Javier is standing at a distance from a flagpole. He sights the bottom of the flagpole at a 4°
angle of depression and the top of the flagpole at a 25°
angle of elevation. If Javier is 6 feet tall, what is the total height, to the nearest foot, of the flagpole?

Answers

Answer 1

Answer: To find the height of the flagpole, we can use the fact that the angles of depression and elevation are complementary angles, meaning that they add up to 90°.

Let's call the height of the flagpole "h". Then, we have:

h - 6 = h * tan(4°) (the height difference between Javier and the bottom of the flagpole)

and

h = 6 + h * tan(25°) (the height of the top of the flagpole as seen by Javier).

By substituting the first equation into the second, we can find h:

h = 6 + h * tan(25°)

h = 6 + h / tan(65°)

h * tan(65°) = 6 + h

h * tan(65°) - h = 6

h = 6 / (tan(65°) - 1)

Using a calculator, we find that h = approximately 43.3 feet. Rounding to the nearest foot, the height of the flagpole is 43 feet.

Step-by-step explanation:


Related Questions

can someone explain the questions attached? thanks

Answers

The probability of landing on the head side of coin and rolling a 3 on the die is found as 1/12.

Explain about the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of feasible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Sample space for tossing a coin: (H,T)

P(head) = 1/2

Sample space for tossing a dice : (1, 2, 3, 4, 5, 6)

P(3) = 1/6

So,

Probability of head with 3 on the die = 1/ 2* 1/6 = 1/ 12

Thus, the probability of landing on the head side of the coin and rolling a 3 on the die is found as 1/12.

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The correct question is-

A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.

Enter your answer as a fraction in the form a/b (for example 2/3, 5/7) or as an integer.

You must spend at least $10 at the grocery store to get a free greeting card

Answers

Answer:

I spent 13.32 at the store the other day...?

Step-by-step explanation:

What is the question.

Go to the dollar section and pick out 10 things and then get the gift card

The table below shows the ratios of black to white keys on pianos of various sizes.


Black A 18 45 72
White 13 B 65 C


Determine which table has the correct values for A, B, and C.

Black 8 18 45 72
White 13 25 65 105

Black 9 18 45 72
White 13 26 65 104

Black 9 18 45 72
White 13 39 65 117

Black 1 18 45 72
White 13 26 65 104

Answers

Using the given ratios found the values of A, B and C, and completed the table as follows:

Black   9   18       45     72

White  13   26     65    104

What is meant by the ratio?

A ratio in mathematics demonstrates how many times one number is present in another. A ratio is what a fraction looks like when it is written as a:b. A ratio is the comparative or condensed version of two quantities of the same type.

Given the table:

Black   A   18   45   72

White  13   B    65    C

The table represents the ratios of black keys to white keys on pianos of various sizes.

The ratio of keys of the piano always remains constant.

So we can write as follows:

A/13 = 18/B = 45/65 = 72/C

To find A, we take the following ratios.

A/13 = 45/65

On solving, we get

A = 45 * 13 / 65 = 585/65 = 9

To find B, we take the following ratios.

18/B = 45/65

B = 18 * 65 / 45 = 1170/45 = 26

To find C,  we take the following ratios.

72/C = 45/65

C = 72 * 65 / 45 = 104

Therefore using the given ratios we can complete the table using the values of A, B and C,

Black   9   18       45     72

White  13   26     65    104

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Two important ingredients for baking bread are
yeast and flour. To make a loaf of bread of at
most
30 servings, maintain a yeast to
flour ratio of 1:200. If you're making a loaf of more than 30
servings, use a ratio of 1:180.
If you're making 30 servings
of bread and using 0.25 oz of yeast, how many ounces of flour do you
need?
If you're making 60 servings of bread and using 540 oz of flour, how many ounces of yeast do you
need?
NOTE: Enter only numerals for each of your answers.

Answers

If you're making 60 servings of bread and using 540 oz of flour, then the number of ounces of yeast you need is 3 oz.

What are proportions?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, to make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180.

If you're making 30 servings of bread and using 0.25 oz of yeast, then

0.25/Flour = 1/200

Flour = 50 oz

If you're making 60 servings of bread and using 540 oz of flour, then

Yeast/540 = 1/180

Yeast = 3 oz

Therefore, if you're making 30 servings of bread and using 0.25 oz of yeast, then the number of ounces of flour you need is 50 oz.

