From a position 7 meters above the ground level in a building, an observer measures the angle of elevation of the top of a flagpole to be 50 degrees, and the angle of depression of the foot of the flag pole is 20degrees. How tall is the flagpole? (2 marks)

Answers

Answer 1

The flagpole is approximately 16.27 meters tall.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

We can solve these equations simultaneously to find h. First, we can rearrange the first equation to get:

x = h / tan(50)

Then, we can substitute this expression for x into the second equation and simplify:

tan(20) = h / (h / tan(50) + 7)

tan(20) = h / (h / 1.1918 + 7)

h(1 - 0.8393 tan(20)) = 7 tan(20)

h = 7 tan(20) / (1 - 0.8393 tan(20))

Using a calculator, we can evaluate this expression to get:

h ≈ 16.27 meters

Therefore, the flagpole is approximately 16.27 meters tall.

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Related Questions

if only the upper 35% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10, what was the lowest score a student could have received and still have passed? g

Answers

The lowest score a student could have received and still have passed the quiz with a normally distributed class is 55.

This is because the upper 35% of a normally distributed class corresponds to a score of 1.5 standard deviations above the mean. Since the mean was 70 and the standard deviation was 10, that would mean the lowest score a student could have received and still have passed the quiz is 70 + (1.5 * 10) = 70 + 15 = 55.

In summary,
1. Start with the mean of the quiz which is 70.
2. Add 1.5 standard deviations which is 1.5 * 10 = 15.
3. The result is the lowest score a student could have received and still have passed the quiz which is 70 + 15 = 55.

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Which value is equivalent to x+4/4+x?
O-4
O-1
O 1
O4

Answers

The correct option for the given radical equation is option C. The value after operation is equal to 1.

Given radical expression:

[tex]\frac{x+4}{4+x}[/tex]

Now, we know that the addition is commutative.

Using commutative property, 4+x = x+4,

So,

[tex]\frac{x+4}{x+4}[/tex]

Both numerator and denominator has same value, hence they could be cancelled.

[tex]\frac{x+4}{4+x}[/tex] = [tex]\frac{x+4}{x+4}[/tex]

[tex]\frac{x+4}{x+4}[/tex] = 1.

Therefore, the value which is equivalent to x+4/4+x is equal to 1.

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Geometry, and Slope. Worth 15 Points
Please Explain

Answers

The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

Given,

x+2y=2

y = 1 - [tex]\frac{x}{2}[/tex]

Slope = -1/2 = [tex]m_{1}[/tex]

Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]

⇒ [tex]m_{1}[/tex] * [tex]m_{2}[/tex] = -1

Then [tex]m_{2}[/tex] = 1/2

Equation of line perpendicular is given by

[tex]y = \frac{1}{2}x + c[/tex]

Since it contains point (5,6)

6 = [tex]\frac{1}{2} (5) + c[/tex]

c= [tex]\frac{7}{2}[/tex]

Then the equation of line is:

[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].

Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

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The following data points represent the number of points the Hawaii Eagles football team scored each game.

17, 33,28,23,10,42,3

Using the data, create and histogram

Answers

The class intervals are given as:

0 - 15 15-30 30-45

2 3 2

What is a Histogram?

A histogram is a graphical representation of the distribution of numerical data. It is a way of summarizing the shape and spread of a set of continuous data values into a series of bins or intervals.

The histogram is a bar graph-like representation of the data, where the data is grouped into intervals or bins on the horizontal axis and the frequency or count of observations falling into each bin is represented by the height of the bar on the vertical axis.

Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.

The class intervals are given as:

0 - 15 15-30 30-45

2 3 2

The histogram is provided below:

Answers

The total cost for the trip reserved under Santos albert's name is $1,500 (option c).

In Excel, we can use the SUM function to add up a range of numbers. To do this, we first need to select the range of cells containing the costs associated with Santos Albert's reservation. In this case, the costs are located in columns C through G for the row corresponding to Santos Albert.

Once we have selected the range of cells containing the costs, we can use the SUM function to add them up. The formula for this would be "=SUM(C5:G5)", where C5 is the first cell in the range and G5 is the last cell in the range. This formula will add up all of the costs in the range and give us the total cost for Santos Albert's reservation.

So, to answer the question, the total cost for the trip reserved under Santos Albert's name is $1500.

Hence the correct option is (c).

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find the steady state response value yss and the steady state error value ess for the systems in figures 5.74 a,b, 5.75, 5.76 for unit step, unit ramp, and unit parabolic inputs.

Answers

Plug the corresponding R(s) for each input type and the transfer functions of the given systems into the equations above to find yss and ess for each case. Keep in mind that some systems might not have a finite steady-state response or error for specific input types, depending on the system's type (order and poles).

