A helicopter is flying over a straight highway between
two exits, A and B. The angle of depression from the
helicopter to exits A and B are 28° and 45°,
respectively. If the exits are 4 miles apart, find the
height of the helicopter

Answers

Answer 1

Answer:

  about 1.3885 miles ≈ 7331 ft

Step-by-step explanation:

The height of the helicopter can be found using the tangent relation, which we know relates the sides and angles of a right triangle by ...

  Tan = Opposite/Adjacent

__

setup

With reference to the attached diagram, the above relation can be used to find the lengths of AC and BC, which we know total 4 miles.

  tan(28°) = h/AC   ⇒   AC = h/tan(28°) = h·tan(90° -28°) = h·tan(62°)

  tan(45°) = h/BC   ⇒   BC = h/tan(45°) = h·tan(90° -45°) = h·tan(45°)

The total distance between A and B is then ...

  AB = AC +BC

  4 = h·tan(62°) +h·tan(45°) = h(tan(62°) +tan(45°))

solution

Dividing by the coefficient of h, we have the value of h:

  h = 4/(tan(62°) +tan(45°)) = 4/(1.88073 +1) ≈ 1.38854 . . . . miles

In feet, that is ...

  (1.38854 mi)(5280 ft/mi) = 7331 ft

The height of the helicopter is 1.38854 miles, or 7331 feet.

A Helicopter Is Flying Over A Straight Highway Betweentwo Exits, A And B. The Angle Of Depression From

Related Questions

Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house. how long does it take jasmin to rake leaves at the second house.

Answers

The Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house.


From the problem:
[tex]= \rm 2\dfrac{1}{3}\times \dfrac{1}{2}[/tex]

[tex]= \rm \dfrac{7}{3}\times \dfrac{1}{2}[/tex]

[tex]= \rm \dfrac{7}{6}[/tex]

[tex]= \rm 1\dfrac{1}{6}[/tex]

Thus, the Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.

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If the cost of labor in the united states is five times greater than the cost of labor in
asia, how much would it cost to produce a pair of nike athletic shoes in the united
states? assuming that all other costs remain the same and the shoes would still sell for
$65 a pair, what would be the percentage difference in profit realized

Answers

Therefore the percentage difference in profit realized will be 66.67 % .

What is Profit ?

Profit, is net income earned after subtracting all dollar costs from total revenue.

In effect, it shows the amount of money a firm has left over after deducting the explicit costs of running the business.

Suppose all the charges for making the shoes is x (other than the labour charge)

Labor charge in Asia is y

And as given in the question Labor Charge in United States is 5y

The final cost off the shoes is $65

Profit in asia = (65-x-y)

Profit in United States = (65-x-5y)

Let's use trial and error method to understand this

suppose the making cost is x = $10  and the labor charge in asia is $5 per shoes so

Profit in Asia = 65-10-5 = $50

Profit in United Stated = 65- 10-25 = $30

the percentage difference in profit realized

= (50-30) * 100 /30

= 2000/30 = 200/3 = 66.67%

Therefore the percentage difference in profit realized will be 66.67 % .

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Need help! will award brainiest

Find the slope of a line that goes through the points (2, 5) and (-4, 3)

Answers

Answer:

[tex]\sf slope: \boxed{\bf \frac{1}{3} }[/tex]

Explanation:

[tex]\sf slope :\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{rise}{run} \ \ \ \ where \ (x_1, \ y_1) ,(x_2, \ y_2) \ are \ points[/tex]

Find slope:

[tex]\rightarrow \sf \dfrac{x_2-x_1}{y_2-y_1}[/tex]

insert values

[tex]\rightarrow \sf \dfrac{3-5}{-4-2}[/tex]

simplify

[tex]\rightarrow \sf \dfrac{1}{3}[/tex]

Answer: -1/3

Step-by-step explanation:

The equation to find the slope of a line is [tex]\frac{y2 - y1}{x2-x1}[/tex]. Y1 is 5, Y2 is 3, X1 is 2, and X2 is -4. Plug these numbers in to get the equation [tex]\frac{5-3}{(-4)-2}[/tex]. 5-3 = 2. (-4)-2 = -6. This gives a slope of 2/-6, which can be reduced by dividing the numerator and denominator by 2 to get a final slope of -1/3.


joan has a square flower bed with a side length of 5 meters filled with tulips. there are a total of 375 tulips in the bed. find the density of tulips
for the area of the bed. round to the nearest tenth if necessary.

Answers

Answer:

the answer is 15

Step-by-step explanation:

density= total population/surface area

density= 375/5^2

density=375/25=15

Write a cosine function that has an amplitude of 2, a midline of 5 and a period of T.