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What is X and Z. please tell me

Answers

x = 5

z = 118°

Step-by-step explanation:

opposite angles are equal

(6x + 32)° = 62°

6x = 62° - 32°

6x = 30°

x = 5°

angles on a straight line add up to 180

180° = 62° + z

z = 180° - 62°

z = 118°

[tex]1\frac{1}{3} :2\frac{1}{3}[/tex]

Answers

Answer:

Given: [tex]1\frac{1}{3} :2\frac{1}{3}[/tex]

To simplify this ratio, convert the mixed fractions into improper fractions:

[tex]\frac{4}{3}[/tex] : [tex]\frac{7}{3}[/tex]

Then to divide ( because ratio = division ) turn around [tex]\frac{7}{3}[/tex] and multiply:

[tex]\frac{4}{3} * \frac{3}{7}[/tex]

Then multiply:

[tex]\frac{12}{21}[/tex]

Finally simplify this fraction by dividing the denominator & numerator by 3:

= [tex]\frac{4}{7}[/tex]

...

A car is bought for £8500
In it's first year it's price reduces by 10%
Each year after that it decreases by 5%
What is the price after 3 years?

Answers

Answer: The price after 3 years is £6904.15

Step-by-step explanation:

After 1 year,  8500*0.9= 7650

7650*0.95=7267.5

7267.5*0.95=6904.125

The price after 3 years is £6904.15

Raul is wrapping a cylindrical package with wrapping paper. He has two different packages to choose from:
Package A has a radius of 1.5 inches and a height of 6 inches
Package B has radius of 2 inches and a height of 3 inches

He has 70 in2 of wrapping paper and he will need to cover all sides of the package.

Using the formula SA = 2π
rh + 2π
r2, determine which of the following packages Raul will have enough wrapping paper to cover.

Package A has a surface area of
Choose...
in2. Package B has a surface area of
Choose...
in2.

Raul will have enough paper to wrap
Choose...

Answers

The package that will have enough wrapping paper to cover is package B

Package A has a surface area of 70. 65 in²

Package B has a surface area of 62. 8 in²

How to determine the surface area

The formula for the surface area of a cylinder is expressed as;

SA = 2πrh + 2π

Given that the parameters are;

r is the radiush is the height of the cylinder

For Package A, substitute the values

= 2 × 3.14 × 1.5 × 6 + 2 × 3.14 × (1.5)²

Multiply the values, we have;

= 70. 65 in²

For package B, substitute the values, we get;

= 2 × 3.14 × 2 × 3 + 2× 3.14 × (2)²

Multiply the values

= 62. 8 in²

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PLEASE ANSWER ASAP THANKS

Answers

The value of x is 97.

What are corresponding angles?

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

We can also have alternate angles which are always equal.

We can also have alternate interior and exterior angles which are equal.

The angles on the same side make upto 180 degrees

We have,

From the figure,

(x - 5) and (x - 9) forms a straight angle.

This means,

x - 5 + x - 9 = 180

Solve for x.

2x - 14 = 180

2x = 180 + 14

2x = 194

x = 97

Thus,

The value of x is 97.

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One way to establish validity of a questionnaire is my measuring:A) The correlation between the score on the questionnaire and another measure of the same conceptB) The alpha value of the reliability coefficientC) How well sunjects perform on the questionnaire at one time compared to another timeD) The consistency by which multiple sunjects are able to complete the questionnaire without error

Answers

The correct option is Option D) The consistency with which several individuals can complete the questionnaire without making an error is one technique to determine a questionnaire validity.

A questionnaire is a sort of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a collection of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Despite the fact that surveys are frequently created so that the answers may be statistically analyzed. Consequently, it may not be practical to conduct a survey using a questionnaire for some demographic groups.

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HELP PLSS I NEED HELPPPPP

Answers

The required measures of length are, as follows:

GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.

What is a rectangle?

A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.

The lengths are given in the question, as follows:

DE = 11

GH = 14

Since DE and GF are opposite sides then both are equal.

So GF = 11

Here GH and HF are equal,

HF = 14

∵ GE = GH + HE = 14 + 14 = 28

As we know that the two lengths of the diagonals are equal in the rectangle.

So GE = DF

So DF = 28

Using the Pythagorean theorem, we have

DG² + GF² = DF²

DG² + 11² = 28²

DG² + 121 = 784

DG² = 663

DG = 25.75

Thus, the measures are, as follows:

GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.