To determine the steady-state response (yss) and steady-state error (ess) values for the given systems, we need to use their transfer functions and input types (unit step, unit ramp, and unit parabolic). Unfortunately, without information about the specific transfer functions for figures 5.74 a, b, 5.75, and 5.76, it is not possible to provide a definitive answer.

In general, for a system with transfer function G(s), you can calculate the steady-state response and error using the Final Value Theorem:

yss = lim (s -> 0) s * Y(s), where Y(s) = G(s) * R(s) is the system's output.
ess = lim (s -> 0) s * E(s), where E(s) = R(s) - Y(s) is the system's error.

For different input types:
- Unit step input: R(s) = 1/s
- Unit ramp input: R(s) = 1/s^2
- Unit parabolic input: R(s) = 1/s^3

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For the following indefinite integral, find the full power series centered at
x=0 and then give the first 5 nonzero terms of the power series. [infinity]
Σ∫(e^9x - 1) / 6x dx
n=0

Answers

From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.

To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:

∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du

We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):

(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du

= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]

= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]

= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))

We can now simplify and group terms to obtain the power series centered at x=0:

(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))

= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))

To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:

n=0: (3/2) × 1 = 1.5

n=1: (3/2) × 9x = 13.5x

n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²

n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³

n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴

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Help please, I will give brainiest

Type the correct answer in each box. Round your answers to the nearest hundredth.

City Cat Dog

Lhasa Apso Mastiff Chihuahua Collie

Austin 24. 50% 2. 76% 2. 86% 3. 44% 2. 65%

Baltimore 19. 90% 3. 37% 3. 22% 3. 31% 2. 85%

Charlotte 33. 70% 3. 25% 3. 17% 2. 89% 3. 33%

St. Louis 43. 80% 2. 65% 2. 46% 3. 67% 2. 91%

Salt Lake City 28. 90% 2. 85% 2. 78% 2. 96% 2. 46%

Orlando 37. 60% 3. 33% 3. 41% 3. 45% 2. 78%

Total 22. 90% 2. 91% 2. 68% 3. 09% 2. 58%

The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.

The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is ______%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is ______%

Answers

The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.

The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.

The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .

2.76% + 2.86% + 3.44% + 2.65% = 11.71%

11.71/3.44 = .2937

.2937 = 29.37%

Probability is just the way that logical something is to occur.

Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.

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This pre-image was reflected over the y-axis.
Use the segment tool to draw the image.
Segment
-10-9-8-7-6-5
H
10
9
8
←Undo
7
6
5
4
3
2
1
-3 -2 -10
y
N
-3
-
Redo
5

Answers

Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis. The pre-point image's (-3, 5) is mirrored to the image's point (3, 5).

What does the y-axis represent?

The x-axis is the horizontal axis and the y-axis is the vertical axis in two-dimensional space. As seen in the image below, they are represented by two number lines that perpendicularly connect at (0, 0).

This is a reflection of the pre-image that was provided over the y-axis:

Segment

10 9 8 7 6 5 -5 -6 -7 -8 -9 -10

Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis, they are reflected to one another.

Similar to this, the pre-point image's (-3, 5) is reflected to the image's point (3, 5).

The x-coordinates of all other locations in the pre-image are negated in the image because they have corresponding points there that are equally spaced from the y-axis.

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5x+2y=10
Find the Y intercept and gradient

Answers

1. Rearrange the equation into y=mx+b

- Subtract 5x on both sides

2y = -5x + 10

2. Divide both sides by 2 to get y by itself.

y = -5/2x + 10/2

y= -5/2x + 5

Answer: y-intercept > 5 gradient > -5/2

This rich aunt invests $37000 in a savings bond for the baby which earns 1.125% interest every quarter. How much total interest has this savings bond earned 24 quarters after the rich aunt invested? [Include a dollar sign in your answer and round to the nearest penny.]

Answers

The total interest earned on a savings bond over 24 quarters with a principal investment of $37,000 and an interest rate of 1.125% per quarter, the savings bond has earned a total interest of $9,990.

The savings bond earns 1.125%/quarter, so its quarterly interest rate is 0.01125. The amount of interest earned in one quarter is the product of the interest rate and the principal amount, which is:

To calculate the interest earned in one quarter, we multiply the principal amount by the interest rate expressed as a decimal.

Interest earned in one quarter = 0.01125 x $37,000 = $416.25

In this case, the interest earned in one quarter is $416.25.

To find the total interest earned over 24 quarters, we multiply the interest earned in one quarter by the number of quarters, which is 24.

After 24 quarters, the total interest earned is:

Total interest earned = 24 x $416.25 = $9,990

Therefore, the savings bond has earned a total interest of $9,990 after 24 quarters.

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the intersection of two events a and b is the event that: a) both a and b occur. b) the union of ac and bc occurs. c) the union of a and b does not occur. d) either a or b or both occur. e) either a or b, but not both. f) none of the above.

