A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the jin mao building in shanghai, china. the person estimates the angle of elevation to the top of the building is about 80º. what is the approximate height of the building
Answers
we know that
in the right triangle ABC
tan 80°=opposite side angle 80°/adjacent side angle 80°
tan 80°=BC/AC----->BC=AC*tan 80°-----> BC=75*tan 80°---> BC=425.35 m
the approximate height of the building=BC+eye level
the approximate height of the building=425.35+1.5----> 426.85 m
the answer is
the approximate height of the building is 426.85 m
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building from the ground is 426.85 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the angle of elevation from the person's view is 80°, while the distance between the person and the base of the building is 75 meters, therefore, using the trigonometric function the height of the building top from the person eye level is,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\Tan(80^o) = \dfrac{\text{Height of the building}}{75\ meters}\\\\\\\text{Height of the building} = 75 \times tan(80^o) = 425.35\ meters[/tex]
Now, we know the height of the building top from a person's eye level, and we also know the person's eye level as well, therefore, the height of the building can be written as,
[tex]\text{Height of the building} = 425.35 + 1.5 = 426.85\rm\ meters[/tex]
Hence, the height of the building from the ground is 426.85 meters.
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
Related Questions
Lupe has 14 stickers that she wants to give to 2 friends. She wants each friend to have the same number of stickers. Select the three statements that describe how Lupe should give the stickers to her friends. Each friend gets 14÷2 stickers. Each friend gets 2 of the 14 stickers. Each friend gets 142 stickers. Each friend gets 7 of the 14 stickers.
Answers
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
It is given that Lupe has 14 stickers that she wants to give to 2 friends.
Total number of stickers Lupe has is 14.
The number of friends is 2.
She wants each friend to have the same number of stickers. It means each friend will get half of 14.
The number stickers Lupe should give to her friends is 14 divided by 2.
[tex]\text{Number of stickers}=14\div 2[/tex]
Write this value in fraction form.
[tex]\text{Number of stickers}=\frac{14}{2}[/tex]
[tex]\text{Number of stickers}=7[/tex]
It means the correct statements are
1. Each friend gets 14÷2 stickers.
3. Each friend gets (14)/2 stickers.
4. Each friend gets 7 of the 14 stickers.
Hence correct options are 1, 3 and 4.
Now evaluate f(x) = 2x4 - 4x3-11x2+3x-6 for x=-2 f (-2) =
Answers
The answer to the given solution is 8.
Given that,
The equation is [tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6[/tex].The x = -2.Based on the above information, the calculation is as follows:
[tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6\\\\= 2(-2)^4 - 4(-2)^3-11(-2)^2+3(-2)-6\\\\= 2\times 16 - 4\times -8 - 11\times 4+ 3 \times -2 - 6\\\\[/tex]
= 32 + 32 - 44 - 6 - 6
= 8
Therefore we can conclude that the answer is 8
Learn more: brainly.com/question/17429689
-5n+22>=-73
[tex] - 5n + 22 \geqslant - 73 = [/tex]
Answers
(note: I know it's greater than or equal to, but I'm just going to use > for the sake of time)
-9n > -95
Divide both sides by -9 (This will flip the sign):
n < -95/9
n [tex] \leq [/tex] -10 5/9
(I'm not sure if you wanted a mixed fraction or not, so...)
Josh is hiking Glacier National Park. He has now hiked a total of 1 7 km 17 km17, space, k, m and is 2 km 2 km2, space, k, m short of being 1 2 2 1 start fraction, 1, divided by, 2, end fraction of the way done with his hike. Write an equation to determine the total length in kilometers ( h ) (h)left parenthesis, h, right parenthesis of Josh's hike.
Answers
17 + 2 = 19 km is 1/2 of the total length, that is,
19 = (1/2)h
(1/2)h = 19 multiply both sides by 2
h = 2*19
h = 38 km
The total length in kilometers is 38 km.
A suit regularly costs $389.90., Bob buys it on sale for $ 265.00 . How much does he save?
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A bookstore costs $90 a day to keep open, and spends $12 for each book it sells. the store charges $18 for each book it sells. If n represents the number of books sold, which equation represents the revenue function for this bookstore?
