ----(1)
2x - 3y - 6 = 0 ----(2)
Solve for 3y in (1).
5x + 3y - 8 = 0
Subtract 5x from both sides.
3y - 8 = -5x
Add 8 to both sides.
3y = -5x + 8
Substitute 3y = -5x + 8 in (2).
2x - (-5x + 8) - 6 = 0
2x + 5x - 8 - 6 = 0
7x - 14 = 0
Add 14 to both sides.
7x = 14
Divide both sides by 7.
x = 2
6. Answer :
x - 3y - 11 = 0 ----(1)
5x + y - 7 = 0 ----(2)
Solve for x in (1).
x - 3y - 11 = 0
Subtract 3y and 11 to both sides.
x = 3y + 11 ----(3)
Substitute x = 3y + 11 in (2).
5(3y + 11) + y - 7 = 0
15y + 55 + y - 7 = 0
16y + 48 = 0
Subtract 48 from both sides.
16y = -48
Divide both sides by 16.
y = -3
Substitute y = -3 in (3).
x = 3(-3) + 11
= -9 + 11
= 2
So,
x = 2 and y = -3
7. Answer :
2x - 3y = -1 ----(1)
y = x - 1 ----(2)
Substitute y = x - 1 in (1).
2x - 3(x - 1) = -1
2x - 3x + 3 = -1
-x + 3 = -1
Subtract 3 from both sides.
-x = -4
Multiply both sides by -1.
x = 4
Substitute x = x in (3).
y = 4 - 1
= 3
So,
x = 4 and y = 3
8. Answer :
-4x + y = 6 ----(1)
-5x - y = 21 ----(2)
Solve for y in (1).
-4x + y = 6
Add 4x to both sides.
y = 4x + 6 ----(3)
Substitute y = 4x + 6 in (2).
-5x - (4x + 6) = 21
-5x - 4x - 6 = 21
-9x - 6 = 21
Add 6 to both sides.
-9x = 27
Divide both sides by -9.
x = -3
Substitute x = -3 in (3).
y = 4(-3) + 6
= -12 + 6
= -6
So,
x = -3 and y = -6
Learn more:
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Mathematics
Thank You!
Answered by: ms115
Answer:
See below for all answers and explanations
Step-by-step explanation:
Problem 1
4x - 3y = 18
4x - 3(-2) = 18 <-- Substituting y = -2
4x + 6 = 18
4x = 12
x = 3
Problem 2
2x + 3y = 7
2x + 3(6x-11) = 7 <-- Substituting y = 6x - 11
2x + 18x - 33 = 7
20x - 33 = 7
20x = 40
x = 2
y = 6x - 11 <-- Substituting x=2 to solve for y
y = 6(2) - 11
y = 12 - 11
y = 1
Problem 3
4x - 5y = -3
4(-3y-5) - 5y = -3 <-- Substituting x = -3y - 5
-12y - 20 - 5y = -3
-17y - 20 = -3
-17y = 17
y = -1
x = -3y - 5 <-- Substituting y = -1 to solve for x
x = -3(-1) - 5
x = 3 - 5
x = -2
Problem 4
-2x - 3y = -12
-2(5y-7) - 3y = -12 <-- Substituting x = 5y - 7
-10y + 14 - 3y = -12
-13y + 14 = -12
-13y = -26
y = 2
x = 5y - 7 <-- Substituting y=2 to solve for x
x = 5(2) - 7
x = 10 - 7
x = 3
Problem 5
5x - 3y - 8 = 2x - 3y - 6 <-- Setting equations equal to each other
5x - 8 = 2x - 6 <-- Eliminating y-variable to solve for x
3x - 8 = -6
3x = 2
x = 2/3
5x - 3y - 8 = 0 <-- Substituting x = 2/3 into first equation
5(2/3) - 3y - 8 = 0
10/3 - 3y - 8 = 0
10/3 - 3y - 24/3 = 0
-14/3 - 3y = 0
-3y = 14/3
y = -14/9
Problem 6
x - 3y - 11 = 0 <-- Solve for x
x - 3y = 11
x = 11 + 3y
5x + y - 7 = 0
5(11+3y) + y - 7 = 0 <-- Substituting x = 11 + 3y
55 + 15y + y - 7 = 0
55 + 16y - 7 = 0
48 + 16y = 0
16y = -48
y = -3
x = 11 + 3y <-- Substitute y=-3 into first equation to solve for x
x = 11 + 3(-3)
x = 11 - 9
x = 2
Problem 7
2x - 3y = - 1
2x - 3(x-1) = -1 <-- Substituting y = x - 1
2x - 3x + 3 = -1
-x + 3 = -1
-x = -4
x = 4