Answers

The intersection of two evens a and b is the event that both a and b occur that is option A is correct.

The intersection of two events A and B is defined as the event that occurs when both A and B occur simultaneously. It is denoted by A ∩ B, where the symbol ∩ represents intersection.

For example, if event A is "getting a head when flipping a coin" and event B is "rolling a 6 on a fair die", then the intersection of A and B would be the event "getting a head when flipping a coin and rolling a 6 on a fair die".

For example, suppose A represents the event "rolling an even number on a dice" and B represents the event "rolling a number greater than 3 on a dice". The intersection of A and B is the event that "rolling a number that is both even and greater than 3 on a dice", which consists of the outcomes {4, 6}.

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Complete Question:

the intersection of two events a and b is the event that:

a) both a and b occur.

b) the union of ac and bc occurs.

c) the union of a and b does not occur.

d) either a or b or both occur.

e) either a or b, but not both.

f) none of the above.

Algebraic Inequalities
Help pls need assistance
DUE today in

Answers

Answer:

8, 8.001, 8.01, 8.1, 9, 11, 13, 16

Step-by-step explanation:

From the instructions given, we know that variable u [tex]\geq[/tex] 8. the [tex]\geq[/tex] sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.

you have taken up gardening for relaxation and have decided to fence in your newrectangular shaped masterpiece. the length of the garden is 4 meters and 52 meters offencing is required to completely enclose it. what is the width of the garden?

Answers

If the length of the garden is 4 meters and 52 meters of fencing is required to completely enclose it, the width of the garden is 22 meters.

To find the width of the garden, we need to use the formula for the perimeter of a rectangle, which is:

P = 2l + 2w

Where:

P = perimeter of the rectangle

l = length of the rectangle

w = width of the rectangle

We know that the length of the garden is 4 meters and the perimeter is 52 meters, so we can plug in the values and solve for the width:

52 = 2(4) + 2w

52 = 8 + 2w

44 = 2w

w = 22

To verify our answer, we can check if the perimeter using this width is indeed 52 meters:

P = 2l + 2w = 2(4) + 2(22) = 8 + 44 = 52

As expected, the perimeter is 52 meters. This means that if we fence in the garden with a width of 22 meters and a length of 4 meters, we will require 52 meters of fencing to completely enclose it.

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1. Compare the two box plots.
Looking at the majority, which group is taller?
Circle.
●
Boys
●
Girls
Which group has a smaller center of data? By how much?
Circle: Boys Girls
by
inches.
Which group has a larger range? Circle.
2. Compare the two dot plots.
● Are the graphs symmetrical or skewed?
Which dot plot has a larger center of data?
Which dot plot has a larger range?
Boys
Girls
Boys
+ + +
60 61
Girls
Height (inches) of Girls and Boys
.
62 63
+
64 65 66 67
+
69
68
+
70
+
71
Number of Fruit Smoothies Sold
+
72
Smoothies
Galore
50 55 60 65 70 75 80 85 90 95 100
Sunshine
Smoothies

Answers

Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

Please help :( I don't quite understand...

Answers

Step-by-step explanation:

For Part A, use the function f(x) to find the average of tests taken.

X is number of test taken

f(x) is the average score given said num of tests taken,x,

We want after test number 3 so using the function,

[tex]f(x) = 0.2x + 79[/tex]

Plug in. 3 for x, and we will get our answer.

[tex]f(3) = 0.2(3) + 79 = 79.6[/tex]

Part B: Use the table for the answer.

When 2 test are taken, the average test score is

So part B is 84.

Part C:

[tex]f(2) = 0.2(2) + 79 = 79.4[/tex]

[tex]g(2) = 84[/tex]

Since

[tex]g(2) > f(2)[/tex]

The science class had a higher average after 2 tests

Answer:

you shoulda payed attention in class

Step-by-step explanation:

also u know it's bad when the test is so hard you can't even cheat on it

hills vanessa is walking up a hill. after walking 40 feet, she has climbed a total of 8 feet vertically. if she walks an additional 25 feet up the hill, how many feet will she have climbed vertically in total?

Answers

Vanessa's vertical climb rate is 0.2 feet per foot of horizontal distance. When she walks 65 feet horizontally up the hill and climbs an additional 25 feet, her total vertical climb will be 21 feet.

For every 40 feet of horizontal distance Vanessa walks, she climbs 8 feet vertically. So her vertical climb rate is 8/40 = 0.2 feet per foot of horizontal distance.

If she walks an additional 25 feet up the hill, her total horizontal distance traveled will be 40 + 25 = 65 feet.

Therefore, her total vertical climb will be 0.2 times her total horizontal distance:

8 + (0.2 * 65) = 8 + 13 = 21 feet

So, Vanessa will have climbed a total of 21 feet vertically after walking 65 feet horizontally up the hill.

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The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line

Answers

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)