Answers
Answer:
[tex]R=6n-90[/tex]
Step-by-step explanation:
Let
R------> the revenue function
n------> the number of books sold per day
we know that
In this problem
[tex]18n[/tex] -----> represent the profit
[tex](12n+90)[/tex] -----> represent the cost
so
The revenue is equal to the profit minus the cost
[tex]R=18n-(12n+90)[/tex]
[tex]R=n(18-12)-90[/tex] ------> equation that represent the revenue function
Simplify
[tex]R=6n-90[/tex]
What is the surface area of a cylinder with a radius of 5 ft and a height of 2 ft?
Answers
Answer:
Its B.
Have a great day! OwO
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
Answers
The dog will win the race.
the answer would be 90% because when you multiply 30% x 30% =90% its the same as 3 x 3 = 9
Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?
Answers
[tex]AB= \sqrt{ (2+3)^{2} + (1-6)^{2} } =5 \sqrt{2} \\ \\ BC= \sqrt{ (9-2)^{2} + (5-1)^{2} } =\sqrt{65} \\ \\ CA = \sqrt{ (-3-9)^{2} + (6-5)^{2} } = \sqrt{145} \\ \\ [/tex]
None of the side lengths are equal, so the triangle formed by the given vertices is a Scalene Triangle. Moreover, the Pythagorean theorem is also not satisfied with given side lengths, so the triangle is NOT a Right Angled Triangle.
After being rearranged and simplified, which two of the following equations could be solved using the quadratic formula?
Answers
1. degree = 2 (i.e. the highest power equals exactly two)
2. the linear term (e.g. 4x, or -5x...) and constant term (e.g. 5, -30, pi, etc.) may or may not be present.
Now let's simplify and examine the given equations, and see if each can be solved with the quadratic formula:
A.
[tex]5x^3+2x-4=2x^2[/tex]
[tex]5x^3+-2x^2+2x-4=0[/tex]
The degree (highest power) is three, so it is not "exactly two". NO.
B.
[tex]5x^2-3x+10=2x^2+21[/tex]
[tex]3x^2-3x-11=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.
C.
[tex]5x^2-3x+10=5x^2[/tex]
[tex]0x^2-3x+10=0[/tex]
[tex]-3x+10=0[/tex]
The degree (highest power) is one, so it is not "exactly two". NO.
D.
[tex]x^2-6x-7=2[/tex]
[tex]x^2-6x-9=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.
Note that it is very important to simplify the equations before checking the degree.
If you need further explanations, please feel free to post in comments.
Answer:
The Answer will Be B and D
Step-by-step explanation:
pleae help thanks a bunch
Answers
You use the Pythagorean theorem to solve this
[tex] a^{2} + b^{2} = c^{2} [/tex]
Put in the values it tells you to
[tex]a^{2} + 4.4^{2} = 5.5^{2} [/tex]
Square the numbers
[tex]a^{2} + 19.36 = 30.25[/tex]
Subtract 19.36 from both sides
[tex] a^{2} = 10.89[/tex]
Take the square root of both sides
a = 3.3
The answer is 3.3
Hope this helps!
Centennial park is evaluating the capacity of the park and have determined that 15 people can comfortably stand in a section that is 5ft by 8ft , the park has dimensions that are 400yds by 200 yds estimate the number of people who can fit in the park
Answers
We have been given that 15 people can comfortably stand in a section that is 5ft by 8ft .
Hence, the area of this section is given by
[tex]A=5\times 8\\ A=40 ft^2[/tex]
Hence, we can say that 15 people can comfortably stand in an area 40 square feet.
Now, we know that 1 yard is equal to 3 feet.
Hence, the area of the section 400yds by 200 yds is equal to
[tex]400\times 3 \times 200 \times 3\\ =720000 ft^2[/tex]
Now, in 40ft^2, 15 people can stand comfortably.
Hence, in 720000 ft^2, number of people can stand comfortably is
[tex]\frac{15}{40} \times 720000\\ \\ =270000[/tex]
Therefore, 270000 people can stand in the park of dimension 400 yds by 200 yds
What is the mode of these numbers? A 40. B 43. C 26 and 31. D. 31 and 43
Answers
Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.
