Jada is visiting New York City to see the Empire State building. She is 100 feet away when she spots it. To see the top, she has to look up at an angle of 86.1 degrees. How tall is the Empire State building?
Answers
The height of the Empire State building is 1466.85 ft
Important information:
- She is 100 feet away when she spots it.
- To see the top, she has to look up at an angle of 86.1 degrees.
calculation:
= 1466.85 ft.
where,
3.90 represent the angle of the top to Jada
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Final answer:
The student is asked to utilize trigonometric functions, specifically tangent, to determine the height of the Empire State Building based on an angle of observation and distance from the building. The height of the building can be estimated by multiplying the tangent of the given angle by the distance.
Explanation:
Given that Jada is 100 feet away from the Empire State Building and looks up at an angle of 86.1 degrees, we can use trigonometry to calculate the height of the building. Specifically, we'll be using the tangent of the angle, which is the ratio of the opposite side (the height of the building) to the adjacent side (the distance from Jada to the building).
To calculate this, use the formula:
tangent of angle = height/distance
By transposing the formula, we can find the height.
Height = Tan(angle) × Distance
Insert the given values:
Height = Tan(86.1°) , 100 feet
Therefore, using the appropriate trigonometric values, you can calculate the approximate height of the Empire State Building. This question does not require the use of a number of stories or the height of one story as previously suggested, as these specifics are not supplied within the question's context.
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Which of these numbers is between 1 and 5/6? A. 6/7 B. 4/5 C. 4/7 D. 11/6
it takes 1 gallon of diesel 1 fuel for a cruise ship to trarel 6 inches how many gallons will it take for the cruise ship to travel 1 mile
Liana started to evaluate the function f(x) = 2x2 – 3x + 7 for the input value 2.f(x) = 2(2)2 – 3(2) + 7 = 2(4) – 3(2) + 7 What is the value of the function when x = 2?
True or false If the graph of two linear equations cross at exactly one point they are called dependent.
Answers
A). 1.5 and 2.9
B). -0.2 and 2.9
C). 2 and 2.9
D). -0.2 and 2
2). What is the solution set of 4x^2-3=11x?
A). {-3/4,1}
B). {1/4,-3}
C). {-1/4,3}
D). {3/4,-1}
3). What would the graph of g(x)=-(x+2)^2+5 look like?
Answers
x = -(11) ± √((11)² - 4(-4)(2))
2(-4)
x = -11 ± √(121 + 32)
-8
x = -11 ± √(153)
-8
x = -11 ± 3√(17)
-8
x = -11 ± 3(4.1)
-8
x = -11 ± 12.3
-8
x = -11 + 12.3 or x = -11 - 12.3
-8 -8
x = 1.3 or x = -23.3
-8 -8
x = -0.1625 or x = 2.9125
x ≈ -0.2 or x ≈ 2.9
The answer is B.
2. 4x² - 3 = 11x
4x² - 11x - 3 = 0
x = -(-11) ± √((-11)² - 4(4)(-3))
2(4)
x = 11 ± √(121 + 48)
8
x = 11 ± √(169)
8
x = 11 ± 13
8
x = 11 + 13 or x = 11 - 13
8 8
x = 24 or x = -2
8 8
x = 3 or x = -0.25
The answer is C.
3. g(x) = -1(x + 2)² + 5
g(x) = -1(x + 2)(x + 2) + 5
g(x) = -1(x(x + 2) + 2(x + 2)) + 5
g(x) = -1(x(x) + x(2) + 2(x) + 2(2)) + 5
g(x) = -1(x² + 2x + 2x + 4) + 5
g(x) = -1(x² + 4x + 4) + 5
g(x) = -1(x²) - 1(4x) - 1(4) + 5
g(x) = -x² - 4x - 4 + 5
g(x) = -x² - 4x + 1
b. 30 units2
c. 24 units2
d. 35 units2
Answers
x y
2 3
7 3
7 10
2 10
It is easier to graph these vertices to avoid confusion.
Length: basis is the y-values : 10 - 3 = 7 units
Width: basis is the x-values: 7-2 = 5 units
Area = Length * Width
A = 7 units * 5 units
A = 35 units² Choice D.
3y = 3x + 15
Which statements about the system are true? Check all that apply.
The system has one solution.
The system graphs parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations graph the same line.
The solution is the intersection of the 2 lines
Answers
The true statements about the system are:
Both lines have the same y-intercept.
The solution is the intersection of the two lines
How to explain the equation
To determine the properties of the system, we can manipulate the equations to a standard form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
2y = x + 10
Divide both sides by 2:
y = (1/2)x + 5
3y = 3x + 15
Divide both sides by 3:
y = x + 5
Both lines have the same y-intercept. The y-intercepts of both equations are 5, so they share the same y-intercept.
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Final answer:
The system has one solution, both lines have the same slope and y-intercept, and the solution is the intersection of the two lines.
Explanation:
To determine which statements about the system of linear equations are true, we can analyze the equations. Let's start by putting both equations in slope-intercept form, y = mx + b.
- Equation 1: 2y = x + 10. Divide both sides by 2 to isolate y. We get y = 1/2x + 5.
- Equation 2: 3y = 3x + 15. Divide both sides by 3 to isolate y. We get y = x + 5.
From the equations, we can see that both lines have the same slope, which is 1/2. Therefore, the statements that are true are:
- Both lines have the same slope.
- Both lines have the same y-intercept.
- The solution is the intersection of the two lines. This means the system has one solution.
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Answers
- 1 2/8
_______
5 5/8
Make sense?
The eight stay the same thing because the denominator is the same if the denominator is not the same so we do the lowest common denominator (LCD).