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solve
(2x-3) (x2+4x-5)

Answers

Answer: 2x^3 + 5x^2 - 10x + 15

Step-by-step explanation:

To multiply two polynomials, you can use the distributive property and multiply each term of one polynomial by each term of the other. In this case, the two polynomials are (2x - 3) and (x^2 + 4x - 5), so we have:

(2x - 3) * (x^2 + 4x - 5) =

2x * x^2 + 2x * 4x - 2x * 5 +(-3) * x^2 + (-3) * 4x - (-3) * 5

Expanding the products, we get:

2x^3 + 8x^2 - 10x - 3x^2 - 12x + 15

Combining like terms, we get: 2x^3 + 5x^2 - 10x + 15

An online app charges $0.99 to download a song and $7.99 membership fee. (A)Write an expression that gives the total cost in dollars to download “s” songs. (B)Then, find the cost of downloading 12 songs. Incorrect work/solutionCorrect work/solution (A) s(0.99 + 7.99) = 0.99s + 7.99s = 8.98s = (B) 8.98(12) = 8.98 x 12 = $107.76 for 12 songs Part A:Explain what this student did incorrectly.

Answers

Answer: The student correctly wrote an expression to find the total cost of downloading "s" songs. The expression is: 0.99s + 7.99. However, they made a mistake when they simplified the expression to 8.98s. The expression should have remained as 0.99s + 7.99, because the $7.99 membership fee does not change regardless of how many songs are downloaded.

In Part B, the student correctly used the expression to find the cost of downloading 12 songs. They multiplied 8.98 by 12 and got the correct answer of 107.76.

Step-by-step explanation:

Penny is vacationing at the beach and decides to purchase a pair of swim goggles and a
sand bucket which she randomly selects off the shelf. When she realizes that they are
both green, she states that "because she selected a green pair of swim goggles, she was
more likely to select a green sand bucket." Do you agree or disagree with Penny's
statement? Justify your thinking

Answers

Answer: I disagree with Penny's statement. The probability of her selecting a green pair of swim goggles and then a green sand bucket is the product of their individual probabilities. The fact that she selected a green pair of swim goggles does not change the probability of selecting a green sand bucket. Each selection is independent of the other, and the probabilities of each event remain the same. So, Penny's statement that "because she selected a green pair of swim goggles, she was more likely to select a green sand bucket" is not valid.

Step-by-step explanation:

If you take - 3/10 of a number and add 1, you get 10. Write an equation to represent the situation. What is the original number

Answers

Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

1. Arturo earns n dollars per hour. Next month
he will receive a 2% raise in pay per hour. The
expression n +0.02n is one way to represent
Arturo's pay per hour after the raise. Write
an equivalent simplified expression that will
represent his pay per hour after the raise.

Answers

The equivalent simplified expression is 1.02n.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Given that, Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour.

The expression n +0.02n is one way to represent Arturo's pay per hour after the raise.

Here, the equivalent expression is n +0.02n= 1.02n

Therefore, the equivalent simplified expression is 1.02n.

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what is c over 2 < -0.75=

Answers

The value of c lies in the interval [tex](-\infty, -1.5)[/tex]

What is inequality?

Inequality is a statement that shows the relationships the two expressions are not equal. It is defined by the symbols like <, >, ≤, ≥.

[tex]\frac{c}{2} < -0.75[/tex]

To find the value of c:

[tex]\frac{c}{2} < -0.75[/tex]

Multiply both sides by 2 we get,

[tex]2\frac{c}{2} < (-0.75)*2[/tex]

⇒c < -1.5

Therefore c<-1.5 is the solution for the given inequality.

It can also be represented in the interval form.

This is given in the interval notation [tex](-\infty, -1.5)[/tex]

Hence, the value of c lies in the interval [tex](-\infty, -1.5)[/tex]

Complete question:

What is the values that c can take when  [tex]\frac{c}{2} < (-0.75)[/tex]?

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What is the degree of 7c3d2

Answers

The degree of the expression 7c³d² is 2

How to determine the degree

From the question, we have the following parameters that can be used in our computation:

Expression = 7c³d²

The degree of an expression is the highest power in the expression

In this case,

7c³ =  Constant

d² = Variable

The highest power of the variable is 2

Hence, the degree is 2

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Simplify the following by rationalizing the denominator. need rightnow pahelp.

