A plane is flying at an altitude of 13,100 ft. The angle of depression from the plane to a control tower is 12º. What is the horizontal distance from the plane to the tower? Answer rounded to the nearest tenth of a foot.
Answers
Answer:
The horizontal distance from the plane to the tower is 2784.5 feet.
Step-by-step explanation:
From the given question, the height of the control tower is not given. But;
Tan θ = \(\frac{Opposite side}{Adjacent side}\)
Tan \(12^{0}\) = \(\frac{x}{13100}\)
x = 13100 × Tan \(12^{0}\)
= 2784.4910
Thus, x = 2784.5 feet
Therefore, the horizontal distance from the plane to the tower is 2784.5 feet.
Answer:
The horizontal distance from the plane to the control tower is 61630.7 ft.
Step-by-step explanation:
Here we have that
Height of flight of plane = 13,100 ft = Opposite side of angle of elevation
Angle of depression from the plane to the control tower = 12°
Therefore, the control tower can be sighted on a straight (hypotenuse) line from the plane with an angle of depression of 12°
Angle of depression from the plane to the control tower = Angle of elevation from the control tower to the plane = 12°
Horizontal distance from the plane to the control tower = Adjacent side of the hypotenuse of the right triangle = (Opposite side of angle of elevation) ÷ (Tangent of angle of elevation)
∴ Horizontal distance from the plane to the control tower = 13,100/(tan(12°)
Horizontal distance from the plane to the control tower = 61630.7 ft. to the nearest tenth of a foot.
Related Questions
The speed of a passenger train is 8 mph faster than the speed of a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 240 miles. Find the speed of each train.
Answers
The speed of the freight train is 30 mph, and the speed of the passenger train is 30 + 8 = 38 mph.
We have,
Let's denote the speed of the freight train as x mph.
Since the speed of the passenger train is 8 mph faster, we can denote the speed of the passenger train as (x + 8) mph.
To find the speeds of each train, we can use the formula:
Speed = Distance / Time
For the passenger train: (x + 8) = 280 / t, where t is the time taken to travel 280 miles.
For the freight train: x = 240 / t, where t is the time taken to travel 240 miles.
Since the times taken for both trains are the same, we can set the two equations equal to each other:
(x + 8) = 280 / t = x = 240 / t
Cross-multiplying the equation, we have:
(x + 8) t = x (280 / t)
xt + 8t = 280
xt - x = 240
Simplifying the equation, we get:
xt - x = 240
x(t - 1) = 240
Dividing both sides by (t - 1):
x = 240 / (t - 1)
Substituting the value of x in the first equation:
(x + 8) = 280 / t
240 / (t - 1) + 8 = 280 / t
Simplifying the equation, we get:
240t + 8(t - 1) = 280(t - 1)
240t + 8t - 8 = 280t - 280
248t - 8 = 280t - 280
280 - 8 = 280t - 248t
272 = 32t
t = 272 / 32 = 8.5
Substituting the value of t in the equation for x:
x = 240 / (t - 1) = 240 / (8.5 - 1) = 30
Therefore,
The speed of the freight train is 30 mph, and the speed of the passenger train is 30 + 8 = 38 mph.
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Please help I would be really happy:)
Answers
Which graph has slope of 2
Answers
Answer:
I think it would be (D)
Step-by-step explanation:
not (B) because it's decreasing
not (A) or (C) because it ain't look right to me
The required graph which has a slope of 2, is given as graph D. Option D is correct.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the Graph 1 is given as,
m = (y₂ - y₁) / (x₂ - x₁)
m = 1 - 2/ 4-0
m = 1/ 4
Similarly,
Slope of the line
B, m = -1
C, m = 1
D, m = 2
Thus, the required graph which has a slope of 2, is given as graph D. Option D is correct.
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Solve the inequality for x= 1 + 2x > -23
Answers
Answer:
x = -12
Step-by-step explanation:
1 + 2x > -23
-1
2x > -24
x < -12
Sarah negotiated a price of $25,290.00 for a new Toyota Camry Hybrid Sedan. She is prepared to give a down payment of 13%. Her credit union offered her a 4-year amortized loan for the remaining amount at a rate of 1.75%.
How much money will be paid in interest?
How much will the car cost, in total?
Answers
Answer: D
Step-by-step explanation:
Select the correct answer from each drop-down menu.
A camp director developed the function m(c) = 12c + 80 to model the total cost of taking c campers on a field trip to the movies.
In the camp director’s function, the number of campers is the _______ variable and the total cost of the trip _________
1. ( independent, dependent )
2. ( changes by a constant factor per camper, Changes by a constant amount per camper )
.
