17. An observer at the top of a 50m lighthouse sights a boat out at sea at an angle
of depression of 15°. A short while later, the same boat is at an angle of
depression of 22° along the same line of sight. To the nearest meter, how far
did the boat travel?
A 6 m
B 7 m
C 20 m
D 63 m
Answers
The distance between the two boats will be equal to 63 meters.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The image is attached with the answer below we can see the two boats at different angles 3 so the distance between the two boats will be calculated as:-
Distance of the boat at an angle of 22 degrees.
[tex]x_1 =\dfrac{50}{tan22}=123\ m[/tex]
Distance of the boat at an angle of 15 degrees.
[tex]x_2=\dfrac{50}{tan15}=186\ m[/tex]
So the distance between the two boats will be:-
x₂-x₁ = 186 - 123 = 63 m
Hence the distance between the two boats will be equal to 63 meters.
To know more about Trigonometry follow
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Related Questions
list and graph four ordered pairs that are vertices of a rectangle with a perimeter of 16 units
Answers
Answer:
just ready my paper
Step-by-step explanation:
Answer:
I found your answer on a website
Step-by-step explanation:
look below
If R is inversely proportional to A, and R = 4 when A = 100, what is the value of R when A = 250 A : .625 B : 1.6 C : 10 D : 6,250
Answers
Answer: (b)
Step-by-step explanation:
Given
R is inversely proportional to A i.e
[tex]R\propto \dfrac{1}{A}\\\\R=\dfrac{C}{A}\quad [\text{C=Constant}][/tex]
when [tex]R=4,\ A=100[/tex]
Insert the values to get C
[tex]\Rightarrow 4=\dfrac{C}{100}\\\\\Rightarrow C=400[/tex]
When A=250
[tex]\Rightarrow R=\dfrac{400}{250}\\\\\Rightarrow R=1.6[/tex]
option (b) is correct
How many 2-digit numbers are multiples of 7?
Answers
answer:
the number of two-digit numbers that are divisible by 7 are 13
Step-by-step explanation:
the multiples of a whole number are obtained by calculating the product of any of the counting numbers and that of the whole numbers. for example, to find the multiples of the number 7, we will multiply 7 by 1, 7 by 2, 7 by 3, etc. the multiples are the product of this multiplication.
PLEASE MARK BRAINLIEST THANK YOU <3
Evaluate the expression 2bc2 for b = 1.5 and c = 5.
Answers
Answer: 30 ?
Step-by-step explanation:
2 x 1.5 x 5 x 2 = 30
hopefully this is right :)
3(c)= 3(5)=15
15(2)= 30
Find the circumference of the circle to the nearest hundredth
11cm
Answers
Question: Find the circumference of the circle to the nearest hundredth
d = 11cm
Answer:
34.54 cm
Step-by-step explanation:
Applying,
P = πd...................... Equation 1
Where P = Circumference of perimeter of the circle, d = diameter of the circle, π = pie
From the question
Given: d = 11 cm
Constant: π = 3.14
Substitute these values into equation 1
P = (3.14×11)
P = 34.54 cm
A quadratic relation has zeros at 3 and –5. The parabola goes through the point (2, –14). What is the equation of the parabola in standard form?
Answers
Answer:
[tex] \displaystyle 2 {x}^{2} + 4x - 30 = 0[/tex]
Step-by-step explanation:
we are given the zeros and a point where it goes through of a quadratic equation
remember that when the roots are given then the function should be
[tex] \displaystyle \: y = a(x - x_{1})(x - x_{2}) [/tex]
where a is the leading coefficient and x1 and x2 are the roots
substitute:
[tex] \displaystyle y = a(x - (3))(x - ( - 5)) [/tex]
simplify:
[tex] \displaystyle y = a(x - 3)(x + 5) [/tex]
now the given point tells us that when x is 2 y is -14 therefore by using the point we can figure out a
substitute:
[tex] \displaystyle a(2 - 3)(2 + 5) = - 14[/tex]
simplify parentheses:
[tex] \displaystyle a( - 1)(7) = - 14[/tex]
simplify multiplication:
[tex] \displaystyle - 7a = - 14[/tex]
divide both sides by -7:
[tex] \displaystyle a = 2[/tex]
altogether substitute:
[tex] \displaystyle y = 2(x - 3)(x + 5) [/tex]
since it want the equation y should be
[tex] \displaystyle 2(x - 3)(x + 5) = 0[/tex]
recall quadratic equation standard form:
[tex] \displaystyle {ax}^{2} + bx + c = 0[/tex]
so simplify parentheses:
[tex] \displaystyle 2( {x}^{2} + 2x - 15 ) = 0[/tex]
distribute:
[tex] \displaystyle 2 {x}^{2} + 4x - 30 = 0[/tex]
hence,
the equation of the parabola in standard form is 2x²+4x-30=0
Someone help me pls
Answers
Answer:
=a^-13/a^-6
=a^-13+6
=a^-7
The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches? StartRoot 2 EndRoot in. 2 StartRoot 2 EndRoot in. 4 StartRoot 2 EndRoot in. 36 StartRoot 2 EndRoot in.
