Answers
We have shown that h = 40 / √(\(tan^{2}\)70°+ \(tan^{2}\) 55° + 1.1472 tan 70° tan 55°).
What is trigonometry?
The relatiοnship between the sides and angles οf triangles is the subject οf the branch οf mathematics knοwn as trigοnοmetry.
A. Here is the diagram that represents the situatiοn:
T (top of tower)
/\
/ \
/ \
/ \
/ \
P Q
P is due sοuth οf the tοwer.
Q is 40 meters east οf the tοwer.
The angle οf elevatiοn frοm P tο the tοp οf the tοwer is 20 degrees.
The angle οf elevatiοn frοm Q tο the tοp οf the tοwer is 35 degrees.
B. Let's use trigοnοmetry tο sοlve fοr h.
Frοm triangle PTQ, we knοw that:
PT = h / tan 20° (using οppοsite οver adjacent)
TQ = h / tan 35° (using οppοsite οver adjacent)
PQ = 40 meters (given)
Frοm triangle PTQ, we can alsο use the Law οf Cοsines:
\(PQ^{2}\)= \(PT^{2}\) + \(TQ^{2}\) - 2 PT TQ cos 125° (using \(a^{2}\) = \(b^{2}\) + \(c^{2}\) - 2bc cos A)
Substituting the values we know:
\((40)^{2}\) =\((h/tan 20)^{2}\) + \(h/tan^{2}\)20° - 2 (h/tan 20°(h/tan 35°) cos 125°
Simplifying the equation, we get:
\((40)^{2}\) = \(h^{2}\) (\(1/tan^{2}\) 20° + 1/tan² 35° - 2/tan 20° tan 35° cos 125°)
\((40)^{2}\) = \(h^{2}\) (\(tan^{2}\) 70° + tan² 55° - 2 tan 70° tan 55° (-0.5736))
\((40)^{2}\) = \(h^{2}\) (\(tan^{2}\) 70° + tan² 55° + 1.1472 tan 70° tan 55°)
\(h^{2}\) = \((40)^{2}\) / (\(tan^{2}\) 70° + tan² 55° + 1.1472 tan 70° tan 55°)
h = sqrt[\((40)^{2}\) / (\(tan^{2}\) 70° + tan² 55° + 1.1472 tan 70° tan 55°)]
h = 40 / sqrt(\(tan^{2}\) 70° + \(tan^{2}\) 55° + 1.1472 tan 70° tan 55°)
Therefore, we have shown that h = 40 / √(\(tan^{2}\) 70°+ \(tan^{2}\) 55° + 1.1472 tan 70° tan 55°).
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Similar Graph
Related Questions
find the value of each variable
Answers
x=5
y= 7.07
.......................................
Answer:
x=5 y=7.07
Step-by-step explanation:
hope it helps you out
Veronica is buying 6 ham sandwiches and 3 cheese sandwiches. Each sandwich
costs $4. The equation below can be used to find Veronica's total cost.
Veronica says all the sandwiches will cost more than $30. Use the drop-down
menus to explain if her statement is reasonable.
4×6+3=0
Answers
Answer: 36
Step-by-step explanation: 6 + 3 = 9.
4 * 9 = 36
Veronica's statement is reasonable because they cost more than $30.
The total amount of sandwiches is $36
Calculations and Parameters:Given that:
She buys 1 sandwich for $4
She buys 6 ham sandwiches and 3 cheese sandwiches
To find the total cost for Veronica would be:
6+3 = 9 total sandwiches
4 * 9= 36 total cost of the sandwiches.
Therefore, Veronica's statement is reasonable because they cost more than $30
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If a family has five girls and plans to have another child, answer the following if the probability of the event of a boy being born is \( \frac{1}{2} \), and births are independent events. a. What is
Answers
In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.
The previous births do not affect the probability of the next birth since each birth is an independent event.
The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.
Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.
In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.
Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.
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Identify m∠MNQ. PLEASE HELP!!!