Answers
Answer:
(a) Independent variable
(b) The constant factor is 12
Step-by-step explanation:
Given
\(m(c) = 12c + 80\)
c = campers
m = total cost
Solving (a) What type of variable is the number of campers (c)
The total cost (m) is dependent on the number of campers (c) for its own value.
In other words, if c changes from 5 to say 7, the value of m will also change.
This implies that the number of campers is an Independent variable
Solving (b): Constant factor
This in other words means, rate of change (or slope)
A linear function is:
\(y = ax + b\)
Where a represents the slope
By comparison with: \(m(c) = 12c + 80\)
Hence, the constant factor is 12
Answer:
dependent, changes by a constant factor per camper.
Step-by-step explanation:
A quarter of a full angle is called a ________ angle.
Answers
Answer:
25 degree angle
Step-by-step explanation:
Answer:
90 degrees
Step-by-step explanation:
Which of the following shapes is a prism? Select All that apply.
A. Shape 1: Circle
B. Shape 2: Cylinder
CShape 3: Rectangular Box
D. Shape 4: Cube
E. Shape 5: Pyramid
F. Shape 6: Cone
Answers
Answer:
C D
Step-by-step explanation:
A store opens at 8am. From 8 until 10am customers arrive at a Poisson rate of four an hour. Between 10am and 12pm they arrive at a Poisson rate of eight an hour. From 12pm and 2pm the arrival rate increases steadily from eight per hour at 12pm to ten per hour at 2pm; and from 2 to 5pm the arrival rate drops steadily from ten per hour at 2pm to four per hour at 5pm. Determine the probability distribution of the number of customers that enter the store on a given day.
Answers
The probability distribution of the number of customers that enter the store on a given day is described as follows:
Poisson with a mean of 70 customers.
What is the Poisson distribution?In a Poisson distribution, the mass function probability that X represents the number of successes of a random variable is given by the equation presented as follows:
\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number.\(\mu\) is the mean in the given interval or range of values of the input parameter.A combination of Poisson variables is a Poisson variable, hence the daily distribution is a Poisson variable with mean given by the sum of these following observations:
8 customers from 8 am to 10 am.16 customers from 10 am to 12 pm.18 customers from 12 pm to 2 pm. (the average over the interval is of 9 an hour).28 customers from 2 pm to 5 pm.Hence the mean is of:
8 + 16 + 18 + 28 = 70 customers.
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9A. What equation represents the proportional relationship depicted in the graph
m=money earned and L=lawns mowed.
A. m = 25L
B. L=15m
C. m=25 + L
Answers
Djdbbdbdbdvbfbfb
A basketball player's chance of scoring a free throw is estimated to be 25. The player tries 20 shots and the number of baskets is recorded. This event is a binomial experiment because
A. there are only two outcomes; the number of trials is not fixed; the probability is the same for each trial; the trails are independent of each other.
B. there are only two outcomes; the number of trials are fixed; the probability is not the same for each trial; the trails are independent of each other.
C. there are only two outcomes; the number of trials are fixed; the probability is the same for each trial; the trails are independent of each other.
D. there is only one outcome; the number of trials are fixed; the probability is not the same for each trial; the trails are independent of each other.
Answers
This event is a binomial experiment because C. there are only two outcomes; the number of trials is fixed; the probability is the same for each trial; the trials are independent of each other.
What is a binomial experiment?A binomial experiment is a random experiment with a fixed number of repeated trials with independent outcomes, successes or failures, yes or no, and heads or tails.
In a binomial experiment, the probability of "success" p is the same for each outcome as the chance of "failure" q is the same for each outcome.
The number of free throw shots in this experiment is 20 and they are either missed or scored.
Thus, the fixed number of trials with only two outcomes satisfied as a binomial experiment.
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i giveee brainlilstttttttt
Answers
Answer:
A
Step-by-step explanation:
Answer:
thanksssssssss
Step-by-step explanation:
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Find the volume of the cylinder to the nearest cubic foot. Use a calculator. A. 236 ft3 B. 942 ft3 C. 251 ft3 D. 75 ft3
Answers
\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)
Answer:
236 ft^3
Step-by-step explanation:
Base radius = 5 ft
Height = 3 ft
Volume = πr^2h
= π × 5^2 × 3
= 75π
= 235.61944901923 feet^3
Nearest Cubic Foot = 236 ft^3
Nearest Cubic Foot:
Hence Answer is:
236 ft^3
Hope this helps!
