a monument stands at level ground. The angle of elevation to the top of the monument taken at a point 405 feet away is 32°. Find the height of the monument.
Answers
= 405 / cos(32)
= 477.5672534
= 477.57 ft (2dp)
The height of the monument is approximately 253.2 feet.
To find the height of the monument, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the height and distance from the observation point.
Step-by-Step Solution:
Identify the given values:
Distance from the point: 405 feetAngle of elevation: 32°Use the tangent function:
tan(θ) = opposite / adjacent
Where θ is the angle of elevation, the opposite side represents the height of the monument (h), and the adjacent side represents the distance from the point (405 feet).
Set up the equation and solve for h:
tan(32°) = h / 405 feet
Using a calculator, find tan(32°):
tan(32°) ≈ 0.6249
So the equation is:
0.6249 = h / 405
Multiply both sides by 405 to solve for h:
h ≈ 0.6249 * 405
h ≈ 253.2 feet
Thus, the height of the monument is approximately 253.2 feet.
Related Questions
Which of the following is the correct simplification of 7•4²÷ 8 -12
Answers
This can be found by solving with PEMDAS. First, you do the 4^2 (4*4), which equals 16. Next, you multiply 16 by 7, to get 112. Then, you'd divide 112 by 8. This gives you 14. Finally, subtract 12 from 14 to get your final answer of 2.
I hope this helps!
A rancher has 300 feet of fencing to enclose a pasture bordered on one side by a river. the river side of the pasture needs no fence. find the dimensions of the pasture that will produce a pasture with a maximum area.
Answers
If events A and B are mutually exclusive, find P(A/B)
A. P(A)
B. 1
C. 0
D. P(A)/P(B)
Answers
By definition,
[tex]\mathbb P(A\mid B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)[/tex]
We're told the two events are mutually exclusive, which means their intersection is disjoint and the probability of their intersection is 0. So the answer is C.
Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .
Answers
First thing first. We need to see if we are working with a unit circle and find the radius.
How to tell if we are working with a unit circle?
We know [tex]x^2 + y^2 = r^2[/tex] is a circle.
We know that to find the radius we can use the following formula:
[tex]r^2 = \sqrt{x^2 + y^2}[/tex]
If [tex]r^2 = \sqrt{x^2 + y^2} = 1[/tex] we are working with a unit circle.
Lets see if it = 1.
[tex]r^2 = \sqrt{4^2 + -7^2}[/tex]
[tex]r^2 = \sqrt{16 + 49}[/tex]
[tex]r^2 = \sqrt{65}[/tex]
Square both sides now
[tex]\sqrt{r^2} = \sqrt{\sqrt{65}}[/tex]
[tex]r = \pm 65^{\frac{1}{4}}}[/tex]
Since we squared, we have a + and a - but we disregard the - because we do not have - radii
[tex]r = 65^{\frac{1}{4}}}[/tex]
We can also say
[tex]r = \sqrt[4]{65}[/tex]
Ok, since r does not equal 1, we are not working with a unit circle but we have found r, which is our radius.
Now that we know the value of r, which is [tex]r = 65^{\frac{1}{4}}}[/tex], we need to look at the identities of cos, csc and tan.
The identities:
[tex]cos \theta = \frac{x}{r}[/tex]
[tex]csc \theta = \frac{1}{y}[/tex]
[tex]tan \theta = \frac{y}{x}[/tex]
Now that we know their identities and know the radius of our circle, we can find the exact values of cos, csc and tan.