Answers
Answer:
∠ MNQ = 40°
Step-by-step explanation:
The inscribed angle MNQ is half the measure of its intercepted arc, so
∠ MNQ = \(\frac{1}{2}\) MQ = 0.5 × 80° = 40°
The value of the angle ∠ MNQ will be 40°. The correct option is D.
What is the angle of chords theorem?When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The inscribed angle MNQ is half the measure of its intercepted arc, so
∠ MNQ = ( 1 / 2 )MQ
∠ MNQ = 0.5 × 80°
∠ MNQ = 40°
Therefore, the value of the angle ∠ MNQ will be 40°. The correct option is D.
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There are two pairs $(x,y)$ of real numbers that satisfy the equation $x+y = 3xy = 4$. Given that the solutions $x$ are in the form $x = \frac{a \pm b\sqrt{c}}{d}$ where $a$, $b$, $c$, and $d$ are positive integers and the expression is completely simplified, what is the value of $a + b + c + d$?
Answers
The value of expression (a + b + c + d) is 20
Consider given equations x + y = 4 ........(1)
and 3xy = 4 .........(2)
The solutions of given equations are of the form \($x = \frac{a \pm b\sqrt{c}}{d}$\)
where a, b, c, and d are positive integers and the expression is completely simplified.
From equation (2),
y = 4/3x
Substitute above value of y in equation (1),
x + y = 4
x + (4/3x) = 4
3x² + 4 = 12x
3x² - 12x + 4 = 0
After solving above quadratic equation we get,
\(x=\frac{6\pm 2\sqrt{6} }{6}\)
Comapring this solution with \($x = \frac{a \pm b\sqrt{c}}{d}$\) we get,
a = 6, b = 2, c = 6 and d = 6
Now we find the value of expression (a + b + c + d)
a + b + c + d
= 6 + 2 + 6 + 6
= 20
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Which postulate /theorem can you use to prove the two triangles shown are congruent?
Answers
single adults: according to a pew research center analysis of census data, in 2012, 20% of american adults ages 25 and older had never been married. suppose that we select random samples from this population of american adults ages 25 and older. for each sample we then calculate the proportion that had never been married. (source: wang, w., and parker, k. (2014). record share of americans have never been married. pew research center.)
Answers
According to the Pew Research Center analysis of census data in 2012, 20% of American adults aged 25 and older had never been married.
If we select random samples from this population, we can calculate the proportion of adults who have never been married in each sample.
This finding indicates a significant proportion of single adults in this demographic group.
The Pew Research Center analyzed the census data and calculated the percentage of unmarried individuals within the specified age range. The sample selection was likely done randomly to ensure representativeness.
The analysis provides valuable insights into the marital status of American adults and offers a snapshot of the population at that particular time. It is worth noting that social and cultural factors, as well as individual choices, contribute to the varying proportions of married and unmarried individuals.
The Pew Research Center's analysis of census data in 2012 revealed that 20% of American adults aged 25 and older had never been married.
This finding sheds light on the prevalence of singlehood in this demographic group, highlighting the importance of understanding and addressing the unique needs and experiences of unmarried adults in society.
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the london eye is a ferris wheel in london, england. the diameter of the wheel is 120 meters and the maximum height it reaches is 135 meters. one revolution takes 30 minutes. how long will it take a passenger to reach 400 feet (121.92 meters)?
Answers
To calculate the time it will take a passenger to reach 400 feet on the London Eye Ferris wheel, we need to convert 400 feet to meters, which is approximately 121.92 meters.
We know that the diameter of the wheel is 120 meters and the maximum height it reaches is 135 meters. Since the wheel takes 30 minutes to complete one revolution, we can use this information to calculate the time it will take to reach 121.92 meters.
To do this, we need to find the fraction of the wheel that corresponds to 121.92 meters. Since the diameter is 120 meters, the radius is 60 meters. This means that the height of the wheel at any point is equal to the radius multiplied by the sine of the angle between the horizontal and the radius. Using trigonometry, we can find that the sine of the angle corresponding to a height of 121.92 meters is approximately 0.9925. This means that the corresponding angle is approximately 81.6 degrees.
