Looking north, two skyscrapers are sighted from the viewing deck of the Empire State Building at 1250 feet up. One skyscraper is sighted at a 20° angle of depression and a second skyscraper is sighted at a 30° angle of depression. How far apart are the two skyscrapers to the nearest foot?
Answer:
Step-by-step explanation:
The angle of depression is the angle between the line of sight and a vertical line.
The distance between the two skyscrapers is 1269ft
I've added as an attachment, a figure that illustrates the scenario
First, we calculate distance AB using the following tangent ratio
[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]
So, we have:
[tex]\mathbf{\tan(60) = \frac{AB}{1250}}[/tex]
Make AB the subject
[tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]
Next, we calculate distance AC using the following tangent ratio
[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]
So, we have:
[tex]\mathbf{\tan(60+10) = \frac{AB + BC}{1250}}[/tex]
[tex]\mathbf{\tan(70) = \frac{AB + BC}{1250}}[/tex]
Make AB + BC, the subject
[tex]\mathbf{AB + BC = 1250 \times \tan(70)}[/tex]
Make BC the subject
[tex]\mathbf{BC = 1250 \times \tan(70) - AB}[/tex]
Substitute [tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]
[tex]\mathbf{BC = 1250 \times \tan(70) - 1250 \times \tan(60)}[/tex]
[tex]\mathbf{BC = 1269}[/tex]
Hence, the distance between the two skyscrapers is 1269ft
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1. Use the mental math strategy of rounding (for example +1/-1, +2/- 2, +10/-10, or +20/-20) to add the following numbers. Write down how you would change the numbers in your head for each question.
Ex. 27 + 51 28+50=78
a. 41 + 16=
b. 79 + 14=
c 580 + 355=
d. 174 + 620=
e. 378 + 210=
Find sin A.
a.
4
sin A = -
3
sin A
b.
4
sin A =
d.
sin A =
Answer:
4/5
sin A = perpendicular/hypotenuse
sinA = 28/35
sinA = 4/5
hope it helps
option B
Answer:
B. Sin A = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Sin A = opposite / hypotenuse
Sin A = 28 / 35
Divide both by 7
28 / 7 = 4
35 / 7 = 5
[tex]\frac{28}{35} = \frac{4}{5}[/tex]
The value of the computer decreased exponentially throughout the five-year period.
What was the average annual of decrease (in dollars per year) over the two-year interval from t=2 to r=4?
table:
_Time___/_Value__
1 / $400.00
3 / $100.00
5 /$25.00
Therefοre , the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be the average yearly rate οf decrease (in dοllars per year) is $100.
Explain functiοn.
Each tοpic, mathematics, variable design, which is and bοth actual and hypοthetical lοcatiοns will be cοvered in the midterm exam questiοns. a catalοg οf the cοnnectiοns between variοus cοmpοnents that wοrk tοgether tο prοduce the same οutcοme. A service is made up οf many unique parts that wοrk tοgether tο prοduce unique οutcοmes fοr each input.
Here,
[tex]= > V(t) = V(0) * e^{(-kt)[/tex]
By using the numbers at times t=1 and t=3, we can determine the decay cοnstant k:
[tex]= > V(1) = 400 = V(0) * e^{(-k1)[/tex]
[tex]= > V(3) = 100 = V(0) * e^{(-k3)[/tex]
[tex]= > 100/400 = e^{(-k3) / e^{(-k1)[/tex]
[tex]= > 1/4 = e^{(-2k)[/tex]
[tex]= > ln(1/4) = -2k[/tex]
[tex]= > k = ln(4)/2[/tex]
[tex]= > k ≈ 0.69315[/tex]
The value οf the cοmputer at times t=2 and t=4 can nοw be determined using the algοrithm fοr V(t):
[tex]= > V(2) = V(0) * e^{(-k2)[/tex]
[tex]= > V(4) = V(0) * e^{(-k4)[/tex]
[tex]= > V(4)/V(2) = e^{(-k4) / e^{(-k2)[/tex]
[tex]= > V(4)/V(2) = e^{(-2k)[/tex]
[tex]= > V(4)/V(2) = e^{(-0.69315*2)[/tex]
[tex]= > V(4)/V(2) =0.5[/tex]
Over this time periοd, the average yearly rate οf decline (in dοllars per year) is:
Ratiο οf decline equals value shift. (time interval)
=> V(2) - V(4) = (rate οf decline) / (4 - 2)
=> (amοunt οf reductiοn) is equal tο (V(2) * (1 - 0.5)) / 2.
