A person observes the top of a radio antenna at an angle of elevation of 5 degrees after getting 1 mile closer to the antenna the angle of elevation is 10 degrees how tall is the antenna to the nearest tenth of a foot?
Answers
The height of the antenna is approximately 5.1 feet.
1. Let's assume the height of the antenna as 'h' feet.
2. We have two angles of elevation: 5 degrees and 10 degrees.
3. When the person is 1 mile closer to the antenna, the change in the angle of elevation is 10 - 5 = 5 degrees.
4. We can use the tangent function to find the height of the antenna. The tangent of an angle is equal to the opposite side divided by the adjacent side.
5. The opposite side is the change in height, which is h feet (since the person moved closer by 1 mile, the change in height is equal to the height of the antenna).
6. The adjacent side is the horizontal distance from the person to the antenna. We can use trigonometry to find this distance.
7. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
tan(5 degrees) = h / x (where x is the horizontal distance in miles)
8. Similarly, after moving closer, the tangent of the angle becomes:
tan(10 degrees) = h / (x - 1)
9. We can solve these two equations simultaneously to find the value of h.
10. Rearranging the equations, we get:
h = x * tan(5 degrees)
h = (x - 1) * tan(10 degrees)
11. Setting the two expressions for h equal to each other, we have:
x * tan(5 degrees) = (x - 1) * tan(10 degrees)
12. Solving this equation for x, we find:
x = tan(10 degrees) / (tan(10 degrees) - tan(5 degrees))
13. Substitute the value of x back into one of the earlier equations to find h:
h = x * tan(5 degrees)
14. Calculate the value of h using a calculator:
h ≈ 1 * tan(5 degrees) ≈ 0.0875 miles ≈ 0.0875 * 5280 feet ≈ 461.4 feet
15. Rounded to the nearest tenth of a foot, the height of the antenna is approximately 5.1 feet.
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Related Questions
Jermaine kicked a soccer ball at a speed of 24 feet per second. If the ball never leaves the ground, then it can be represented by the function H(t) = −16t2 + 24t. Determine the time the ball traveled. (1 point) t = 24 seconds t = 8 seconds t = 1.5 seconds t = 0.67 seconds
Answers
The time that the ball traveled is given as follows:
1.5 seconds.
How to obtain the time traveled by the ball?The quadratic function determining the ball's height after t seconds is given as follows:
H(t) = -16t² + 24t.
The roots of the quadratic function in this problem are given as follows:
-16t² + 24t = 0.
16t² - 24t = 0
8t(2t - 3) = 0.
Hence we apply the factor theorem as follows:
8t = 0 -> t = 0.2t - 3 = 0 -> 2t = 3 -> t = 1.5.Hence the time is given as follows:
1.5 - 0 = 1.5 seconds.
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Given the statement, TSR: ABC and the diagram
of the right triangle TSR, determine the
approximate length of BC
Answers
HELP PLS ASAPPP!!!
algebra problem; solving linear inequalities !!! :)
Answers
Answer: x = -3/2
Step-by-step explanation:
hich of the following expressions is never a prime number when p is a prime number? (a. p2 16, b. p2 24, c. p2 26, d. p2 46, e. p2 96)
Answers
From the given expressions of prime numbers, the following are never a prime number:
Option b. p²+ 24
Option c. p²+ 26
Prime number is represented by 'p'
The expressions which can never be a prime number is given by :
Let us consider value of p = 1
a. p²+ 16
⇒1² + 16
⇒17 a prime number
b. p²+ 24
⇒1² + 24
⇒25 is not a prime number.
c. p²+ 26
⇒1² + 26
⇒27 is not a prime number.
d. p²+ 46
⇒1² + 46
⇒47 a prime number.
e. p²+ 96
⇒1² + 96
⇒97 a prime number.
Therefore, the expression represented by option b. p²+ 24 and option c. p²+ 26 can never be a prime number.
The above question is incomplete , the complete question is :
Which of the following expressions is never a prime number when p is a prime number?
a. p²+ 16 b. p²+ 24 c. p²+ 26 d. p²+ 46 e. p²+ 96
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Find the exAct length of a line segment whose endpoints are (4,-5) and (6,-2).
Answers
Answer:
Square root of 13
Step-by-step explanation:
distance between two points = under root (x2-x1)^2 + (y2-y1)^2
here, (x1,y1)=(4,-5) & (x2,y2)=(6,-2)
Substitute values and finally you can get it..
PLEASE HELP- ITS URGENT-
Answers
Answer:
x = 20°
Step-by-step explanation:
here's your solution
=>. we know that, sum of two opposite interior angle is equal to one exterior
=> (3x)° + (3x -20)° = (7x - 40)°
=> 6x - 20° = 7x - 40
=> - x = - 20
=> x = 20
hope it helps
Answer:
20°
Step-by-step explanation:
C.20 is the correct answer.
An artist's canvas has sides measuring 3x + 5 and 2x + 1 inches.
What is the area of the canvas? Show all work.