Since the wheel takes 30 minutes to complete one revolution, which is 360 degrees, we can find the time it will take to reach 121.92 meters by multiplying the fraction of the wheel corresponding to 81.6 degrees by 30 minutes. The fraction of the wheel is 81.6/360, which is approximately 0.2267. Multiplying this by 30 minutes gives us the answer: approximately 6.8 minutes. Therefore, it will take a passenger approximately 6.8 minutes to reach 400 feet (121.92 meters) on the London Eye Ferris wheel.
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Graph y = x + 4?!?!?
Answers
Answer:
place a point at (0, 4) and (-4, 0) and draw a line through them
Step-by-step explanation:
to graph something, place a point at the slope intercepts.
to find the y intercept, set x to 0
y = 0 + 4
y = 4
the y intercept is 4, or (0, 4)
to find the x intercept, set y to 0
0 = x + 4
0 - 4 = x + 4 - 4
0 - 4 = x
-4 = x
the x intercept is -4 or (-4, 0)
Slope: 1 means up 1 over 1
Y- int (0,4)
What is the slope of the line represented by the equation y=4/5x-3? A.-3 B.-4/5 C.4/5 D.3
Answers
Answer:
4/5
Step-by-step explanation:
y = 4/5 x -3
This is written in slope intercept form
y =mx + b where m is the slope and b is the y intercept
the slope is 4/5 and the y intercept is -3
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inches.
If the area of the rectangle is 22 square inches, what is the value of the unknown number?
inches
Answers
The answer is unknown number of inches for the long sides is 14.
Let's solve this problem step by step. We know that the short sides of the rectangle are 2 inches. Let's denote the unknown number of inches for the long sides as 'x'. According to the problem, the long sides are three less than this unknown number, so the length of the long sides can be expressed as 'x - 3'.
The area of a rectangle is given by the formula A = length × width. In this case, the area is given as 22 square inches, and the width (short side) is 2 inches. We can now set up the equation:
22 = 2 × (x - 3)
Simplifying the equation, we have:
22 = 2x - 6
Adding 6 to both sides, we get:
28 = 2x
Dividing both sides by 2, we find:
x = 14
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7x+5 and 12x *
A: Yes, they are equivalent
B: No, they're not equivalent
Answers
Answer:
No they are not equivalent.
Step-by-step explanation:
7x + 5 stays the same. You cannot combine them since they aren't like terms.
12x isnt 7x + 5. Therefore no they are not equivalent.
Find the mean, median, mode and range 28,45,53,28, 47 show work please
Answers
Value of mean is, 40.2
Value of median is, 45
Value of mode is, 28
Value of range is, 25
Given that;
Data set is,
⇒ 28, 45, 53, 28, 47
Now, We can arrange into ascending order as;
⇒ 28, 28, 45, 47, 53
Hence, Value of mean is,
⇒ (28 + 28 + 45 + 47 + 53) / 5
⇒ 40.2
And, The value of median is,
⇒ (5 + 1) / 2
⇒ 6/2
⇒ 3rd term
⇒ 45
The value of mode =28
And, The value of range is,
⇒ 53 - 28
⇒ 25
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how many cups of granulated sugar in a 5 pound bag
Answers
There are approximately 11.25 cups of granulated sugar in a 5 pound bag.
To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.
First, we multiply the number of pounds (5) by the conversion factor:
5 pounds * 2.25 cups/pound = 11.25 cups
Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.
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56 dvide 9 please help me with steps
Answers
Answer: 6 your welcome :)
What is the result of multiplying the first equation by −3
and adding to the second equation?
5x−2y=−2
3x+y=12
A. −10x+8y=15
B.−12x+7y=18
C. 12x+7y=18
D.8x−y=10
Answers
Answer:i got u mate
The answer is a _10×+8y=15
Step-by-step explanation:
Suppose you want to figure out how likely it would be to spin red and flip tails. We call red and tails the event.