El 160% de T es igual a N que tanto porciento de N es el 60% de T
Answers
Answer:
sólo pasa por 100% nomás
A wave is traveling with a speed of 500 m/sec and has a wavelength of 10 m. Determine its frequency.
λ= speed/frequency
frequency=speed/ λ
speed= λfrequency
Group of answer choices
500 Hz
5000 Hz
50 Hz
5 Hz
Answers
Answer:
C. 50 HzStep-by-step explanation:
Formula to be used:
frequency=speed/ λSubstitute values:
frequency= 500 m/sec / 10 m = 50 1/sec = 50 HzOption C is correct one
seroiosly help please
A 43-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
21.09 feet
24.20 feet
37.47 feet
49.34 feet
Answers
The side of the triangle is 43 and the angle is 29.37. We need to find the adjacent side of the angle, using the opposite side that is given. Tangent would use opposite/adjacent. Solve
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
I need help ASAP
FIND THE VALUE OF M
Answers
Answer:
80
Step-by-step explanation:
80+20=100
X,(x-36) What is the value of x
Answers
The value of x is 63
How to determine the valueTo determine the value of the variable, we have that;
Angles at a point is equal to 360 degreesComplementary angles are defined as angles that sum up to 90 degreesSupplementary angles are defined as angles that sum up to 180 degreesAngles on a straight line is equal to 180 degreesFrom the information given, we have that;
x and x - 36 are complementary angles
Now, equate the angles to 90 degrees, we have;
x + x - 36= 90
collect the like terms, we get;
2x = 90 + 36
add the terms
2x =1 26
Divide by the coefficient
x = 63
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Complete question:
The angles X,(x-36) are complementary. What is the value of x
find f(2) PLEASE HELP SOLVE!! MATH!!!
Answers
The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:
f(2) = 0.172.
How to obtain the numeric value of the function?The function for this problem is defined as follows:
f(x) = 14/[3 + ae^(kx)]
When x = 0, y = 2, hence we can obtain the coefficient a as follows:
2 = 14/(3 + a)
6 + a = 14
a = 8.
Hence:
f(x) = 14/[3 + 8e^(kx)]
When x = 1, y = 1/2, hence the coefficient k is given as follows:
0.5 = 14/(3 + 8e^k)
1.5 + 4e^k = 14
4e^k = 12.5
e^k = 12.5/4
k = ln(12.5/4)
k = 1.14.
Hence:
f(x) = 14/[3 + 8e^(1.14x)]
Then the numeric value of the function at x = 2 is given as follows:
f(2) = 14/[3 + 8e^(1.14(2))]
f(2) = 0.172.
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Jayden invested $22,000 in an account paying an interest rate of 2.5% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $30,400?
PLEASE HELP
Answers
Answer:
12.9
Step-by-step explanation:
30400=
30400=
\,\,22000e^{0.025t}
22000e
0.025t
Plug in
\frac{30400}{22000}=
22000
30400
=
\,\,\frac{22000e^{0.025t}}{22000}
22000
22000e
0.025t
Divide by 22000
1.3818182=
1.3818182=
\,\,e^{0.025t}
e
0.025t
\ln\left(1.3818182\right)=
ln(1.3818182)=
\,\,\ln\left(e^{0.025t}\right)
ln(e
0.025t
)
Take the natural log of both sides
\ln\left(1.3818182\right)=
ln(1.3818182)=
\,\,0.025t
0.025t
ln cancels the e
\frac{\ln\left(1.3818182\right)}{0.025}=
0.025
ln(1.3818182)
=
\,\,\frac{0.025t}{0.025}
0.025
0.025t
Divide by 0.025
12.9360062=
12.9360062=t
t = 12.9
12.9
It would take approximately 6.5 years (rounded to the nearest tenth of a year) for the value of the account to reach $30,400.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
To solve this problem, we can use the formula for continuous compounding:
⇒ \(A = Pe^{rt}\)
where, A is the amount in the account, P is the principal (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
We know that;
P = $22,000,
r = 0.025 (2.5% expressed as a decimal),
and A = $30,400.
Hence, We can solve for t by plugging in these values:
\($22,000 e^{0.025t}\) = 30,400
Dividing both sides by $22,000, we get:
\(1.3818 = e^{0.025t}\)
Taking the natural logarithm (ln) of both sides, we get:
ln(1.3818) = 0.025t
Solving for t, we get:
t = ln(1.3818)/0.025
t ≈ 6.53 years
Therefore, It would take approximately 6.5 years (rounded to the nearest tenth of a year) for the value of the account to reach $30,400.