Answers

phase shift is 0

General equation

y=AcosB(x-C)+D

c is phase shift

y=AcosBx+D

Midline is D

y=AcosBx+5

A is amplitude

y=2cosBx+5

B is period

2π/T

So

Final equation

y=2cos(2πx/T)+5

Not mandatory from now

For some special cases 2π/T=omega

So Equation yields

y=2cos([tex]\omega x[/tex])+5

Answer:

[tex]f(x)=2 \cos (2x)+5[/tex]

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift

Given:

Amplitude = 2  ⇒  A = 2[tex]\sf Period=\pi \implies \dfrac{2 \pi}{B}=\pi \implies B=2[/tex]mid-line = 5  ⇒  D = 5

Inputting the given values into the standard form:

[tex]\implies f(x)=2 \cos (2x)+5[/tex]

venessa is solving a video game puzzle to open a secret door she must collect between 400 grams (g) and 500 grams (g) of gems she can only collect one type of gem

type of gem mass
Ruby 128.3
Emerald 195.2
Diamond 147.6

Which of the gems should Vanessa try to collect?
A. rubies
B. emeralds
C. diamonds
D. none of the gems will work for opening the secret door​

Answers

the answer is c
explanation

You decide to buy a tablet for college. The tablet you want is currently on sale for 29% off the original price. If the original price was $899, what is the current price? Round your answer to the nearest cent (2 decimal places).

Answers

Answer:

638.29

Step-by-step explanation:

This is the answer because 29 percent of 899 is somewhere around 260.71

Substract that and you get 638.29

Over the closed interval [3, 8], for which function can the extreme value theorem be applied?

Answers

Answer:

ITS C

Step-by-step explanation:

trust

Urgent Please Help!!!!

What percentage of scores lie in the shaded region? Use the empirical rule to find your answer.

Answers

Answer:

81.5%

Step-by-step explanation:

f(x) = x + 3
g(x) = 7x +4
What does (f+g) (x)equal?
To obtain credit, provide your answer with no spaces. Example answer: 42x+9

Answers

f(x)=x+3g(x)=7x+4(f+g)(x)=?now,(f+g)(x)=x+3+7x+4 =8x+7

How Do You Graph This Equation

Answers

Answer:

Rearrange both inequalities to make y the subject.

Momentarily swap the inequality sign for an equals sign in order to calculate two points for each line.

Inequality 1

[tex]2y \leq x-10[/tex]

[tex]\implies y < \dfrac{1}{2}x-5[/tex]

[tex]x=0\implies y=\dfrac{1}{2}(0)-5 \implies (0,-5)[/tex]

[tex]x=4 \implies y=\dfrac{1}{2}(4)-5 \implies (4,-3)[/tex]

Inequality 2

[tex]x+y\leq -3[/tex]

[tex]\implies y\leq -x-3[/tex]

[tex]x=0\implies y=-(0)-3\implies (0,-3)[/tex]

[tex]x=4\implies y=-(4)-3\implies (4,-7)[/tex]

When graphing inequalities

< or > : dashed line

≤ or ≥ : solid line

< or ≤ : shade below the line

> or ≥ : shade above the line

Therefore,

Inequality 1:  plot points (0, -5) and (4, -3) and draw a solid line through them.

Inequality 2: plot points (0, -3) and (4, -7) and draw a solid line through them.

Shade the area below both lines from where the lines intersect.

Answer:

See below ~

Step-by-step explanation:

Inequality 1 :

Convert into y = mx + b form2y ≤ x - 10y ≤ x/2 - 5

Taking 2 points :

0 ≤ x/2 - 5x/2 ≥ 5x ≥ 10⇒ Point 1 = (10, 0)

y ≤ 0 - 5y ≤ -5⇒ Point 2 = (0, -5)

Inequality 2 :

x + y ≤ -3y ≤ -x - 3

Taking 2 points :

0 ≤ -x - 3x ≤ -3Point 1 = (-3, 0)

y ≤ 0 - 3y ≤ - 3Point 2 = (0, -3)

Plot the two 2 lines using the 2 points and shade as per the sign of the inequality. The result will be this graph :

I don't understand this equation, I need a little help...

x + 14 = 14, x

Answers

x=0
explanation: 0+14=14

Apples cost $1.60 at the farmers market. They cost
1.5 times as much at the grocery store.
Select all the equations that show the cost of apples at
the grocery store, g.
(Select all that apply.)
g=1.5 1.60
g=1.60 1.5
1.5g = 1.60
g=1.5 1.60
g÷1.5 1.60

Answers

Answer:

G = 1.60 x 1.5, G = 1.5 x 1.60, and G ÷ 1.5 = 1.60

Step-by-step explanation:

^ ^

Simplify.
√63 somebody please help

Answers

Answer:

7.93

Step-by-step explanation:

What is the range of f(x) = 3x + 9?