Answers
Answer with Explanation: We need to find the probability of obtaining the red and tails when the two are flipped at the same time:
\(\begin{gathered} P\left(R\right)=\frac{1}{2} \\ P\left(T\right)=\frac{1}{2} \end{gathered}\)The probability of the red and tails or P(Red and Tails) is as follows:
\(\begin{gathered} P\left(R\text{ and }T\right?=P\left(R\right)\times P\left(T\right) \\ \therefore\rightarrow \\ P\left(R\text{ and }T\right?=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ P\left(R\text{ and }T\right?=\frac{1}{4} \end{gathered}\)Conclusion: Therefore the probability is (1/4) or 25%.
Dominique had $250 to spend at the mall. She bought jeans for $27.50, a sweater for $32.75, and 3 shirts for $12.50 each. How much money does she have left after shopping?
Answers
Answer:
152.25
Step-by-s152.25tep explanation:
Answer:
Dominique has $162.25 dollars left after shopping.
Step-by-step explanation:
250 - 17.50 - 32.75 - 12.50 x 3
250 - 17.50 - 32.75 - 37.5
232.5 - 32.75 - 37.5
199.75 - 37.5
162.25
If 18 children share 452 candies equally, how many candies will be left unshared?
Answers
Answer:
Around 25
Step-by-step explanation:
452 candies/18 children
= 25.11111111
Meaning there are around 25 left
Answer:
452 divided by 18 equals
25 with a remainder of 2
Step-by-step explanation:
hello how are you doing today
Answers
I am doing fine thanks bro.
What is the Next number in this series 7 11 19 35?
Answers
Answer:
67
Step-by-step explanation:
we have a gap between 1st and 2nd terms of 4. a gap between 2nd and 3rd of 8. 16 for next gap. the gap doubles every time.
so we expect gap between 4th and 5th terms to be 2 X 16 = 32.
35 + 32 = 67. that is the next number in the sequence.
in one right triangle the legs are 21cm and 28cm. the legs of the second right triangle are 15cm and 20cm. are these triangles are similar?
Answers
Answer:
Yes
Step-by-step explanation:
21÷7=3
24÷7=4
15÷5=3
20÷5=4
Simplify -(3xy^4)^-4
Answers
Answer:
\(\frac{-1}{81x^4y^16}\)
Step-by-step explanation:
→Rewrite the expression so that the exponent is no longer negative. To do this, you write it as:
\(\frac{-1}{(3xy^4)^4}\)
→Apply the exponent (4) to the 3, x, and \(y^4\):
\(\frac{-1}{81x^4y^16}\)
List the first 4 terms of this sequence
Answers
The first four terms of the sequence is 6, 9, 12 and 15
How to determine the first four termsThe definition of the function is given as
a₁= 6
aₙ = aₙ₋₁ + 3
The above definitions imply that we simply add 3 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₂ = 6 + 3
a₂ = 9
Also, we have
a₃ = 9 + 3
a₃ = 12
Lastly, we have
a₄ = 12 + 3
Evaluate the equation
a₄ = 15
Hence, the value of a₄ is 15
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Complete question
List the first 4 terms of this sequence
a₁= 6
aₙ = aₙ₋₁ + 3
A student wonders if people of similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms, then she measures the next man whom each woman dates. Here are the data (heights in inches): Women: 64 65 65 66 66 70 Men: 68 68 69 70 72 74 Determine whether each of the following statements is true (T) orfalse (F). (a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger. (b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date. (c) There is a positive association between the heights of men and women.
Answers
Answer:
(a) False
(b) False
(c) True
Step-by-step explanation:
(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.
No, since changing the units of measurement does not change the correlation coefficient
(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.
Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation
(c) There is a positive association between the heights of men and women.
We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women
The random variable w has a geometric distribution with p=0.25. approximately how far do the values of w typically vary, on average, from the mean of the distribution?