[tex]cos \theta = \frac{x}{r} = \frac{4}{65^{\frac{1}{4}}}[/tex]
[tex]csc \theta = \frac{1}{y} = \frac{1}{-7}[/tex]
[tex]tan \theta = \frac{y}{x} = \frac{-7}{4}[/tex]
The exact values for cos, csc and tan given the point (4,-7) are:
[tex]cos \theta = \frac{4}{65^{\frac{1}{4}}}[/tex]
[tex]csc \theta = \frac{1}{-7}[/tex]
[tex]tan \theta = \frac{-7}{4}[/tex]
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
Let be a Point of the form [tex](x,y)[/tex] that is the Terminal Side of angle [tex]\theta[/tex], in sexagesimal degrees. By Trigonometry, we know that the Cosine, Cosecant and Tangent of the Angle are, respectively:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
If we know that [tex]x = 4[/tex] and [tex]y = -7[/tex], then the exact value of all the trigonometric relations are:
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\cos \theta = \frac{4}{\sqrt{4^{2}+(-7)^{2}}}[/tex]
[tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex]
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex]
[tex]\csc\theta = \frac{\sqrt{4^{2}+(-7)^{2}}}{4}[/tex]
[tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex]
[tex]\tan \theta = \frac{y}{x}[/tex]
[tex]\tan \theta = -\frac{7}{4}[/tex]
The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.
Please see the related question for further details: https://brainly.com/question/15225546
How many hours minutes and seconds are in 2165 days?
Answers
2165 days x 24 hours = 51,960 total hours
there are 60 minutes per hour
51,960 x 60 = 3,117,600 total minutes
there are 60 seconds per minute
3,117,600 x 60 = 187,056,000 total seconds
What is the degree measure of angle A?_____ degrees
Answers
Vertical angles are congruent
Angle A is vertical angles to the angle that measures 80
The answer is 80
Hope this helps!
Which figure shows how a shape can be rotated about an axis to form the given object?
Answers
The answer is as shown in the attachment which is the first diagram (on the left) on the second row which is highlighted in the attachment
That is the only figure which when rotated about the axis will form a cylindrical form as required.
The top two will form into a solid sphere and the last would form into a solid cylinder and not the one as required.
Answer:
Option C.
Step-by-step explanation:
In this question we will go by every option.
Option A). When a circle showing in the figure is rotated then a hollow ring will be formed.
Option B). In this option when a circle like structure with two layers is rotated about an axis it will forms a ring with two layers. Inner part of the ring will be empty.
Option C). In this option when a vertical strip is rotated by the axis, it will form the cylinder similar to the object shown in the figure.
Option D). In this option when a strip attached to the axis is rotated, a sold cylinder is formed.
Therefore Option C. is the correct option.
Bernard weighs 7.5 pounds at birth. assuming his development proceeds normally, he should weigh about _____ pounds by his first birthday. 22.5 24.5 20.5 18.5
Answers
Given Bernard weighs 7.5 pounds at birth.The question is asking us to assume that Bernard development proceeds normally.We need to find Bernard birth after a year.
It is observed that birth of a child triples or is thrice (3 times ) the weight at birth.As Bernard is weighing 7.5 pounds so he will triple or be 3times of this weight.
Bernard weight after a year= 3x7.5=22.5 pounds.
please show me how to answer this
Answers
how much tax you need to pay on a taxable income of 40,000
Answers
2017 RETURNS FILED IN 2018:
Single earning in this tax bracket $37,951 to $91,900, the tax rate is 25%.
Married/Joint earning in this tax bracket $18,651 to $75,900, the tax rate is 15%.
2018 RETURNS FILED IN 2018:
Single earning in this tax bracket $38,701 to $82,500, the tax rate is 22%.
Married/Joint earning in this tax bracket $19,051 to $77,400, the tax rate is 12%.
Hope this helps! :)
A dog kennel uses 90 lb of dog food per day. How many pounds are used in a year?
Answers
Lindsay's watering can holds 12 quarts of water. She uses 1 pint of water on each of her flowers.
How many flowers can she water?
Answers
12 quarts x 2 = 24 pints
1 flower = 1 pint
she can water 24 flowers
She can water 24 flowers using 12 quarts.
1 quart consists of how many pints?1 quart consists of 2 pints
So, 12 quarts = 12*2 =24 pints
It is given that she uses 1 pint of water on each flower.
So, 24 pints can be used to water =24*1 =24 flowers.
Therefore, She can water 24 flowers using 12 quarts.