The artist laid the canvas flat on the floor and poured some paint in the center. The paint flows at a rate of r(t) = 2t where t represents time in minutes and r represents how far the paint is spreading on the canvas. The area of the paint can be expressed as A[r(t)]= rur?. What is the area of the circle created by the paint?
If the artist wants the circle to be at least 300 in?, will it be that large in 5 minutes? Support your answer with your work.
Answers
The area of the circle created by the paint is given by the expression 4πt².
The area of the circle is 100π, which is approximately 314.16 in².
The circle will be at least 300 in² in 5 minutes. Yes.
To find the area of the canvas, we multiply the lengths of its sides:
Area = (3x + 5) × (2x + 1)
Expanding the expression:
Area = 6x² + 3x + 10x + 5
Combining like terms:
Area = 6x² + 13x + 5
The area of the canvas is given by the expression 6x² + 13x + 5.
Now, let's find the area of the circle created by the paint.
The area of a circle is given by the formula A = πr², where r represents the radius.
The radius is given by the spreading of paint, which is r(t) = 2t.
Substituting the value of r(t) into the formula, we have:
A[r(t)] = π(2t)²
Simplifying:
A[r(t)] = π(4t²)
A[r(t)] = 4πt²
Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.
Substitute t = 5 into the area formula:
A[r(5)] = 4π(5)²
A[r(5)] = 4π(25)
A[r(5)] = 100π
Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.
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Factorise fully the following
9x^2+3x^3
Answers
Answer:
\(3x^2\left(3+x\right)\)
Step-by-step explanation:
Look for common factor: \(3x^{2}\) since we take the least exponent
and between numbers (3,9) the common factor is 3.
Thefore, we need to divide \(3x^2\) by the equation.
\(3x^2(3+x)\).
Step-by-step explanation:1. Write the expression.\(9x^2+3x^3\)
2. Find a common denominator for both expressions, based on the x variable.\(\frac{9x^2}{3x^2} +\frac{3x^3}{3x^2} \\ \\3x^2(3+x)\)
3. Express your result.\(9x^2+3x^3=3x^2(3+x)\).
At a furniture store, 20% of chairs are blue, 50% orange and 30% black. A blue chair has a 20% probability of being comfortable. A chair that is not blue has a 5% probability of being comfortable. What is the probability that a comfortable chair in the store is blue?
Answers
The probability that a comfortable chair in the store is blue is 4%
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Proportion of blue chairs = 20%
Proportion of orange chairs = 50%
Proportion of black chairs = 30%
Comfortable Blue chairs = 20%
Comfortable non-blue chairs = 5%
The required probability is then calculated as
Probability = Proportion of blue chairs x Comfortable Blue chairs
Substitute the known values in the above equation, so, we have the following representation
Probability = 20% * 20%
Evaluate
Probability = 4%
Hence, the probability is 4%
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What is the solution of the equation below ?
Answers
Answer:
d = ±7i
Step-by-step explanation:
d^2 -1 = -50
Add 1 to each side
d^2 -1 = -50
d^2 = -49
Take the square root of each side
sqrt(d^2) = sqrt(-49)
d = sqrt(-1) sqrt(49)
d = i( ±7)
d = ±7i
Answer:
A.
Step-by-step explanation:
d^2-1= -50
First, add 1 to both sides.
d^2= -49
Take the square root of both sides:
d=√-49
Since i^2=-1
d=i√49
d= ±7i
Hope this helps!
Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
Answers
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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To assess the effectiveness of a kindergarten-readiness program, 15 children from a random sample were each given a diagnostic assessment before beginning the program and a follow-up assessment after completing the program. For each child, the difference in the score points between the two assessments was calculated and used to create the 95 percent confidence interval (20.1,23.9)(20.1,23.9).
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
A) For all children in the program, 95 percent of the children will have a mean difference in scores of between 20.1 points and 23.9 points.
B) There is a 0.95 probability that the mean difference in scores for all children in the sample is between 20.1 points and 23.9 points.
C) There is a 0.95 probability that the mean difference in scores for the children in the program is between 20.1 points and 23.9 points.
D) We are 95 percent confident that the mean difference in scores for all children in the program is between 20.1 points and 23.9 points.
E) We are 95 percent confident that the mean difference in scores for the children in the sample is between 20.1 points and 23.9 points.
Answers
Answer:
D) We are 95 percent confident that the mean difference in scores for all children in the program is between 20.1 points and 23.9 points.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
95 percent confidence interval (20.1,23.9)
We are 95% sure that the population mean(that is, the mean for all children in the program) is in this interval. So the correct answer is given by option D.
Which to be used to write an inequality?A. C.=D.+
Answers
The symbols > and < can be used to write an inequality. (Options A and B)
Select the correct sentences in the passage. Which statements are true? Any two squares are either similar or congruent. If two lines are parallel, they never intersect. If all the angles of a polygon are congruent, then it is a square. The intersection of two lines always forms 4 congruent angles. A line can be drawn through any two distinct points.
Answers
The correct sentences in the passage are option A, option B, and option E.
Any two squares are either similar or congruent. If two lines are parallel, they never intersect.A line can be drawn through any two distinct points.Let's check all the options, then we have
Any two squares are either similar or congruent. The statement is true.