Answers
The values of w typically vary, on average, from the mean of the distribution about 3.46.
How to illustrate the deviation?The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
For a geometric(p = 0.25) distribution, the variance is computed here as:
Var(X) = (1 - p)/ p2 = (1 - 0.25) / 0.252 = 12
Therefore, the standard deviation is computed as:
= ✓(12) = 3.46 observations.
This is the standard deviation of the given distribution here.
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Describe in words the region of represented by the equation(s) or inequality. x=z
Answers
The equation x = z represents a line in three-dimensional space that passes through the origin and has a slope of 1.
The equation x = z represents a line in three-dimensional space. In this case, the line is a diagonal line that extends infinitely in both the positive and negative directions. It passes through the origin (0, 0, 0) and has a slope of 1.
To understand this visually, imagine a coordinate system with x, y, and z axes. The line x = z can be represented by points such as (1, 0, 1), (-2, 0, -2), (3, 0, 3), and so on. These points all lie on the line where the x and z coordinates are equal.
You can also think of this equation as saying that the x-coordinate of a point is always equal to its z-coordinate. So if you have a point like (2, 0, 2), the x and z coordinates are equal, satisfying the equation x = z.
In terms of the region represented by this equation, it's a straight line that extends infinitely in both the positive and negative directions in the x-z plane. All points on this line have the property that their x and z coordinates are equal.
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The equation x = z represents a line in a three-dimensional coordinate system.
The equation x = z represents a line in a three-dimensional coordinate system. In this equation, the x-coordinate is always equal to the z-coordinate. This means that for any point on the line, the x-coordinate and the z-coordinate have the same value.
To understand this visually, imagine a three-dimensional coordinate system with x, y, and z axes. When x = z, it means that the points on the line have the same x and z values, while the y-coordinate can take any value. This line extends infinitely in both the positive and negative directions along the x and z axes.
For example, if we take the point (1, 2, 1) on this line, we can see that the x-coordinate (1) is equal to the z-coordinate (1). Similarly, if we take the point (-2, 5, -2), the x-coordinate (-2) is equal to the z-coordinate (-2).
In conclusion, the equation x = z represents a line in a three-dimensional coordinate system where the x-coordinate is always equal to the z-coordinate.
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Jill bought a lamp for $40. She sold it at a garage sale for $12. What was the approximate decrease?
Answers
Answer:
$28
$40 - $12 = $28
_______
I'm not sure if i read the question properly.
Please tell me if I'm wrong.
PLS HELP THIS IS VERY IMPORTANT
Answers
Answer:
22 degrees
Step-by-step explanation:
The total degree of a triangle is 180 degrees.
we are given two degrees already; 90 degrees (from the right angle sign) and 68 degrees from the problem. If we create an equation to reflect this we can find the missing angle:
180 = 90 + 68 + x
180 = 158 + x
x = 22
Step-by-step explanation:
<TSU=68
<STU=90
<SUT=
90+68=158
180-158=22
Kaci earned scores of 78, 88, 87, and 91 on her first four science tests. Shehas one more test to take and wants to get an average score of 80 or more on hertests.The following is the inequality that represents this situation, where I is the score ofher fifth test(78+88+87+91+x)5> 80What is the minimum score Kaci can receive on her fifth test to have an averagescore of at least 80?
Answers
Given:
Kaci earned scores of 78, 88, 87, and 91 on her first four science tests.
She has one more test to take and wants to get an average score of 80 or more on her tests.
Let the score of the final test = x
So, the average of the scores will be equal to or greater than 80
So, we have the following inequality
\(\frac{78+88+87+91+x}{5}\ge80\)Solve for x:
\(\begin{gathered} \frac{78+88+87+91+x}{5}\ge80\rightarrow\times5 \\ 78+88+87+91+x\ge80\times5 \\ 344+x\ge400 \\ x\ge400-344 \\ x\ge56 \end{gathered}\)So, the minimum score will be 56