Answers

Answer:

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.

Exact Form:

3√2+2

    7

Decimal Form:

0.89180581

x^2+y^2=100 is it a function?

Answers

The equation x^2+y^2=100 is not a function

How to determine if it is a function

From the question, we have the following parameters that can be used in our computation:

x^2 + y^2 = 100

The above equation is a circle equation

As a general rule, we have

Circle equations are not functions and they do not represent a function on a graph

Hence, x^2+y^2=100 is not a function

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8 A crystal paperweight
is shaped like a cylinder with a star-shaped hole. The
top of the star-shaped hole is shaped like a square with four points that are
identical equilateral triangles. The height of the cylinder is 3 centimeters. Find
the volume of the paperweight.


Please Help ASAP!!!

Answers

The volume of the paperweight is 79.3 cm³.

What is a cylindrical shape?

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

From the given information, The area of the star-shaped cutout is,

A square has a side length of 2 cm, and four equilateral triangles have a side and a height of 2 cm.

So, The area of the star-shaped cutout is,

= (2×2) + 4×(1/2)×2×2.

= 4 + 8.

= 12 cm.

Now, The volume of the star-shaped cut-out is,

= 12×height,

= 12×3.

= 36 cm³.

And the volume of the cylinder is,

= π(1 + 2 + 0.5)²×3.

= π(3.5)²×3.

= 115.4 cm³

Therefore, The volume of the paperweight is,

= 115.4 - 36 cm³.

= 79.3 cm³.

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From the top of a 450-foot cliff, a hiker looks down at a river below. Her angle of
depression to the near and far banks of the river are 80° and 50° respectively, as
shown in the picture. Based on this information, how wide is the river?

Answers

The width of the river is calculated by the tangent of the angle will be 293 feet.

What is a right-angle triangle?

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Observing a river below from the top of a 450-foot cliff, a hiker. Her depression lies at an angle of 80° to the near bank and 50° to the far bank of the river.

The horizontal distance when the angle is 80° is given as,

tan 80° = 450 / x₁

x₁ = 84.64 feet

The horizontal distance when the angle is 50° is given as,

tan 50° = 450 / x₂

x₂ = 377.59 feet

The width of the river is given as,

W = x₂ - x₁

W = 377.59 - 84.64

W = 292.95

W ≈ 293 feet

The width of the river is calculated by the tangent of the angle will be 293 feet.

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Need help, please, thanks!

Answers

The earnings in the simple interest and compound interest for a 5 year period is in the table below where S is for Suzanne and D is for Derrick

            S - annual interest  S - Balance   D - annual interest   D - Balance

Year 1                 147                   3147                      147                    3147

Year 2                294                  3294                     301.2                 3301.2

Year 3                441                   3441                      462.96              3462.96

Year 4                588                  3588                     632.65              3632.65

Year 5                735                   3735                     810.65               3810.65

How to solve simple interest

Simple interest is calculated by the formula

principal x time x rate / 100

In the problem

Principal = $3000

rate = 4.9%

time is varying from 1 to 5

For the first year we have

= 3000 * 1 * 4.9 / 100

= 147

Compound interest the formula is

Principal(1 + rate)^(year) - 1)

For the first year, (the rate is already divided by 100 to get 0.049) we have

= 3000(1 + 0.049)^(1) - 1)

= 147

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Solve for x . circles tangent 1 A. 12 B. 10 C. 42 D. 9

Answers

8 is the measure if the angle x in the given diagram.

Circle geometry

The point where two lines meet is known as an angle. The given diagram is a circle geometry.

Using the theorem, angle at the arc is twice the angle at the vertex, we will have:

80 = 2(4x + 8)

80/2 = 8x + 8

40 = 4x + 8

4x = 40 - 8

4x = 32

x = 32/4

x = 8

Hence the value of x from the diagram given is 8

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PLEASE HELP 25 POINTS!! NO LINKS

Answers

Answer:

C i think

Step-by-step explanation:

Convert 2 pints into milliliters. Round your answer to the nearest whole number.

Answers

Answer: 946 ml

Step-by-step explanation: 1 pint= 473.2

2*

473.2= 946.4

=946 ml

-3x² + 2x-5 = y
-x+2=-y

Answers

Answer:     \left(h,\:k\right)=\left(\frac{1}{3},\:\frac{14}{3}\right),\:p=\frac{1}{12\

Step-by-step explanation:

Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).

