From a point 300 feet above ground in a firetower, a ranger spots two fires in the George Washington National forest. The angle of depression made by the line of sight from the ranger to the first fire is 3oand the angle of depression made by the line of sight from the ranger tothe second fire is 2o. The angle formed by the two lines of sight is 0117. Find the approximate distance between the two fires.
Answers
Answer:
The answer is "[tex]\bold{17456.6 \ ft}[/tex]"
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\sin \theta = \frac{P}{h}\\\\\to BC =x\\\\\to BD =y\\\\[/tex]
The height of tower (AB) = 300 ft
Distance = CD
[tex]\Delta ABC \\\\\sin \theta = \frac{AB}{AC}\\\\\sin (2.5) = \frac{300}{AC}\\\\Ac= \frac{300}{\sin (2.5)}\\\\AC= 6877.68 \\\\\Delta ABD \\\\\sin \theta = \frac{AB}{AD}\\\\\sin (1.3) = \frac{300}{AD}\\\\AD= \frac{300}{\sin (1.3)}\\\\AC= 1322.33[/tex]
calculating CD :
[tex]CD^2 = AC^2 +AD^2 -2\cdot AC \cdot AD \cdot \cos(117^{\circ}) \\\\CD = \sqrt{(6877.68)^2 +(13223.23)^2 -2\cdot (6877.68) \cdot (13223.23) \cdot \cos(117^{\circ})}\\\\CD =\sqrt{47302482.1824 + 174853811.6329 - 82576463.207}\\\\CD= \sqrt{304732757.02}\\\\CD= 17456.6 \ ft[/tex]
Related Questions
Complete the recursive formula of the arithmetic sequence 20, 26, 32, 38, ....
Answers
Answer:
a(1) = 20 or 14. Does Khan say that the first term of the sequence shown is the 1'st term or not.
a(n) = a(n-1) + 6
If not correct then I'm sorry
Step-by-step explanation:
Answer:
a(1) = 20
a(n) = a(n-1) + 6
Step-by-step explanation:
The resting heart rates for a group of men involved in a clinical trial of a new medication were recorded at the beginning of the study. The results in beats per minute were
Answers
This is also a rational and irrational worksheet so which one would it be?
Answers
which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an= -2 + (n-1)3?
Answers
Answer: C.[tex]\left \{ {{a1=-2} \atop {an=a(n-1)+3}} \right.[/tex]
because it is the arithmetic progression with d = 3
=> a(n) = a1 + (n - 1).3
so, have: a1 = -2
an = a(n-1) + 3
Step-by-step explanation:
Which relation is a function?
A) {(2,3). (5,8).(-4,-1). (9.7), (2.1)}
B) {(2,3). (5,8).(-4-1). (9.7). (5,7)}
C) {(2,3). (5.8).(-4,-1). (9.7).(-2.1)}
D) {(2,3). (5.8).(-4,-1). (5,7), (-2,1)}
Answers
Hope this helps
Have a happy holidays
37 The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which
1 centimeter represents 20 kilometers. What is the actual distance between these two cities in
kilometers?
Record your answer in the boxes below
If you are testing on paper, record your answer for number 50 in the boxes below.
If you are testing online, type your answer in the box for question number 50 exactly as you
would have put it in the boxes below.
Answers
Answer:
[tex]70\ \text{kilometers}[/tex]
Step-by-step explanation:
The scale of the map is 1 centimeter distance on the map represents 20 kilometers of actual distance.
The distance between the two cities is 3.5 centimeters on the map
[tex]1\ \text{centimeters on the map}=20\ \text{kilometers of actual distance}[/tex]
So,
[tex]3.5\times 20=70\ \text{kilometers}[/tex]
So, the distance between the two cities is [tex]70\ \text{kilometers}[/tex].
The relationship (3,2)(2,5) (8,5) (3,6) is a function
A True
B) False
Answers
Hope this helped!
Drag each tile to the correct box. Not all tiles will be used. Consider the following función. F(x) = 4x + 7
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Starting with the original function, swap the variables x and y, then solve for y. The resulting function is the inverse of the original function.
Answer: The person that answered at the top is a legend!! The picture below is just proof that he/she is right!! :)
What is the value of the “t” in the equation: 12t − 2(t − 5) = 60 ?
Answers
Answer:
First write the given equation[tex]{:}\longrightarrow\tt 12t +2 (t-5)=60 [/tex]
Simplify[tex]{:}\longrightarrow\tt 12t+2t-10=60 [/tex]
[tex]{:}\longrightarrow\tt 14t-10=60 [/tex]
[tex]{:}\longrightarrow\tt 14t=60+10 [/tex]
[tex]{:}\longrightarrow\tt 14t=70 [/tex]
[tex]{:}\longrightarrow\tt t=\cancel{\dfrac {70}{14}}[/tex]
[tex]{:}\longrightarrow\tt t=5 [/tex]
[tex]\therefore\sf t=5 [/tex]
Find the area of this isosceles trapezoid.