y = x - 1 <-- Substitute x=4 to solve for y
y = 4 - 1
y = 3
Problem 8
-4x + y = 6 <-- Solve for y in first equation
y = 6 + 4x
-5x - y = 21
-5x - (6+4x) = 21 <-- Substituting y = 6 + 4x
-5x - 6 - 4x = 21
-9x - 6 = 21
-9x = 27
x = -3
y = 6 + 4x <-- Substitute x = -3 to solve for y
y = 6 + 4(-3)
y = 6 - 12
y = -6
helpp me pleass ..........
Answers
Answer:
Step-by-step explanation:
1 and 7 is Corresponding
2 and 8 is Alternate exterior
this is what I know but I am not sure
find a dimension of a rectangle whose width is 2 miles less than its length, and whose area is 80 square miles?
Answers
Answer:
Step-by-step explanation:
For this type of question, it helps to draw the rectangle and label its sides. Label the length x. We are given that the width is 5 miles less than the length, which can be represented algebraically as x-5. So, if y = width, then we have y = x-5.
We are also given that the area is 84 square miles, so how do we find the area of a rectangle? The formula is Area = length * width. Substituting in what we know, we get 84 = x(x-5). We distribute on the right hand side to get 84 = x^2-5x, which is equivalent to x^2-5x-84=0. This can be factored as (x-12)(x+7)=84. The solutions are x=12 or x=-7, but we ignore x=-7 because we cannot have negative length. Thus, the length of the rectangle is 12 miles and the width is 12-5=7 miles.
helpppppppppppppppppppppppppp
Answers
Answer:
6, 12, 24, 48, 96.
All the terms are multiples of 6.
Step-by-step explanation:
The given rule is to multiply by 2.
To find the next 4 numbers, we need to multiply 6, and the products that we've obtained after.
First number:
[tex]6 \times 2 = 12[/tex]
12 is our first number.
Second Number:
[tex]12 \times 2 = 24[/tex]
24 is our second number.
Third Number:
[tex]24 \times 2 = 48[/tex]
48 is our third number.
Last Number:
[tex]48 \times 2 = 96[/tex]
96 is our last number.
All the terms are multiples of 6.
Proof:
*When you divide 12 by 6, 24 by 4, 48 by 8, 96 by 16, the quotient is 6.6 has multiples of 12, 24, 48, and 96.6 has multiples of 12, 24, 48, and 96.12, 24, 48, and 96 have a factor of 6.Sum of two numbers 120 and difference is 60. Find two
numbers.
Answers
Answer: 30&90
Step-by-step explanation:
Ms Bonilla is saving for a vacation she currently has 150 in her savings account and plans to add $25 to the account each week .
Enter a function, S(w) that describes the total amount in her savings account as a function of weeks , w
Answers
Answer and Step-by-step explanation:
Alright, so when creating any type of math problem, it is important to identify the parts of the problem and where they go. First, we need to start by putting the problem together. We will use one of the most common forms of equations of math, also known as the linear equation of y=mx+b.
So we have: S(w)=__x + __. S(w) is also equal to f(x), which is also equal to y. So: y= __x + __.