=> (amοunt οf decline) is equal tο (V(2) * 0.5) / 2.
=> V(2) / 4 equals (rate οf decline)
=> (rate οf reductiοn) equals 400 / 4
=> rate οf decline) = $100 annually
As a result, οver the twο-year periοd frοm t=2 tο r=4, the average yearly rate οf decrease (in dοllars per year) is $100.
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A 1. Explain the key difference between permutations of three out of a
group of seven objects and combinations of three out of a group of
seven objects.
Answer:
Step-by-step explanation:
im clueless
what is the scale factor plz help plzz
Answer:
c
Step-by-step explanation:
What is the partial fraction decomposition in terms of X? Review the work showing the first few steps in writing a partial fraction decomposition. 6 O + 121-25 B 2.x - 3 А + 2-3 (21 - 3)² 412-12: +9 (2x - 3) 6 43 - 12x - 25 = A(2x - 3) + B 2.x - 3 (2:- 3) 12x - 25 = 2Ax - 3A + B 6 7 + 2x - 3 (2x - 3)2 7 2x - 3 (2,-3)
After partial fraction decomposition the correct expression we get,
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{6}{2x-3} - \frac{7}{(2x-3)^2}[/tex]
Hence option fourth is correct.
Partial fractions is a technique used in mathematics to decompose a rational function into simpler fractions.
It involves breaking down a rational function with a denominator of a higher degree into a sum of fractions with simpler denominators.
The given expression is,
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{A}{2x-3} + \frac{B}{(2x-3)^2}[/tex]
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{A(2x-3) + B}{4x^2 - 12 x + 9}[/tex] [since (a-b) = a² + b² -2ab]
Simplifying we get
⇒ 12x - 25 = A(2x - 3) + B
⇒ 12x - 25 = 2Ax + (B - 3A)
Comparing the coefficients we get
2A = 12
⇒ A = 6
And B - 3A = -25
Put the value of A we get
B = -7
Hence,
After substituting the values of A and B in the given expression we get
[tex]\frac{12x - 25}{4x^2 - 12 x + 9} = \frac{6}{2x-3} - \frac{7}{(2x-3)^2}[/tex].
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Select all the equations that are true. Explain your thinking.
Answer:
A,D,E,
Step-by-step explanation:
2. Solve for b.
(a - 3)
Answer:
Step-by-step explanation:
Sum of angles inside triangle is 180
b + (a -3) + 90 =180
b + a - 3 + 90 = 180
b + a + 87 = 180
b + a + 87 -87 = 180-87
b + a = 180-87
b + a = 93
b = 93 -a
Susan has 50% more books than Michael. Michael has 40 books. If Michael buys 8 more books, will Susan have more or less books than Michael? Use any method to solve the problem
Answer:
Susan has more books than Michael.
Step-by-step explanation:
If Susan has 50% more books and Michael has 40 books, that means Susan has 1.5 times 40 = 60
40 + 8 = 48
60 is more than 48, so Susan has more books than Michael
Find the volume: 5ft 5ft 8ft 3ft
Answer:
120ft
Step-by-step explanation:
8 x 3 x 5
Select the correct type of solution set for the system
Answer:
no solution
Step-by-step explanation:
A survey of 7th grade students found that 18 out of 32 students prefer to buy their lunch at school instead of bring it from home. What percent of students is that? Write your final answer as a percentage.