Answers
Answer:
431
Step-by-step explanation:
can I get help with some algebra polynomial in standard form
Answers
Step-by-step explanation:
Standard form :
1. = x⁴ - 2x² + 3
2. = 5m³ - 3m² + 9m - 7
hope this will be helpful for you and plzzz mark my answer as brainlist plzzzz vote me also....
Which ratio is less than 7/15?
1. 9/15
2. 2/5
3. 3/5
4. 24/45
Answers
9/15, 6/15, 9/15, 8/15
Solution: 2. 2/5
answer with work please
Answers
Answer: 1. 4
2. 12
3. 6
4. 8
Step-by-step explanation:
Nicole rented a scooter while she was on vacation. She paid an initial rental fee of $50 plus a daily fee of $ 25 each day. The total cost was for the rental was $300. How many days did Nicole rent the scooter
Answers
Answer: Nicole rented the scooter for 10 days.
Step-by-step explanation:
50 + 25 = 75 (Day 1)
75 + 25 = 100 (Day 2)
100 + 25 = 125 (Day 3)
125 + 25 = 150 (Day 4)
150 + 25 = 175 (Day 5)
175 + 25 = 200 (Day 6)
200 + 25 = 225 (Day 7)
225 + 25 = 250 (Day 8)
250 + 25 = 275 (Day 9)
275 + 25 = 300 (Day 10)
(I need the work too please!)
The yearly cost for cross-fit classes is $250 more than yoga classes. And, the
yearly cost for a gym membership is $100 more than yoga classes. Combined,
the cost for all the different plans are $1250. Determine the cost of the gym
membership, yoga, and cross-fit classes.
Answers
Answer:
I am not sure if this was the correct method to solve the question, however it gives the right results if you check it.
Step-by-step explanation:
3x+250+100=1250
3x= 900
x=300
yoga: 300, cross fit: 550 (300+250), gym: 400(300+100)
Latoya needs to make a total of deliveries this week. So far she has completed of them. What percentage of her total deliveries has Latoya completed?
Answers
Answer: 35%
Step-by-step explanation:
You did not give the numbers. Let me help out by giving some figures and explain with that.
Latoya needs to make a total of 60 deliveries this week. So far she has completed 21 of them. What percentage of her total deliveries has Latoya completed?
To solve this, we divide 21 by 60 and then multiply by 100. This will be:
= (21 / 60) × 100
= 7/20 × 100
= 35%
Please I need help on this
Answers
Answer:
i cant see the picture that well
if you answer this i will give brainliest
Answers
Answer:
Hey can you post this again please
Step-by-step explanation:
It wont let me put in the answer i tried to copie and paste it but it didnt work
A cake recipe calls for 1.5 cups of milk and 3 cups of flower. Seth made a mistake and used 5 cups of flour. How many cups of milk should he use to keep the proportions correct?
Answers
Answer:
2.5 cups of milk
Step-by-step explanation:
Given that,
A cake recipe calls for 1.5 cups of milk and 3 cups of flower.
Seth made a mistake and used 5 cups of flour.
We need to find number of cups of milk he use to keep the proportions correct. Let he used x cups of milk.
[tex]\dfrac{1.5}{3}=\dfrac{x}{5}\\\\x=\dfrac{1.5\times 5}{3}\\\\x=2.5[/tex]
Hence, he should use 2.5 cups of milk.
Can you show the working out
Answers
1/4+1/4=1/2
So her cats eat 1/2 a tin of cat food every day.
Next we will try to find the unit rate:
1/2 • 2 = 1
So it takes her cats 2 days to eat 1 tin multiply 2 by 9 because 9 tins and 2 days for 1 tin
2 • 9 = 18
18 days for 9 tins of cat food is the answer
Maria throws a softball straight up into the air with an initial velocity of 50 ft/sec. The ball leaves her hand when it is exactly 4 ft. Above the ground. Write an equation that models the situation.
Answers
Answer:
The equation that models the situation is [tex]s_{f} = 4+\frac{v_{f}^{2}-2500}{64.348}[/tex].
Step-by-step explanation:
Let suppose that effects from air friction and Earth's rotation can be neglected, so that the softball can be modelled experiment a free fall, that is, an uniform accelerated motion due to gravity. From we know the initial velocity and position of the position and we can determine the final position of the ball as a function of the final velocity:
[tex]v_{f}^{2} = v_{o}^{2}+2\cdot a \cdot (s_{f}-s_{o})[/tex] (1)
Where:
[tex]s_{o}[/tex], [tex]s_{f}[/tex] - Initial and final position of the softball, measured in feet.