Let's start filling this equation in. So, because it says that she will add 25 dollars each week, The problem is addition. Also, the 25 dollars each week will represent the mx in this situation. Here's why:
The x in this can stand for the amount of week she added this 25 dollars to her account. So:
y= 25x + __.
Now, we can add the 150 to the problem because that is what she started with for this one-time deal. So now we have:
y= 25x + 150.
You can now where everything is represented, but we are not done. Let's change y and x back into S(w) and w like the question asks us to have. So:
S(w)= 25w + 150.
If you want to solve this question, just replace the number of weeks in place of all w's in the equation, like this: S(2)= 25(2) + 150.
I hope that this helps.
Benjamin threw a rock straight up from a cliff that was 60 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h=-16t^2+68t+60, how long will it take for the rock to hit the water?
Answers
Answer:
5 sec
Step-by-step explanation:
Hit the water, means h = 0
Solve -16t^2 + 68t +60 =0
4t^2 - 17t - 15 = 0
(4t + 3)(t - 5) = 0
so t = 5 sec
A flagpole is 45 feet tall. A rope is tied to the top of the flag pole and secured to the ground 10 feet from the base of the flagpole. Will a 35 foot piece of rope be long enough to secure the flagpole? Justify your answer.
i give brainliest
Answers
Answer:
So the answer would be no, because the length of the rope is needs to be 46 and 35 is not long enough
Step-by-step explanation:
A flagpole, rope and the length of secure point from the flagpole are forming the right triangle, where the rope is a hypotenuse. Let a = 45 and b = 10ft. Use Pythagorean Formula to find length of the rope c
a² + b² = c²
Since we are going to solve for c, we set up the equation like this:
c² = 45² + 10² (Substitute into formula)
c² = 2,025 + 100 (Add)
c² = 2,125 (Simplify)
√c² = √2,125 (Take the square root from both sides)
c = 46.09772228646444 (Round to the nearest whole number)
c = 46
So the answer would be no, since the length of the rope needs to be 46ft long and a 35 foot piece of rope is not long enough.
A school cafeteria surveys the students to see if there is demand for more
gluten-free meal choices. The results are in the table.
Total
Eat gluten-free Not Interested in
food gluten-free food
Buy lunch
20
50
70
Pack lunch
SO
20
70
Total
20
20
740
The school decides to offer more gluten free options. Which of these reasons
is supported by the survey data?
O A. Of the students who buy lunch, the yobability a student is
interested in gluten free food is greater than the probability a
student isnt interested in gluten free food
OB of the students who pack lunch the probability a student is
Interested in gluten-free food is greater than the probability a
student is interested in gluten free food
O c The probability that a student is interested in gluten free food is
greater than the probability that he or she is not interested in
gluten free food
The probability that a student buys lunch is greater than the
probability that he or she packs lunch
Answers
Answer:
B. Of the students who pack lunch, the probability a student is interested in gluten free food is greater than the possibility a student isn’t
Step-by-step explanation:
Solve the equation.
[tex]\sqrt{y^{2} -20y+100 }= y-10[/tex]
Answers
Notice that
y² - 20y + 100 = y² - 2•10y + 10² = (y - 10)²
Then
√(y² - 20y + 100) = y - 10
is equivalent to
√((y - 10)²) = y - 10
|y - 10| = y - 10
If y ≥ 10, then |y - 10| = y - 10, and
y - 10 = y - 10 ⇒ 0 = 0
so there are infinitely many solutions, y ≥ 10.
Otherwise, if y < 10, then |y - 10| = -(y - 10), and
-(y - 10) = y - 10 ⇒ 10 = -10
which is false, so there are no solutions in this case.
[tex]\\ \tt\hookrightarrow \sqrt{y^2-20y+100}=y-10[/tex]
[tex]\\ \tt\hookrightarrow y^2-20y+100=(y-10)^2[/tex]
[tex]\\ \tt\hookrightarrow y^2-20y+100=y^2-20y+100[/tex]
Both sides are equal
Hence
No solution3x9+7 use pemdas right answers only
Answers
Answer:
[tex]\huge\boxed{\sf 34}[/tex]
Step-by-step explanation:
P = Parenthesis
E = Exponents
D = Division
M = Multiplication
A = Addition
S = Subtraction
In that order:
= 3 × 9 + 7
Multiplying first
= 27 + 7
Adding after
= 34
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
34
Step-by-step explanation:
3 x 9 + 7
Using PEMDAS M is first and M is multiplication so you multiply first.