If two lines are parallel, they never intersect. The statement is true.
If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.
The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.
A line can be drawn through any two distinct points. The statement is true.
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Give a precise and thorough example of a function with a minimum at a value where its derivative is undefined.
Answers
The required example of a function with a minimum at a value where its derivative is undefined is f(x) = |x|.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
A function that has a minimum at a point where its derivative is undefined is the absolute value function. The absolute value function is defined as:
f(x) = |x|
At x = 0, the absolute value function has a minimum value of 0. However, the derivative of the absolute value function is undefined at x = 0, because the function is not differentiable there.
At x < 0, the absolute value function is decreasing and therefore has a negative derivative. At x > 0, the absolute value function is increasing and therefore has a positive derivative. At x = 0, the behavior of the function changes abruptly from decreasing to increasing, which makes the derivative undefined. Despite this, the absolute value function still has a minimum value of 0 at x = 0.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 9854 total votes, how many no votes were there?
Answers
There were approximately 6056 no votes.
Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.
Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.
The total number of votes is given as 9854, so we can set up the following equation:
\(5x + 8x = 9854\)
Combining like terms, we have:
\(13x = 9854\)
To solve for x, we divide both sides of the equation by 13:
\(x = \frac{9854 }{13}\)
\(x \approx 757.23\)
Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.
Now, we can find the number of no votes by multiplying x by the ratio of no votes:
No votes \(= 8x\)
\(= 8 \times 757\)
\(= 6056\)
Therefore, there were approximately 6056 no votes.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
90+51+x=180(sum of interior angles of a triangle)
141+x=180
x=180-141
x=39 degree
Step-by-step explanation:
please help, if you do thank you so muchhh ur a life saver
Answers
Based on the information, we can infer that the theoretical probability of these colors would be 33.33%. However, the table reflects different data.
How to calculate the theoretical probability of drawing the colors?To calculate the theoretical probability of each color we must perform the following mathematical operation.
Bearing in mind that 300 is 100% of the people, we must divide 300 by 3 to know how many people should choose a specific color. In this case, every 100 people should choose a different color.
Additionally, these 100% would represent 33.33% of the total population.
100 * 100 / 300 = 33.33%
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statement for expression 2y-9 is _____
Answers
Answer:
9 subtracted from y multiplied by 2
A perpendicular bisector of DC is AB and a perpendicular bisector of AB is DC. the intersection of AB and DC is at E. Which equation is true?
EB =CD
AE= DE
DE = CE
CD= CE
AB=CD
Answers
Answer: DE = CE
Step-by-step explanation: AB is a continuous line so the distance from A to E could be different than the distance from D to E.
DE = CE is true.
A perpendicular bisector is a line that divides another line into two equal parts and is also perpendicular to it.
Here, we are given that AB is the perpendicular bisector of DC and DC is a perpendicular bisector of AB.
This means that AB and DC are the perpendicular bisectors of each other at the point of intersection, that is, E.
Now, since AB bisects DC at point E
⇒ DE = CE
and similarly, DC bisects AB
⇒ AE = BE
Apart from these two equalities, we cannot infer anything else from the given information.
Thus, out of the given options, we can see that only option 3, that is, DE = CE is true.
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Find perimeter of rectangle when length = 4.6m and breadth = 360cm
Answers
Answer:
16.4 m²
Step-by-step explanation:
length = 4.6 m
breadth = 360 cm = 360 ÷ 100 = 3.6 m
Perimeter = 2*(l + b)
= 2 * ( 4.6 + 3.6)
= 2 * 8.2
= 16.4 m²
Find the dot product of m=−4i−j and n=5j.
Answers
d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (3, 2) and point (5, 4) rounded to nearest 10th
Answers
Find the output, y, when the input, x, is -9.
y =
Answers
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another, calculate the probability that exactly one of the next three vehicles fail. (give your answer as a decimal number with 3 digits of precision.)
Answers
The probability that exactly one of the next three vehicles fail is 0.737 .
Given :
64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another .
probability that exactly one of the next three vehicles fail is :
P = 1 - probability that all of the next three vehicles passes .
= 1 - 64 % * 64 % * 64 %
= 1 - 64/100 - 64/100 - 64/100
= 1 - 0.64 * 0.64 * 0.64
= 1 - 0.4096 * 0.64
= 1 - 0.262
= 0.737
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Which numbers are between 9.23 and 9.25
Answers
Answer:
9.24
Step-by-step explanation:
describe this diagram help please
Answers
Answer:
U are finding the slope. so the vertical line is ur rise(x value) and the horizontal line is ur y value. Hopefully that helped
28453 dg a t
porfa ayudenme
pipipipi
Answers
Answer:
488
Step-by-step explanation:
You divide 28453 by 58.3053278689 and get 488.
Shadows cast angles at equal measures, making triangles formed by shadows similar.
Lance the alien is 5 feet tall. His shadow is 8 feet long.
Answers
Answer:
the third side is 9.43
Step-by-step explanation:
the length from his head to the shadow of his head is the same as
\(5^{2}\) + \(8^{2}\) = \(c^{2}\)
so we solve this to get c = 9.43