Answers
Answer:
2.83 inches
Step-by-step explanation:
The formula for surface area of cube = 6s²
Where
s = side length of cube
S.A = 6s²
s² = S.A/6
s = √S.A /6
For cube a
Surface area = 1200 in²
Hence,
side length = √1200/6
Side length = √200
= 14.14 inches
For cube b
Surface area = 768 in²
Hence,
side length = √768/6
Side length = √128
= 11.13 inches
How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?
Therefore,
14.14 inches - 11.13 inches
= 2.83 inches
Answer:
It’s B
Step-by-step explanation:
:)
Can anyone solve this quick no links
Answers
Answer:
Option 2
24(2) = 48
24+ 12= 36
48 + 36 + 96 = 180
Answer:
96 + 2x + (x + 12) = 180
-96 -96
2x + (x + 12) = 84
-2x -2x
x + 12 = 84 - 2x
-x -x
12 = 84 - 3x
-84 -84
-72 = -3x
divide by -3 on both sides
24 degrees = x
Find the values of x and y.
Answers
Answer: y=37.5degrees and x=110degrees
Step-by-step explanation: sum of angle in a quadrilateral =360 and opposite angles=180. 115+2y=180,2y=180-115=75. 2y/2=75/2. therefore y=37.5. while x=70+x=180,x=180-70=110. x=110
Pls help will mark brainliest
Answers
a) 11/9
b) 2
c) 32
trig question above plz plz plz help
Answers
1. B
2.C
Mr.Jones rents an office in a building for $600 a month. His office has an area of 1,250 square feet. At the same rate, how much will it cost to rent an office with an area of 3,000 square feet?
Answers
Answer:
$1440
Step-by-step explanation:
From the above question:
We know that the rate is
1250 ft² = $600
3000 ft² = x
Cross Multiply
1250ft² × x = 3000ft² × $600
x = 3000ft² × $600/1250ft²
x = $1440
Therefore, at the same rate, the cost of an office with an area of 3000 square feet is $1440
what two numbers that can be added to -13 but also be multiply to 36
Answers
Answer:
-9,-4
Step-by-step explanation:
Answer:
the required numbers are -4 and -9.
Step-by-step explanation:
-9×-4=36
-9+(-4)=13
Someone please help me ASAP
Answers
Answer:
There is 1 boy per 2 girls
Step-by-step explanation:
Answer:
1/2, 0.5, or 1 boy for every 2 girls
Step-by-step explanation:
14/28 is 0.5 or 1/2
1) 17, 29, 32, 9, 30, 14, 8, 39, 11, 32, 23
Minimum :
Maximum:
Q1:
Q2:
Q3:
Answers
Answer:
Minimum: 8
Maximum: 39
Q1: 11
Q2: 23
Q3: 32
Step-by-step explanation:
Set the numbers into numerical order
8 9 11 14 17 23 29 30 32 32 39
Then separate into quarters
[8 9 11] [14 17 23] [29 30 32] 32 39
I speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I?
Answers
Answer:
Step-by-step explanation:
Answer:
An echo
Step-by-step explanation:
Item 9
A store receives a delivery of 2 cases of perfume. Each case contains 10 bottles. Each bottle contains 80 millimeters of perfume.
How many milliliters of perfume in all does the store receive in this delivery?
94 mL
160 mL
800 mL
1,600 mL
Answers
Answer:
1,600 ml
there is 20 bottles all together in both boxes. Multiply 20 times 80 to get 1,600 ml in all
The membership fee at a sports club was $600 per year. Each year, the membership fee increased by 7%. The cost of membership, y, can be modeled by the equation y=600(1.07)^x, where x is the number of years.
How many years will it take for the cost of the membership to be $900?
Choose the answer that gives the correct logarithmic equation and answer.
x=log1.5(1.07)
x=6
x=log1.07(1.5)
x=6
x=log(1.51.07)
x=1
x=log(1.071.5)
x=1
Answers
Answer:
x = log1.5/log1.07
x = 6
Step-by-step explanation:
900 = 600(1.07)^x
Divide both sides by 600
1.5 = 1.07^x
Take the log of both sides
log1.5 = x log1.07
Divide both sides by log1.07
log1.5/log1.07 = x
x = log1.5/log1.07
use calculator
x = 6
someone pls help!! :/
Answers
Answer:
104
Step-by-step explanation:
ok so to find the area of this triangle you need to use the number you have witch are 16 and 13 so we wana find the area of one side of the triangle witch it has mark ware it needs to be split and so 16 / 2 is 8 and so we have 2 pairs of 8 and now you multiply hight by width and get 8 x 13 is 104 so we devide that by two in order to get one section of the triandle so 104 / 2 is 52 and thats one side of the triangle and now we add 52 by 52 and get 104
A. The graph shows four points on the line and the triangles resulting from sketching on the rise and run from one point to the next. Viewing the graph or R-value as a transversal to the rise and run segments, are the two pairs of corresponding angles along the transversal congruent? Explain.