27 + 7
You then add because that’s what is left.
34
Your answer is : 34
Hope it helps! Stay safe!
Someone pls help me
Answers
[tex]\huge\boxed{\boxed{Hello!}}[/tex]
How to Find the Area of a Rectangle:
A=LW, where L stands for Length and W stands for Width.
In this case, L is 4 cm more than the width, and the width is 10 cm.
Thus, the length is 14 cm.
Multiply 14 by 10:
A=140 cm²
[tex]\huge\boxed{\boxed{\pmb{Answer:{\boxed{\sf{A=140cm^{2} }}}}}}[/tex]
Hope it helps!
Enjoy your day!
Please feel free to ask if you have any doubts.
✷[tex]\mathfrak{MistySparkles}[/tex]✷
hope this helps x
write as a polynomial. a(a+9b)^2
Answers
First, you square (a+9b) which will become (a^2+81b^2)
Then, you multiply it by a and you will get a^3+81ab^2
One number is six more than the other. Their sum is 42. Find the numbers.
Answers
Answer:
18 and 24.
Step-by-step explanation:
x + (x + 6) = 42
x + x + 6 - 6 = 42 - 6
x + x = 36
2x = 36
2x/2 = 36/2
x = 18
42 - 18 = 24 The numbers are 18 and 24.
The required two numbers are 18 and 24 and number is 6 more than the the smaller number.
Given, that one number is 6 more than other.
Let the number be x.
Let the other number be x + 6 .
Rewriting in form of equation, that sum of two numbers is 42.
x + (x + 6) = 42
Subtract 6 from both sides.
x + x + 6 - 6 = 42 - 6
Combine like terms,
x + x = 36
2x = 36
Divide by 2 on both sides,
2x/2 = 36/2
x = 18
Thus one number is 18.
The other number is 6 more than 18,
18 + 6 = 24
Thus the two numbers are 18 and 24.
Know more about algebra,
https://brainly.com/question/16934260
#SPJ3
a figure is dilated by a factor of six
Answers
If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of 6.
Step-by-step explanation:
The objects that have the same shape are known as similar figures. Since they are similar in shape it doesn't necessary for those objects to have the same size.
Dilation is the process that enlarges or shrinks the size of an object to its similar figure without changing its size. The Dilation is based on a factor that makes the object to enlarge or shrink.
Since its size has changed so as the perimeter will be changed for both of the figures. The perimeter of an object remains same as the scale factor used to dilate the object.
Consider a square with its side as 2 cm initially and dilated with factor 3.
Perimeter of the square = 4 a. where a is the side.
Then the perimeter of the square will be 8 cm initially.
After dilation the side of the square will be changed as 6.
Then the perimeter will change as 24 cm.
Thus the perimeter of the square initially has increased 3 times after dilation.
9th grade math (i think, or 8th grade)
Answers
Answer:
28.26
Step-by-step explanation:
a=3.14159...(pi)r^2
The area equals pi or 3.14•r^2
3.14•3^2 = 9 because there is a radius of 3
9•3.14 equals 28.26 ft squared :)
I had 2000 dollars but a frog take 1000? how much do i have
Answers
Answer:
1000 dollars
Step-by-step explanation:
2000-1000 = 1000
*PLEASE HELP* *IRRELEVANT ANSWERS WILL BE REPORTED AS SPAM*
A plane left Chicago at 8:00 A.M. At 1:00 P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip? (include units)
Find slope:
Then find the average speed of the plane for the trip
Answers
Answer:
300 miles/hour
Step-by-step explanation:
The average speed = 1500 / 5
Take 2points
(8,0)(13,1500)Slope:-
[tex]\\ \rm\hookrightarrow m=\dfrac{1500-0}{13-8}[/tex]
[tex]\\ \rm\hookrightarrow m=\dfrac{1500}{5}[/tex]
[tex]\\ \rm\hookrightarrow m=300[/tex]
Avg speed=Rate of change=300mphHelp me please please please
Answers
Answer:
24 [tex]in^{3}[/tex]
Step-by-step explanation:
volume formula= l x w x h
Box A:
4 x 3 x 4 = 48
Box B: 48/2 = 24
Write the number.