Answers
now, "same" could be anything whatsoever, you name it, a whole polynomial, a whole anything whatsoever.
[tex]\bf \cfrac{\sqrt{2}}{\sqrt{2}}=\cfrac{\sqrt{3}}{\sqrt{3}}=\cfrac{100000000}{100000000}=\cfrac{eggs}{eggs}=\cfrac{miles}{miles}=\cfrac{\frac{\quad \sqrt{3}}{\sqrt[5]{17}}\quad }{\frac{\sqrt{3}}{\sqrt[5]{17}}}=\cfrac{whatever}{whatever}=1[/tex]
now, that said, let us use 1 in this case then ... hmmmm we simply need a "y" in the denominator, so we simply multiply the denominator AND numerator by "y", y/y = 1 btw.
[tex]\bf \cfrac{3}{14}\cdot \cfrac{y}{y}\implies \cfrac{3y}{14y}[/tex]
PLZ HURRY!!
If a Professional basketball player earns $3 million playing 125 games per year and plays an average of 40 minutes per game, how much does he earn per second of playing time?
Answers
24,000/40= 600 per minute
600/60= 10 per second
$10 per second.
The rate of the number of bags mishandled by the airlines fell to 4.77 bags per 1000 passengers in 2011. At this rate,
estimate how many bags would be mishandled for 1650 passengers.
Answers
describe a situation where it is easier to use decimals than fractions and explain why
Answers
When you must multiply non whole numbers, decimals are easier to manipulate in the sense that setting up a multiplication problem with decimals rather than fractions is much simpler and easier to calculate.
Dynatashia has a list of items she needs to buy at the store. She has written down the items and the advertised prices as shown: Hamburger – $3.99 per pound Hamburger buns – $1.29 2-liter soda – 3 for $2.00 Dynatashia buys 1.5 pounds of hamburger, 1 package of buns and 3 of the 2-liter bottles of soda. Her receipt is shown below. 2-ltr soda 2@3/$2 $1.34 Hambrg 1.5 lb@3.99 $5.99 Hbuns 1@1.69 $1.69 2-ltr soda 1@3/$2 $0.67 Determine if Dynatashia's receipt is correct. a. Yes, Dynatashia's receipt is correct. b. No, Dynatashia paid too much for soda. c. No, Dynatashia paid too much for hamburger. d. No, Dynatashia paid too much for buns.
Answers
Answer:
D. No, Dynatashia paid too much for buns.
Step-by-step explanation:
We are given that,
The actual cost of the items are,
Items Cost
Hamburger $3.99 per pound
Buns $1.29 per packet
2-liter soda $2 per 3 bottle
As, she bought 1.5 pounds of hamburgers, 1 packet of buns and 3 bottles of 2-liter soda.
So, she has to pay,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.29 × 1 = $1.29
For soda bottles = $2
But from the receipt, we see that she pays,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.69 × 1 = $1.69
For soda bottles = 1.34 + 0.67 = $2
That is, she has to pay $1.29 for the packet of the buns but she paid $1.69 for the buns.
Hence, the receipt is not correct as Dynatashia paid too much for the buns.
Answer: D
Step-by-step explanation:
edg
plz help me
it sounds confusing
Answers
[tex]2700 \times 3^m = 2700 \times 3^{-3}= \dfrac{2700}{3^3} = \dfrac{2700}{27} = 100[/tex]
m = -3
3^-3 = 1/27
1/27 × 2,700 = 2,700/27
2,700/27 simplified = 100
Answer = 100
Hope this helped☺☺
Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.
Answers
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8
Distributive property:
(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8
Both methods are efficient, it all depends with the users preference
Final answer:
To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.
Explanation:
The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:
First: Multiply the first terms in each binomial (3x×x = 3x²).
Outer: Multiply the outer terms (3x×1 = 3x).
Inner: Multiply the inner terms (8×x = 8x).
Last: Multiply the last terms in each binomial (8×1 = 8).
Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.
Using the Distributive Property
This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.
Using a Table
Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.
While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.
hello can you please help me posted picture of question
Answers
you just have to find the solution to Y.