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14 m equals how many mm
Answers
xoxo-Sky
The beginning balance in Cash was $3,500. Additional cash of $2,000 was received. Checks were written totaling $2,500. The cash balance is Question 3 options: $2,000. $6,000. $4,500. $3,000.
Answers
5500-2500 = $3000 so it would be 3000
use the Pythagorean theorem to determine if a triangle with sides lengths 2 feet 4 ft 5 ft is a right triangle
Answers
2^2 + 4^2 = 5^2
Multiply:
4 + 16 = 25
20 = 25
This is not true.
This is not a right triangle
at 6am the temperature is -5°f the temperature rises 6°f by noon what is the temperature at noon?
Answers
(-5)+6=1
If you use a number line, and start from -5 and "count right 6 times", you should get 1 degree Fahrenheit.
Hope this helped!!! c:
Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4
Answers
y +1 = 4(x +3) . . . . . . point-slope form
y = 4(x +3) -1 . . . . . .. another point-slope form
y = 4x +11 . . . . . . . . . slope-intercept form
4x -y +11 = 0 . . . . . . . general form
4x -y = -11 . . . . . . . . . standard form
A jar contains 8 large red marbles, 5 small red marbles, 7 large blue marbles, and 4 small blue marbles. if a marble is chosen at random, which of the conditional probabilities is larger, p(red|large) or p(large|red)?
Answers
totally = 24 marbles
P(red)= 13/24
let A red and B large
P(A/B)= P(A∩B)/P(B)
P(B)= 15/24 =.625
P(A∩B)= 8/24 = .333
P(A/B) =.333/.625 =.533
P(B/A) =.625/.333= 1.875
so the probability of p(large/red) is larger.
A plane left on time at noon on Monday. It arrived at its destination at 8:16PM the same day, which was 16 minutes late. On average, how many seconds did the plane fall behind every fifteen minutes?
Answers
So total expected time of the journey was = 8 hours
8 hours means 8 x 60 minutes = 480 minutes
480 minutes can also be seen as 32 groups of 15 minutes each as 15 x 32 = 480.
In 32 groups of 15 minutes each the plane was late by a total of 16 minutes.
So, in every 15 minute the plane was late by 16/32 minute = 0.5 minute
Thus, we can conclude that on average the plane fall behind 0.5 minutes in every 15 minutes
To find the average delay per fifteen-minute interval, convert the total delay of 16 minutes into seconds, then divide by the number of fifteen-minute intervals between noon and 8:00 PM, yielding an average delay of 30 seconds per interval.
The question asks us to calculate how much time the plane fell behind schedule, on average, every fifteen minutes. Since the plane arrived 16 minutes late, we first need to convert this delay into seconds: 16 minutes is equal to 960 seconds (16 minutes imes 60 seconds/minute). To calculate the plane's average delay per fifteen-minute interval, we divide the total delay in seconds by the total number of fifteen-minute intervals between noon and the expected arrival time at 8:00 PM, which is 32 intervals (8 hours ×4 intervals/hour). Therefore, the average delay per interval is 960 seconds \/ 32 intervals = 30 seconds per interval.
Instructions:Select the correct answer from the drop-down menu. In the figure, sin ∠MQP = cos N and sin R sin R and sin N cos N and sin M cos R and sin N .
Answers
sin ∠MQP = sin(56) = 0.829cos ∠N = cos(56) = 0.559sin ∠R = sin(34) = 0.559sin ∠N = sin(56) = 0.829cos ∠N = cos(56) = 0.559sin ∠M = sin(90) = 1cos ∠R = cos(34) = 0.828
Based on these findings, it is obvious that sin ∠MQP is equal to cos ∠R and sin ∠N.Thus, the correct choice is "cos R and sin N".
Answer:
Cos R and sin N
Step-by-step explanation:
QM Q2.) Find the multiplicities of the greatest zero, second greatest zero, and the smallest zero.
Answers
First check out the zeros (first box).
Step One.
Put brackets around terms 1 and 2 and another set around terms 3 and 4.
f(x) = (x^3 + 8x^2) - (4x + 32) Watch out that you change the sign on the 32. Minus signs can be devastating. The idea is that when the brackets are removed, the question will be exactly as it was before you put the brackets there.