Answers

The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:

The equation is in the form  

dy/dx +P(x)y=Q(x)yⁿ,  where P and Q are functions of x or constants, this is called Bernoulli's equation.

Now, we have to substitution using 

[tex]v = {y}^{1 - n} [/tex]

Differentiating both side with respect to 'x'

[tex]v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'[/tex]

we get,

[tex]= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)[/tex]

Now, by using 

[tex]v' = {y}^{1 - n} [/tex]

The given equation is expressed as:

[tex]v + (1 - n)p(x)v = (1 - n)q(x)[/tex]

or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)

The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.

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a || b and p is a transversal. If m 1 = 140°, find the
measure of each angle giving one reason for each answer.
(The first one is done for you.)

Answers

Answer:

Angle 4 = 140

Angle 3= 40

Angle 5=140

angle 6=40

angle 7=40

Step-by-step explanation:

Adjacent angles are congruent. Thats how I can tell angle 4 is 140. And also how i can tell angle 3 is 40. Any questions?

im not explaining the rest im too tired

btw I also do 8th math lol it stinks.

A cylinder-shaped scoop has a base radius of 2 centimeters and a height of 5 centimeters. The scoop has a mass of 14.9 grams when empty. The scoop is completely filled with water. One cubic centimeter of water has a mass of one gram. What is the mass of the scoop of water in grams, including the mass of the scoop? Describe how you found your answer. Round to the nearest tenth.

Answers

Answer:

  77.7 g

Step-by-step explanation:

You want the mass of a cylindrical scoop of radius 2 cm and height 5 cm when it is filled with water at 1 g/cm³, and has an empty mass of 14.9 g.

Water

The mass of the water will be the product of its volume and its density. The volume is that of a cylinder with radius 2 cm and height 5 cm. That volume is given by the formula ...

  V = πr²h = π(2 cm)²(5 cm) ≈ 62.83 cm³

The mass of the water is then ...

  (62.83 cm³) × (1 g/cm³) = 62.83 g

Total mass

The total mass of the water-filled scoop is the sum of its empty mass and the mass of the water:

  scoop + water = 14.9 g + 62.8 g = 77.7 g

The mass of the scoop and water is 77.7 grams.

Other Questions
Is it hard to get into St Paul's nursing school? what the main idea of the song scrub what does the note say that the dark-haired girl give winston? Find and balance the account :$4,800 principal earning 1%, compounded semi-annually, after 24 years A $6,094.73B $6,098.35C $5,410.37D $232,704.00 Who specifically rejected aristotle and instead embraced empiricism?A. DescartesB. BaconC. BraheD. Kepler Find one point on the plane y=-3 and two non-parallel vectors that are parallel to the plane y=-3. A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 6.0 m above the ground. The ball lands 25 m away. What is his pitching speed? OhtFind the lengthof the diagonal4 in11 in YQ and XP are altitudes to the congruent sides of isosceles triangle WXY. the accounting term for a situation where two or more people act in coordination to circumvent internal controls is When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a . When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Please prepare an essay discussing the Native Americas that have emerged in Louisiana. Please make sure to include in your discussion their origin. (Louisiana Native Indians) Determine the moles of aluminium ions in 1.25mol of AI203 Ownership passes to the buyer when purchased goods are received by the buyer from a public carrier if the goods are shipped.a. Trueb. False summarize the remaining alphabet soup agencies and their goals. Does CVS do urine tests? Diego rounded a number to the nearest whole number and got 12.Which number could be the number Diego rounded to the nearest whole number? Identify the true statements about why performance measures (metrics) are crucial to the success of a process. (check all that apply.) multiple select question. A. the standards and rewards associated with metrics need to be ignored to reduce negative rewards. B. a metric should be designed to close the gap between what is valued by the customer and what is intended by the organization. C. metrics need to address the aspects that are important to the customer as well as the org The following statements are all true. Which one counts as an "exception to the rule" in being unusual for our solar system? Venus does not have a moon. Jupiter has a very small axis tilt. The diameter of Earth's Moon is about 1/4 that of Earth. Saturn has no solid surface. The diameter of Earth's Moon is about 1/4 that of Earth. show that the cross product of two vectors v and w, explicitly defined as ijkv jwk , transform as a dual vector under rotation. note that the levi-civita symbol is a symbol here and does not transform under rotation. hint: remember that for any matrix mi j , we have `mn det(m)