[tex]( \frac{-b}{2a},y( \frac{-b}{2a})) [/tex]
b = coefficient of x term = 8
a = coefficient of squared term = 2
So,
[tex] \frac{-b}{2a}= \frac{-8}{4}=-2 [/tex]
and
[tex]y(-2)=2(-2)^{2}+8(-2)+1=-7 [/tex]
Therefore, the vertex occurs at (-2, -7)
So, the correct answer is option C
I WILL MARK BRAINLIEST PLEASE HURRY
Answers
according to the given equation the centre of this circle is in the poit (6;7) and its radius =4 units.
Using this data, it is possible to define right choice: D.
answer: graph D.
A car tire has a radius of 15 inches. Suppose the car is traveling at 60 miles per hour (1 mile = 5,280 feet). What is the approximate rate of spin, in revolutions per minute, of the tire? Round the answer to the nearest whole number.
Answers
Speed of the car = v = 60 miles per hour
= 60 x 5280 feet per hour
= 316800 feet per hour
= 316800 x 12 inches per hour
= 3801600 inches per hour
= 3801600/60 inches per minute
= 63360 inches per minute
Angular velocity = w = ?
v = r w
w = v/r
So,
w = 63360/15
= 4224 radians per minute
= 4224/2π revolutions per minute
= 672 revolutions per minute
So, the angular velocity of the tire is 672 revolutions per minute
Circumference = 2π×15/12 = 7.85398 feet. (1 foot=12 inches)
7.85398 feet = 7.85398/5280 = 0.001487496522 miles
In 1 hour, it travels 60 miles. This means it travels (60/60) miles in 1 minute.
So, it travels 1 mile in 1 minute.
The rate of rotation = 1/0.001487496522
= 672.27rpm
To the nearest whole number = 672 rpm
Alexander is riding his bicycle to school. After one mile he is a third of the way there. How much more does he have to ride
Answers
1 mile = (1/3)*(distance to school)
Multiply this equation by 3 and you have
3 mile = (distance to school)
You also know that
(distance ridden so far) +(remaining distance) = (distance to school)
Subsituting given information, this is
1 mile + (remaining distance) = 3 mile
Subtracting 1 mile from this equation gives
(remaining distance) = 2 miles
Alexander has 2 miles more to ride.
how many ounces of 30% hydrochloric acid solution and 80% hydrochloric acid solution must be mixed to get 10 oz of 50% hydrochloric acid solution
Answers
This diagram tells you the constituents 80% and 30% solution are in the proportion 20:30 or 2:3 or 4:6 to make the mix having 50% hydrochloric acid. Note that the numbers 4 and 6 add to 10, the number of ounces of solution we want.
4 ounces of 80% solution must be mixed with 6 ounces of 30% solution to make 10 ounces of 50% solution.
What are the zeros of the polynomial function f(x) = (x – 6)(x – 2)(x + 7)?
Answers
So,
x - 6 = 0
⇒ x = 6
x - 2 = 0
⇒ x = 2
x + 7 =0
⇒ x = -7
Thus the zeros of the given function are x = 6, x = 2 and x = -7
hey can you please help me posted picture of question
Answers
1. The figure shows a parabola whose vertex is (0,0).
2. The x² indicates that the red parabola shown in the figure is vertical
3. and the sign - indicates that the red parabola opens down.
Therefore, you can conclude that the red parabola has the equation f(x)=-x²
So, the answer is B.
Shifting 4 units down means subtracting 4 from the function value.
So, G(x) = 4 - x²
Thus,
F(x) = G(x) - 4
F(x) = 4 - x² - 4 = - x²
Therefore, the correct answer is option B
5,895÷36
show all your work
Answers
____
The calculator is certainly faster.
Mrs. Daly's reading classes were surveyed about their reading preferences. the data is summarized in the table below.
given that a student is in 9th grade, what is the probability that they like to read non-fiction novels, based on this data?
Answers
Answer:
0.60
Step-by-step explanation:
A jar contains two red marbles, three green marbles, ten white marbles and no other marbles. two marbles are randomly drawn from the jar without replacement. what is the probability that these two marbles drawn will both be red? express your answer as a common fraction.
the denominator HAS to be 15C2
but what's the numerator?