Step Two
Pull out any common factors.
f(x) = x^2(x + 8) - 4(x + 8)
Step Three.
If there is a common binomial pull it out as well. This is the hardest part of the problem. The binomials have to be exactly alike (in this case they are).
f(x) = (x + 8) (x^2 - 4)
Step Four
Factor (x^2 - 4). This is an exact difference of squares. It factors into
x^2 - 4 = (x + 2)(x - 2)
Step five
Find the zeros.
f(x) = (x + 8)(x - 2)(x + 2)
x + 8 = 0
x = - 8
x + 2 = 0
x = - 2
x - 2 = 0
x = 2
I know you didn't ask for all of this, but when someone asks a question, it's always a good idea to check the work done. In your case it was all correct. That's a very good thing.
Definition
Multiplicity is the number of times a root appears in the solution of a polynomial.
For example, g(x) = (x - 5)^2 (x - 4)
The five would have a multiplicity of 2 because the equation is really
g(x) = (x - 5)(x - 5) ( x - 4). There are 2 roots that are the same (both are 5).
4 has a multiplicity of 1 in this example.
Answer
The largest root is 2. It has a multiplicity of 1
The second largest root is -2. It has a multiplicity of 1
The tiniest root is - 8 . It has a multiplicity of 1
Exercise 3.8 asked you to write a method called quadratic that solves quadratic equations and prints their roots. recall that a quadratic equation is a polynomial equation in terms of a variable x of the form a x2 + b x + c = 0. the formula for solving a quadratic equation is:
Answers
x=[-b+/-√(b²-4ac)]/2a
where a,b and c are the respective coefficients as indicated in the quadratic form.
CC=\frac{5}{9}(F - 32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answers
My work:
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III is true
If the graph of the function h is defined by = h(x)+x^2+9 is translated vertically downward by 9 units, it becomes the graph of a function g. Find the expression for
gx
Answers
Solution:
The graph of h(x) = x²+9 translated vertically downward by 9 units means that each point (x, h(x)) is shifted onto the point (x, h(x) - 9), that is,
(x, h(x)) → (x, h(x) - 9)
The translated graph that represents the function is defined by the expression for g(x):
g(x) = h(x) - 9 = x² + 9 - 9 = x²
h(x) = x²+9 → g(x) = x² shows that the graph of the equation g(x) = x² moves the graph of h(x) = x²+9 down nine units.
A test is worth 50 points. Multiple-choice questions are worth 1 point, and short-answer questions are worth 3 points. If the test has 20 questions, how many multiple-choice questions are there?
A. t for test, q for questions
B. m for multiple choice, s for short answer
C. s for short answer, t for test
D. p for points, m for multiple choice
apex mcr
Answers
S * Q + M * Q = P
Representations:
S = The amount of points for short-answer questions.
M = The amount of points for multiple-choice questions.
Q = Number of questions for each of the type of questions that add up to the total number of questions on the test (20 questions).
P = Total points on the test.
Since there is a total of 50 points on the 20 question test, you would need to divide up the amount of questions there are for each of the type there are on the test, short-answer, and multiple-choice.
3 * Q + 1 * Q = P
Now find how many of the type of questions there are out of 20 questions on the test that would add up to the total number of points on the test.
3 * Q + 1 * Q = 50
(15 + 5 = 20 questions on the test, 15 and 5 can be used for the number of questions for each type of question on the test).
3 * 15 + 1 * 5 = 50
45 + 5 = 50
50 = 50
So, your total number of multiple choice questions are: 5.
And, your total number of short answer questions are: 15.
I would go with D. for your answer. I may be wrong.
I hope this helps.
~ Notorious Sovereign
A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water in simplest form?