B. What is the relationship between the two resulting triangles? Explain your answer.
C. Use the relationship from Part B to state the relationship between corresponding sides of the resulting triangles.
D. Use the properties of similar triangles to explain why the slope, or rise-to-run ratio, is constant between any two points on the line.
E. Use any two points to find the unit rate for this proportional relationship. Show your work.
Answers
Answer:
A. Yes
B. The triangles are similar
C. The corresponding sides are proportional
D. The slope of ΔABC = tanθ₁ = tanθ₂ = The slope pf ΔDEF, therefore, the slope of any two points on the line are congruent by similar triangles
E. The rate of proportionality = 2
Step-by-step explanation:
A. From the given graph, given that the angles are formed between the transversal and lines parallel to the R-value axis and the transversal and lines parallel to the thickness axis, the angle formed by the transversal and each parallel lines are corresponding angles and are therefore congruent
The tan of one of the angles on each triangle are
On the uppermost triangle, tanθ₁ = (9.42 - 3.14)/(3 - 1) = 3.14
On the other triangle, tanθ₂ =(25.12 - 12.56)/(8 - 4) = 3.14
tanθ₁ = tanθ₂
∴ θ₁ = θ₂
ΔABC and ΔDEF are right triangles, therefore, all the angles of ΔABC and ΔDEF are congruent
B. Given that the interior angles of the triangles formed by the line the graph are congruent, the triangles are similar by AA similarity postulate
C. Given that the triangles are similar, the length of the corresponding sides of the triangles are proportional
D. Given that the slope is the tangent of the angle between the line of the graph and the Thickness axis, and that the angle is the same for both triangles, (∠θ₁ and ∠θ₂) the slope or the rise-to-run ratio is constant for the two triangles and also for any two points on the line
E. The Unit of proportionality is found using any two points as follows;
Using points used to show the proportional relationship on triangle ΔABC are (8, 25.12) and (4, 12.56) and on triangle ΔDEF, the two points used to show proportional relationship are (3, 9.42), and (1, 3.14)
The ratio of the corresponding sides on ΔABC and ΔDEF are
[tex]\overline {AC}[/tex]/[tex]\overline {DF}[/tex] = (25.12 - 12.56)/(9.42 - 3.14) = 2
[tex]\overline {BC}[/tex]/[tex]\overline {EF}[/tex] = (8 - 4)/(3 - 1) = 2
Therefore, the unit rate of proportionality which is the scale factor = 2.
help! I'll mark as brainliest
Answers
Answer:
25°
Step-by-step explanation:
First, Half of a full circle is 180°. So You want to add 125 + 35, which will get you 155. Now, You need to subtract 180 - 155. You will get 25. Hope this helps!
Answer:
Hello! answer: x = 20
Because 20 + 20 + 35 + 35 + 125 + 125 = 360
Hope that helps!
A rectangle has a length of (x+5)and a with of x Write down the expression for the area of a rectangle If the area is 24cm²,find the value of
Answers
Answer: Width = 3cm
Length = 8cm
Step-by-step explanation:
Length = x+5 cm
Width = xcm
Area = 24cm²
Area of a rectangle = length × width
x × (x + 5) = 24
x² + 5x = 24
x² + 5x - 24 = 0
x² + 8x - 3x - 24 = 0
x(x + 8) - 3(x + 8) = 0
x - 3 = 0
x = 3
Width = 3cm
Since length = x + 5 = 3 + 5 = 8cm
Length = 8cm
72.5 = -4 + 8.5h
76.5 = 8.5h
Answers
Answer:
you didnt include the options to choose from but, i saw this on edge and the answer is B. :)
Step-by-step explanation:
This is an example of what form of a number?
3×3×3×3×3×3×3×3×3
A) standard
B) expanded
C) written as a power
Answers
Answer: B you will say 3×3×3×3 and then you muntiply
The two-way frequency table shows the work performance ratings for a random sample of Which statement is correct?
Select one:
O Most males received a rating of 4.
O The fewest number of employees received a rating of 1.
O Most females received a rating of 3.
О The largest number of employees received a rating of 3.
Answers
Answer:
The fewest amount of employees received a rating of 1.
Step-by-step explanation:
A rectangle has a length of 5 units and an area of 132 square units. What is the width of the
rectangle?
A:12 units
B:20 units
C:28 units
D:24 units
Answers
Answer:
26.5, C
Step-by-step explanation:
The answer is 26.4. So, the closest would be 28
In which polygon does the sum of the measures of the interior angles equal the sum of the measures of the exterior angles?
Answers
(confirmed by 2 experts)
let me know if i’m wrong
Choose the statistical question. * please help now
How much do the dogs in the pound weigh?
How tall are you?
What is your favorite color?
Answers
Answer:
The question, 'How much do the dogs in the pound weigh?' is the statistical question.
Hope this helps.
help me plz im stuck on this one question :{
Answers
Answer:
C
Step-by-step explanation:
There's 7 points between point P and E
Hope this helped :)