[tex]a[/tex] - Acceleration, measured in meters per square second.
[tex]v_{o}[/tex], [tex]v_{f}[/tex] - Initial and final velocities of the softball, measured in feet per second.
If we know that [tex]v_{o} = 50\,\frac{ft}{s}[/tex], [tex]a = -32.174\,\frac{m}{s^{2}}[/tex] and [tex]s_{o} = 4\,ft[/tex], then the equation that models the situation is:
[tex]v_{f}^{2} = 2500-64.348\cdot (s_{f}-4)[/tex]
Then, we clear the final position of the softball:
[tex]-\frac{v_{f}^{2}-2500}{-64.348} = s_{f}-4[/tex]
[tex]s_{f} = 4+\frac{v_{f}^{2}-2500}{64.348}[/tex]
The equation that models the situation is [tex]s_{f} = 4+\frac{v_{f}^{2}-2500}{64.348}[/tex].
Choose the correct preposition to complete the sentence. To facilitate a quick getaway, the cunning thief parked the car perpendicular the building.
Answers
Answer:
The answer is TO
Step-by-step explanation:
Answer:
C. To
Step-by-step explanation:
edg 2020
Which number goes in the box to make a true equation?
]X 10 = 42.000
Answers
Answer:
x=4200
Step-by-step explanation:
10x=42000
x=4200
Write an equation of the line that goes through the point (6, 12) and has a slope of 2 3 .
Answers
Answer:
3y = 2x + 24
Step-by-step explanation:
The correct question is as follows;
Write an equation of the line that goes through the point (6, 12) and has a slope of 2/3
Solution
Here, we have a point and a slope, and we want to write the equation of the line
The method we shall use here is the point slope method
Mathematically, that will be;
y-y1 = m(x-x1)
(x1,y1) = (6,12)
m = 2/3
y-12 = 2/3(x-6)
3(y-12) = 2(x-6)
3y-36 = 2x - 12
3y = 2x -12 + 36
3y = 2x + 24
With Department A sales of $200,000, Department B sales of $600,000, and overhead expense to be allocated of $25,000, the distribution of overhead to Department A based on sales is:
Answers
Answer:
6,250$ is the overhead for department a
The distribution of overhead to Department A based on sales is $6250.
What is an overhead expense?A recurring cost of running a firm is referred to as overhead or overhead charge. While operating expenses like material and labor, overheads could easily be linked to or recognized with any one revenue unit.
They are operating costs for a business that cannot be connected to the creation or production of a good or service. They are really the costs a business must pay to remain open, independent of how successful it is.
Department A has sales of $200,000
Department B has sales of $600,000
Therefore the ratio between the two departments will be:
200000: 600000
= 1 : 3
The overhead expense for both the department combined are $25,000
The share of department A will be at
= 25000 * (1/4)
= $6250
Learn more about overhead expense, Here:
https://brainly.com/question/20417612
#SPJ5
Brian is baking apple pies to donate to a local retirement home. Apples are selling for $2.90 a pound. How much will it cost Brian to buy 3.8 pounds of apples
Answers
Step-by-step explanation:
Brian would need $2.90 * 3.8 = $11.02 to buy the 3.8 pounds of apples.
Answer:$11.02
Brian would need ($2.90 * 3.8 = $11.02)to buy all the 3.8 pounds of apples.
3x + 5y = 25
x - 2y = -6
______This equation can be solved for _____
easily.
Answers
The height of a triangle is 7 cm and the height of a similar triangle is 21 cm. How much larger is the
area of the larger triangle?
Answers
Answer:I'm pretty sure the ratio is 3:1
Step-by-step explanation:
Write four and five-eighths as an improper fraction and as a mixed number.
A. start fraction 37 over 8 end fraction, 5Four-eighths
B. start fraction 44 over 8 end fraction, 5Four-eighths
C. start fraction 37 over 8 end fraction, 4start fraction 5 over 8 end fraction
D. start fraction 32 over 8 end fraction, 4start fraction 5 over 8 end fraction
PLEASE HELP WORTH 20 POINTS
Answers
Answer:
the answer is c.
Step-by-step explanation:
i multiply the 4 by the 8 on the denominator and add that answer to the numerator which equal to 37/8
and the mixed number stays the same since its already mixed.
Answer:
C
Step-by-step explanation:
kinda need this and my brain wont work today
Answers
=-1*(-3)*4*16=
=3*64=192