Answers
cleaner:water
1 1/2:12
simplifying the above we get:
3/2:12
multiplying both sides by 2 we get:
2×3/2:12×2
3:24
hence the answer is 3:24
four friends share 3 fruits bars equally how much does each friend get
Answers
each friend gets 0.75 of a bar
The average weekly income of teachers in one school district is $750 with a standard deviation of $85. Find the percentage of teachers earing more than $825 a week?
Answers
Standard deviation = $85
P(X>$825) = ?
Z = (X-mean)/Standard deviation = (825-750)/85 ≈ 0.88
From Z-table, P(X=825) = 0.8106
Therefore,
P(X>$825) = 1 - P(X=$825) = 1-0.8106 = 0.1894 = 18.94%
Percentage of teachers earning more than $825 is 18.94%.
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. y = cos x (3 + v5)8 dv sin x
Answers
[tex]y(x)=\displaystyle\int_{\cos x}^{\sin x}(3+v^5)^8\,\mathrm dv[/tex]
(If the limits are in the wrong order, just multiply the result by -1)
Split the integral at an arbitrary value between [tex]\cos x[/tex] and [tex]\sin x[/tex], and write [tex]y(x)[/tex] as
[tex]y(x)=\displaystyle\left\{\int_{\cos x}^c+\int_c^{\sin x}\right\}(3+v^5)^8\,\mathrm dv[/tex]
[tex]y(x)=\displaystyle\int_c^{\sin x}(3+v^5)^8\,\mathrm dv-\int_c^{\cos x}(3+v^5)^8\,\mathrm dv[/tex]
Then by the FTC,
[tex]\dfrac{\mathrm dy}{\mathrm dx}=(3+\sin^5x)^8\cdot\dfrac{\mathrm d\sin x}{\mathrm dx}-(3+\cos^5x)^8\cdot\dfrac{\mathrm d\cos x}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\cos x(3+\sin^5x)^8+\sin x(3+\cos^5x)^8[/tex]
The first part of the Fundamental Theorem of Calculus provides a method to find the derivative of a function. However, clarity is needed in the question as it has extra elements. If we consider the derivative of y = cos x (3 + √5)8 sin x, it would be f'(x) = -sin x (3 + √5)8 sin x + cos x (3 + √5)8 cos x.
Explanation:Since the question asks for the derivative of the function y = cos x (3 + √5)8 dv sin x, we'll need to use the First Part of the Fundamental Theorem of Calculus. This theorem states that if a function f is continuous over the interval [a, b] and F is an antiderivative of f on [a, b], then the definite integral from a to b of f(x) dx equals F(b) - F(a). In this case, we have y = cos x (3 + √5)8 dv sin x which sadly is not clear due the presence of apparently extra and possibly typographical elements.
Assuming, the question intends to find derivative of y = cos x (3 + √5)8 sin x, we can proceed as follows:
Let f(x) = cos x (3 + √5)8 sin x. Then by applying the chain rule, we get: f'(x) = -sin x (3 + √5)8 sin x + cos x (3 + √5)8 cos x.
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SCIENCE HELP 10 POINTS!!!!!
The greenhouse effect traps heat near earth's surface. Greenhouse gases in the atmosphere—carbon dioxide, water vapor, methane, and nitrous oxide—allow the shorter waves of ultraviolet radiation from the sun to enter earth's lower atmosphere. However, these gases do not allow the longer wavelengths of infrared radiation to pass back out to the outer atmosphere. The result is that the lower atmosphere heats up.This result happens naturally, but it can be accelerated by human activities. Since the late 1800s, human activity has greatly altered the amount of greenhouse gases that enter the atmosphere. Burning fossil fuels, farming, and clearing forests, as well as industry, have all contributed to increases of carbon dioxide (CO2), methane, nitrous oxide, and other greenhouse gases in the atmosphere.The result is that temperatures in the troposphere have gone up. Many scientists identify this increase in greenhouse gas emissions as contributing directly to global warming. This suggests that human activity has had an impact on the global climate.
The author argues that in modern times, the greenhouse effect *
A.helps keep the Earth warm
B.has increased because of human activity
C.is in a natural cycle of changing
D.has changed local weather patterns
Answers
C.is in a natural cycle of changing