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Salsk061 [2.6K]
2 years ago
9

A forest ranger in a 140-foot observation tower sees a fire moving in a direct path toward the windmill by the lake. The angle o

f depression to the fire is 3°, and the angle of depression to the windmill is 8°. To the nearest foot, how close is the fire to the windmill?
Mathematics
1 answer:
Hoochie [10]2 years ago
3 0
To get how close the windmill is to the fire we proceed as follows:
distance from watch tower to the fire will be:
tan θ= opposite/adjacent
opposite=140 ft
adjacent=x
θ=3°
hence
tan 3=140/x
x=140/tan 3
x=2,671.36 ft

the distance from watch tower to windmill will be:
tan θ=opposite/ adjacent
θ=8°
opposite=140 ft
adjacent=y
thus
tan 8=140/y
y=140/tan8
y=999.15 ft
the distance between fire and wind mill will be:
2,671.36-999.15
=1675.21~1675 ft (to the nearest ft)

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Question 9 (3 points)
Mila [183]

From the dot plot, we have that 90.91% of the students have 5 or more vowels in their first and last  names.

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

The dot plot states that:

  • 2 students have 4 vowels in their first and last name.
  • 3 students have 5 vowels.
  • 8 students have 6 vowels.
  • 9 students have 7 vowels.

Then:

  • Total of 2 + 3 + 8 + 9 = 22 students.
  • 3 + 8 + 9 = 20 have or more vowels.

p = \frac{20}{22} \times 100\% = 90.91\%

90.91% of the students have 5 or more vowels in their first and last  names.

A similar problem is given at brainly.com/question/14354536

5 0
2 years ago
A mattress store sold 1,330 mattresses in one year. If 30% of the mattresses sold were king size mattresses, how many king size
kodGreya [7K]

The total number of mattresses that are sold in a year = 1,330

Percentage of King size mattresses sold = 30% = 30/100 = 0.3

Next, we have to calculate the actual number sold by using the formula given below:

Number of king size mattresses sold = Total mattresses sold in a year * percentage of king size mattresses sold

Number of King Size mattresses sold = 1,330*0.3 = 399

Number of king size mattresses sold = 399


3 0
2 years ago
Read 2 more answers
Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11inc
babunello [35]

For this case, the first thing we are going to do is write the generic equation of motion for the vertical axis.

We have then:

h = \frac {1} {2} gt ^ 2 + vo * t + h0

Where,

  • <em>g: acceleration of gravity </em>
  • <em>vo: initial speed </em>
  • <em>h0: initial height </em>

For the first body:

h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21

For the second body:

h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

By the time both bodies have the same height we have:

h1 = h2\\

\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

Rewriting we have:

\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50

\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21

\frac {19} {12} * t = 29

Clearing time:

t = 29 (\frac {12} {19})\\t = 18.31s

Answer:

 it takes 18.31s for the two window washers to reach the same height

6 0
2 years ago
Read 2 more answers
In a golf tournament, Sam played 4 rounds and was within 2 strokes of par for all 4 rounds of the tournament. If par is 72 on th
In-s [12.5K]

Given:

|x-4(72)|=2

To find:

The highest and lowest scores Sam could have made in the tournament.

Solution:

We have,

|x-4(72)|=2

|x-288|=2

It can be written as

x-288=\pm 2

Add 288 on both sides.

x=288\pm 2

x=288-2 and x=288+2

x=286 and x=290

Therefore, the highest and lowest scores Sam could have made in the tournament are 290 and 286 respectively.

8 0
2 years ago
A professor uses a video camera to record the motion of an object falling from a height of 250 meters. The function f(x) = –5x2
Romashka [77]

Answer:

The answer is approximately 5.09 seconds.

Step-by-step explanation:

The given equation is:

f(x) = -5x^2 + 250

To find the elapsed time, x, set the equation equal to 120 and solve for x:

-5x^2 + 250 = 120

-5x^2 = -130

x^2 = -130/-5 = 26

x = Sqrt(26) = 5.09 seconds.

8 0
2 years ago
Read 2 more answers
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