Answer: 56.25%
Step-by-step explanation: You would divide 18 over 32, which would get the decimal 0.5625. Then you would multiply this by 100/100 which would get 56.25/100. This would get you 56.25%.
help me with all of it if u can
Answer:
Answers: (4. = 3) (5. = 9) (6. = 20)
If 1 lb = 2 c, then 1 1/2 c = _____ lb
Answer: b=
10.873127c2hn11t
4l
Step-by-step explanation:
Answer:
0.75 lb cause proportions
On her lunch break, Audrey grabs a meal with her two coworkers. If everyone paid an equal amount of $8.50, then how much was the total bill?
Answer:
$25.50
Step-by-step explanation:
3 people including Audrey went on the lunch break. If each spent $8.50, the total bill can be calculated in two ways
Method 1
$8.50 x 3 = $25.50
Method 2
$8.50 + $8.50 + $8.50 = $25.50
Why must you use the HEIGHT of the parallelogram, NOT the length of the slanted side of the parallelogram, to determine its area?
2. What is the value of f(x)=2/3x+1/4 when x=6
What is the y coordinate?
Answer:
2
Step-by-step explanation:
Pythagorean Theorem is annoying..
Answer:
c = 10
Step-by-step explanation:
8² + 6² = c²
64 + 36 = c
64 + 36 = 100
[tex]\sqrt{100\\[/tex] = 10
Hope this helps :)
can play 18 holes of golf in 180 minutes. Calculate what is his average rate in number of minutes per holes?
If you are given x2 + 15x + 9, what does the expression equal if x=2
Answer:
43
Step-by-step explanation:
2(2) + 15(2)+ 9 = 43
Answer:
43
Step-by-step explanation:
2 x 2 = 4
4 + (15 x 2) = 34
34 + 9 = 43
A girl weight increased by 12% between her tenth and four teen birthdays . If she weighed 45kg on her tenth birthday. What did she weigh on her fourteenth birthday
Help ASAP PLEASEEE ILL GIVE BRAINLIEST
Answer:
3/18 = 6/ DG
Step-by-step explanation:
There’s an option D on the bottom you just can’t see.
Someone please help with this question
Answer:
B. 25
Step-by-step explanation:
30 + 35 + 10 = 75
100 - 75 = 25
Answer:
it's B (25%) players play the woodwinds.
Step-by-step explanation:
35% + 10% + 30%= 75%
100% - 75%= 25%
a rectangular prism measures 3 in by 8 in by 9 in. what is the side length of a cube with the same volume?
Answer:
6 in.
Step-by-step explanation:
Rectangular prism
V = lwh l = 8 W = 3 h = 9
= 8(3)(9)
= 216
Cube
[tex]V = s^{3}[/tex] where s = length of side
216 = [tex]s^{3}[/tex]
[tex]s = \sqrt[3]{216}[/tex] = 6
Alexis bought 4 cupcakes that cost $1.05 each. She paid with a five dollar bill. How much change did Alexis receive?
Answer:
Ans (change recieved) = $0.80
Step-by-step explanation:
because 1 cupcake cost $1.05, 4 of them cost $4.2 because you multiply 4 cupcakes by the cost ($1.05) to obtain the total cost of the four cupcakes.
in order to know the change she recieved . you subtract the $5 bill she paid with the total cost of the 4 cupcakes
$5.00 - $4.20 = $ 0.80
Marvin has 2 rabbits. The number of rabbits triples
every year. Marvin needs 100 pounds of food to feed
one rabbit per year. How many pounds of food will
Marvin need to feed his rabbits during the third year?
Select one:
o
900
O
1200
600
1800
Answer:
1800
Step-by-step explanation:
Answer:
1800 pounds
Step-by-step explanation:
1st year: 2 rabbits
2nd year: 6 rabbits
3rd year: 18 rabbits
18 x 100 = 1800
hope this helps :)
Function Notation: f(x)= -4+22; f(12)
Answer:
f(x)=-4x+22
f(12)=-4×12+22=-48+22=-26 if your
Step-by-step explanation:
question is f(x)=-4x+22
What is the area? square kilometers
Answer:
Step-by-step explanation:
The area of a trapezoid is the height times the average of its parallel bases.
A=h(b1+b2)/2, in this case
A=14(4.6+8.7)/2
A=7(4.6+8.7)
A=7(13.3)
A=93.1 km^2