{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}

Answers

From the given options we can think that x is
in the exponent of 3.
So, the given function is actually f(x) = 3^x +9
Now, we need to find the range of given
function.
We can see that first term is and exponential
term 3^x and second term is 9
We know that 3^x will always be greater than
O.
Therefore, 3^x +9 would always be greater
than 9.
Therefore, range would be y>9.
So, the correct option is B) (y | y > 9}.

HEY GUYS THIS IS MY FINAL MATH ASSIGNMENT OF THE YEAR... PLS JUST HELP ME FIND THE DOMAIN AND RANGE THANK YOU

Answers

Answer:

domain: all real numbers (-∞,∞)

range: y ≤ 64

Step-by-step explanation:

since the domain is arn,

and range is the coordinates

coordniate (top or bottom-most point)

downward facing so the top

(2, 64)

since it is downward facing we use ≤ instead of ≥

y value is 64 (just as x is 2)

your answer is y ≤ 64

hope this helps:)

Answer:

[tex]D=[x E R | {x = \infty} ][/tex]

[tex]R = [yER| y\leq 64][/tex]

Step-by-step explanation:

1) Identify whether the [tex]x[/tex] and [tex]y[/tex] values are continuous

2) Since [tex]x[/tex] will continue below the [tex]x[/tex]-axis, it will approach infinity.

   Therefore [tex]D=[x E R | {x = \infty} ][/tex]

3) Since [tex]y[/tex] ONLY continues below 64, [tex]R = [yER| y\leq 64][/tex]

Congruent figures Practice -2 measurement of angle F

Answers

Answer:

m∠F = 45°

because

Corresponding

Parts of

Congruent

Triangles are

Congruent

which of the following is equivalent to 10x+15

10(x+5)
10(x+15)
5(2+3)
5(2x+3)

Answers

Answer:

The last one  5(2x + 3)

Step-by-step explanation:

5 × 2x = 10x

5 × 3 = 15

10x + 15

Answer: 5(2x+3)
Distributive property

A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons. One crayon is chosen at random. Write each probability as a fraction, a percent, and a decimal

Answers

The probability of getting black crayons is 0.3, blue crayons 0.2, red crayons  0.25, yellow crayons 0.15, and white crayons 0.1.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

A box contains 6 black crayons, 4 blue crayons, 5 red crayons,3 yellow crayons, and 2 white crayons.

One crayon is chosen at random.

The total number of crayons = 20

The probability of getting black crayons

= 6/20

= 0.3

The probability of getting blue crayons

= 4/20

= 0.2

The probability of getting red crayons

= 5/20

= 0.25

The probability of getting yellow crayons

= 3/20

= 0.15

The probability of getting white crayons

= 2/20

= 0.1

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A bag contains 7 red marbles, 12 orange marbles, 18 yellow marbles, and 5 purple marbles. a marble is drawn at random from the bag. what is the probability that the marble drawn will not be orange? 130 112 27 57

Answers

Answer:

its 5/7

Step-by-step explanation:

no of marbles that r not orange = 30

no of total marbles = 42

probability = 30/42

= 15/21

= 5/7

I hope my answer is helpful

what does tally mean?

Answers

Answer:

To mark or take note of.

Step-by-step explanation:

i just need the edges, correct answer gets brainliest

Answers

Answer:

28

Step-by-step explanation:

counting all the lines pretty much

Answer:

its 8x3 for edges so 24 and its 8x2 for vercicles its 16 but for the faces its 8+2 = 10 so you are chillin :)

I need help!! Thanks

Answers

[tex]\text{Given that,}~ f(x) = 3x+5~ \text{and}~ g(x)=\sqrt{x^2 +3}\\\\(g \circ f)(-1)\\\\=g(f(-1))\\\\=g(3(-1) +5)\\\\=g(-3+5)\\\\=g(2)\\\\=\sqrt{2^2+3}\\\\=\sqrt{4+3}\\\\=\sqrt{7}[/tex]

The graph shows how the annual budget for a company is divided by department. Use this graph to answer the questions below

Answers

Answer: a) the answer is engineering

Step-by-step explanation:

because since it is a circle, it's out of 360 degrees, and 1/4 means first you divide 360 with 4, and you get 90. So, i checked which department is exactly 90 degrees and saw that engineering is 90 degrees

Can someone help please?

Answers

The answer is -9 !!! because 3 to the power of -2 is -9

What is the surface area?
4 m
5 m
12m

Answers

Answer:

Where is the picture of the surface area?

Step-by-step explanation:

I need the picture in order for me to help your question.