18 ones
9 tens
2 hundreds
Answers
Answer:
308
Step-by-step explanation:
Over the last three evenings, Diane received a total of 105 phone calls at the call center. The third evening, she received 4 times as many calls as the second evening. The first evening, she received 9 fewer calls than the second evening. How many phone calls did she receive each evening?'
Answers
Answer:
Make an eqaution from here.
Let’s make evening 2 “x”
So the first evening has 9 less then the secon evening so…
x-9
Of course theres the second evening (x).
X-9+x
Then the third evening has 4 times as much as the second meeting so…
x-9+x+4x
And when solved, it has to equal 105.
So solve from here.
Combine like terms.
6x-9=105
Isolate
6x=114
x= 19
First evening is 9 less then 19, so 10.
The second evening was 19 calls.
The third evening was 4 times the second evening so, 19*4= 76
1st night = 10
2nd night= 19 calls
Thrid night= 76 calls
In 157.83, the 3 is at the tenths place value.
Select one:
True
False
Answers
Answer:
False
Step-by-step explanation:
Your answer is false because the 3 in 157.83 is in the hundereths place not the tenths place.
I hope it helps! Have a great day!
Lilac~
NEED HELP ASAP
Write an explicit formula for an, the nth term of the sequence 22, 20, 18,....
Answers
Answer:
I thino the awnser is 103.5
Step-by-step explanation:
Answer:
16,12,10,8
Step-by-step explanation:
a+(n-1)d
20-22=18-2=-2
x^4 - 3x^2 - 10 = 0 using the u
Answers
Answer:
[tex]x ^ { 4 } - 3 x ^ { 2 } - 10 = 0\\Let, t = x^{2} \\\rightarrow \: t^{2}-3t-10=0 \\\\\\t=\frac{-\left(-3\right)(+/-)\sqrt{\left(-3\right)^{2}-4\times 1\left(-10\right)}}{2} \\t=\frac{3(+/-)7}{2} \\\\So,\\t = 5 \: and \: -2\\\\Then,\\x = \sqrt{5} \: and \: -\sqrt{5}[/tex]
Hope it helps ⚜
What is the volume of this right rectangular prism?
A rectangular prism with a length of 6.1 centimeters, a width of 5.4 centimeters, and a height of 8 centimeters.
Enter your answer as a decimal to the nearest hundredths place in the box.
Answers
There are 6 children that each want to eat half of a chocolate bar. If they buy a
package of 4 chocolate bars, how many will be left over after they've eaten?
Answers
Answer:There would be 1 chocolate bar left over
Step-by-step explanation: 2 people can eat 1 bar.
Answer:
1 chocolate bar
Step-by-step explanation:
Since they want to eat 1/2 a bar, 2 people can eat 1 bar. 6 total children / 2 that eat 1 bar = 3 chocolate bars eaten
4 original chocolate bars - 3 already eaten = 1 remaining chocolate bar
Based on the Diagram below
Answers
Answer:
BD=ALTITUDES
CD=MEDIANS
AD=ANGLE BISECTORS
Pa help po sana plsss
Answers
Answer:
Check the attachment.
Pythagorean Theorem Study Guide answers
Answers
Answer:
the theorem states that the length of the hypotenuse when squared is equal to the addition of the adjacent and opposite when squared
can I have help pls
Answers
option b would be the correct one