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What is the best estimate of the measure of the angle shown?
Answers
Answer:
141
I got it right
CAN SOMEONE HELP. i will give 150 points if some one can explain and solve you have to find the missing angle measures.
Answers
Answer:
\angle ACB=40^{\circ}, \angle ABC=63^{\circ}
Step-by-step explanation:
Finding x:
We know that \(\angle DAB=180^{\circ}\), because it's a straight line. So, \(\angle CAB=180^{\circ}-103^{\circ}=77^{\circ}\).
We know that the sum of the angles of any triangle will be \(180^{\circ}\).
So, we have that \((3x-14)+(3x+9)+77=180\).
Combining like terms on the left gives \(6x+72=180\).
Subtracting \(72\) from both sides gives \(6x=108\).
Dividing both sides by \(6\) gives \(x=18\).
Finding missing angle measures:
\(\angle ACB=3x-14=3(18)-14=54-14=40\).
\(\angle ABC=3x+9=3(18)+9=54+9=63\).
So, \(\angle ACB=40^{\circ}\) and \(\angle ABC=63^{\circ}\) and we're done!
Note: \(\angle ACB+\angle ABC=\angle CAD\). Coincidence? If not, try and prove it!
You want to frame a 6 inch by 9-inch picture. The frame has a two-inch width. Calculate the area of the framed photo.
Answers
Answer:
It's either 108 or 54, the area is 54 in^2 and the volume of the frame is 108^3
Step-by-step explanation:
Volume (if that is what its asking) would be 54 in^2
i need help with this ^
Answers
Answer:
33
Step-by-step explanation:
6z - 18 = 180
6z = 198
z = 33
The hole for a support needs to be 4 feet deep. It is currently 2 feet 9 inches deep. How much deeper
must the hole be? Use pencil and paper. Show two ways to solve this problem. Use the conversion
12 inches
factor
1 foot
The hole needs to be inches deeper.
Enter your answer in the answer box and then click Check Answer
All parts showing
CA
Review progress
Questions
Back
Type here to search
O
T
Answers
Answer:
1 ft 3 inches
Step-by-step explanation:
What is the slope of the line that passes through the points (-9,-9) and (-6,-12)? Write your answer in simplest form.
Answers
Answer:
your slope is 1
Step-by-step explanation:
You would use the formula y2-y1/x2-x1=m you would do -12-(-9)/-6-(-9)
which would give you 3/3 which simplifies to 1.
Slope of the line is -1
Given coordinates of two points;
(X1 , Y1) = (-9, -9)
(X2 , Y2) = (-6, -12)
Find:
Slope of the line
Computation:
\(Slope\ of\ the\ line =\frac{y2 - y1}{x2 - x1}\)
By putting values;
\(Slope\ of\ the\ line =\frac{(-12 + 9)}{(-6 + 9)}\)
\(Slope\ of\ the\ line = \frac{-3}{3}\)
Slope of the line = -1
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Jason is buying wings and hot dogs for a party. One package of wings costs $7. Hot dogs cost $5 per package. He must spend no more than $40. Write and inequality to represent the cost of Jason’s food for the party. Jason knows that he will be buying at least 5 packages of hot dogs. Write an inequality to represent this situation. Graph both inequalities. Give two options for Jason when buying wings and hot dogs.
Answers
An inequality to represent the cost of Jason’s food for the party is
An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is
The two options for buying wings and hot dogs include the following:
One (1) package of wings and five (5) packages of hot dogs.Two (2) packages of wings and five (5) packages of hot dogs.How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of wings.Let the variable y represent the number of packages of hot dogs.Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;
7x + 5y ≤ 40
Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;
y ≥ 5
Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.
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Find the lateral area for the regular pyramid.
4/10 sq. units
2√10 sq. units
12 sq. units
6√10 sq. units
Answers
The lateral area for the regular pyramid. is 4√10 sq. units , Option A is the correct answer.
What is a Pyramid ?Pyramid is a three dimensional figure made of combination of basic figures.
A triangular pyramid is given in the question
The lateral area for the pyramid is
The stant height is given by
l = √10
Lateral Surface Area = (1/2) * Perimeter of the base * lateral height
Lateral Surface Area = (1/2) * 8 *√10
Lateral Surface Area = 4 √10 sq. units
Therefore Option A is the correct answer.
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Please please look at the picture and answer the question thank you so much
Answers
Answer:
t = I/(Pr)
Step-by-step explanation:
We divide P*r on both sides to isolate t and we get t=I/(P*r)