A sociologist wishes to test . the sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. to calculate a p-value for the test in excel, the sociologist should use:

Answers

Answer:

One-sample Z-test

Step-by-step explanation:

As the sample size is greater than 30, assuming the data is a simple random sample, and that the data has a normal distribution, the sociologist should conduct a one-sample z-test to calculate the p-value.

PLEASEEE HELP 100 POINTS
Write the equation of a circle whose center is at the origin and that contains the point (-3, 0).

Answers

Radius

√(-3)²+(0)²√93units

So

equation of circle

(x-h)²+(y-k)²=r²(x-0)²+(y-0)²+3²x²+y²=9

Answer:

[tex]x^2+y^2=9[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

center = (0, 0)point on circle = (-3, 0)

Substitute the given values into the formula and solve for r²:

[tex]\implies (-3-0)^2+(0-0)^2=r^2[/tex]

[tex]\implies (-3)^2+(0)^2=r^2[/tex]

[tex]\implies 9=r^2[/tex]

Substitute the center and found value of r² into the formula to determine the equation of the circle:

[tex]x^2+y^2=9[/tex]

Use an equation to write 2 x (2/3) as a multiple of a unit fraction.

Answers


Simplify the expression.
Exact Form
4/3
Decimal Form:
1.3
Mixed Number Form:
1 1/3

Which function does this graph represent?!? I’ll mark yours expert verified whoever helps plss 60 points

Answers

Answer:

B) [tex]f(x)=-3(x+1)^2+2[/tex]

Step-by-step explanation:

Notice that the graph of the parabola opens downward. This tells us that the leading coefficient of the function must be negative. Hence, we can rule out answers A and D.

Also, notice that our vertex is [tex](h,k)\rightarrow(-1,2)[/tex], which when we plug into vertex form, we get [tex]y=a(x-h)^2+k\rightarrow y=a(x-(-1))^2+2\rightarrow y=a(x+1)^2+2[/tex].

This means that B is the correct function that represents the graph.

Other Questions
Read the following excerpt from Winston Churchill's "Their Finest Hour" speech: Here is where we come to the Navy - and after all, we have a Navy, Some people seem to forget that we have a Navy. We must remind them. For the last thirty years I have been concerned in discussions about the possibilities of oversea invasion, and I took the responsibility on behalf of the Admiralty, at the beginning of the last war, of allowing all regular troops to be sent out of the country. That was a veryserious step to take, because our Territorials had only just been called up and werequite untrained. Therefore, this Island was for several months particularly denuded of fighting troops. The Admiralty had confidence at that time in their ability to prevent a mass invasion even though at that time the Germans had a magnificent battle fleet in the proportion of 10 to 16, even though they were capable of fighting a general engagement every day and any day, where as now they have only a couple of heavy ships worth speaking of the Scharnhorst and the Gneisenau. We are also told that the Italian Navy is to come out and gain sea superiority in thesewaters. If they seriously intend it, I shall only say that we shall be delighted to offer Signor Mussolini a free and safeguarded passage through the Strait of Gibraltar in order that he may play the part to which he aspires. There is a general curiosity in the British Fleet to find out whether the Italians are up to the level they were at in the last war or whether they have fallen off at all.Analyze the effectiveness of this excerpt, How does it function within the speech as a whole? How doesthe structure of the excerpt help to convey the speech's purpose and arguments? Support your argumentwith evidence from the speech. 12. If four coins are flipped, find the probability of obtaining two heads and two tails. what is meant by cruel and unusual punishment find the value of xplease help me out here ill do anything Ovulation involves the release of the _____________ from a mature follicle. If a 714-mile trip takes 17 hours, the average speed is? Simplify the following algebraic expressions.A) -2x + 5 + 10x - 9B) 3(x + 7) + 2(-x + 4) + 5x hello, anyone i need either 2 original poems or 2 analyzed poems and they have to talk about identity, finding oneself or something with a similar topic/theme. pleaseee i need it quick Which checking account would be best for nathan? account a account b account c account d Given that 5 cos (x+8.5) - 1 = 0 0 x 90, calculate correct to the nearest degree, the value of x. Calculate no.between 2 and 2.5 Look at the image below. Find the area of the parallelogram. Mr. Smith works 26 hours and earns $468. If Mr. Smith works for 16 hours, how much does he earn?I got $ 288 but I just want to make sure What are the implication of location, shape and size of Ethiopia and the horn on the physical environment, socioeconomic and political aspects what is meant by mid year population? Rotate RST 90 counterclockwise around the origin. what are trends in GPS ? Which conclusion is most likely supported. 36. How many 13 -card hands dealt from a standard deck will have exactly seven spades? Those who believe judges should be free from the pressures of public support A -want judges to be dependent on the other government branches B- expect judges to focus on the will of the people in judicial review C- expect judges to run for election rather than seek appointments D- favor the appointment of judges to their positions over elections