A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°. What is the angle between the ground and steepest slope on the real rollercoaster?
The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?
To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.
The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.
The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.
That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)
The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.
That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,
the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°
The negative sign indicates that the angle is measured below the horizontal line.
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-4x +1 = -11 – 2x What is it?
Answer:
x=6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
4x + 1 = -4
-11 - 2x = -2
-4 - 2 = -6
Which of the following is NOT a transformation?
Translation
Reflection
Rotation
Construction
Dilation
Write an equation for each linear relationship. Describe the graph of the linear
relationship. State the slope and y-intercept.
Therefore , the solution of the given problem of equation comes out to be slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0).
Explain equation.Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could analyze data provided by y + 7, split 12 into two parts, and create y + 7.
Here,
This linear relationship's expression can be found by first determining the slope using the following formula:
=> slope = (y-change) / (change in x)
=> slope = (2 - (-2)) / (4 - 0) = 4/4 = 1
Consequently, the line's inclination is 1. We can now determine the equation using the point-slope form of a line's equation:
=> y - y1 = m(x - x1)
where (x1, y1) is a location on the line and m denotes the slope. We have a choice between the two points provided, so let's use (0, -2):
=> y - (-2) = 1(x - 0)
=> y + 2 = x
By taking 2 away from both edges, we arrive at:
=> y = x - 2
slope = (0 - (-4)) / (1 - (-3)) = 4/4 = 1
=> y - y1 = m(x - x1)
=> y - (-4) = 1(x - (-3))
=> y + 4 = x + 3
=> y = x - 1
A line with a slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0), represents the graph of this linear connection.
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A rectangular box without a top is have a volume of 12 cubic feet. Find the dimensions of
the box that will have minimum surface area.
Which of the following sets of ordered pairs represents a function?
{(10,5), (10,-5), (5,10), (5,-10)}
{(10,5), (-10,-5), (5,10), (-5,-10)}
{(-6,-1), (13,8), (1,6), (1,-10)}
{(3,5), (-17,-5), (3,-5), (-17,5)}
The sets of ordered pairs that represents a function are {(10,5), (-10,-5), (5,10), (-5,-10)} and {(-6,-1), (13,8), (1,6), (1,-10)}
Ordered pair of a functionOrdered pairs are written as a coordinate (x, y). For the given x coordinate points to be a function, the value of its x coordinates (domain) must not be repeated.
From the given ordered pairs, {(10,5), (10,-5), (5,10), (5,-10)} and {(3,5), (-17,-5), (3,-5), (-17,5)} are not functions since there is repetition in their domains.
Hence the sets of ordered pairs that represents a function are {(10,5), (-10,-5), (5,10), (-5,-10)} and {(-6,-1), (13,8), (1,6), (1,-10)}
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What should you substitute for x in the second equation (bottom equation) in order to solve the system by the substitution method?
We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
The given system of equations are 2x-1/3y = -2...(1)
3x+y=1...(2)
We solve this system of equations by using substitution method.
Let us solve for x in equation to substitute it in equation (2).
2x=-2+1/3y
Divide both sides of equation by 2.
x=-1+1/6y
Now plug in the value of x in equation 2.
Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
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Write 53% as a fraction. There is no need to simplify your answer.
Answer:
0.53
Step-by-step explanation:
A child has the magnet numbers 1 through 50 on their fridge. What is the probability that the child will choose a number that is not a multiple of 9?
The probability that the child will choose a number that is not a multiple of 9 is 90%.
What is probability?Probability refers to the chance or likelihood that an expected outcome occurs when multiple developments or events could have happened.
Probability describes the ratio between expected favorable outcomes and possible outcomes.
Probability as a ratio is described as a fractional value when it is not 100% certain or uncertain.
In such cases, probability hovers between zero and 1.
The multiples of 9 from 1 through 50 are five (9, 18, 27, 36, and 45).
The other numbers from 1 to 50 are 45 (50 - 5).
The probability of choosing a multiple of 9 is 10% (5/50 x 100).
The probability of choosing a number that is not a multiple of 9 is 90% (45/50 x 100) or (1 - 0.05).
Thus, the probability that the child chooses a non-multiple of 9 between 1 and 50 is 90%.
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Match the later drop-down
1) The expression 2⁻ˣ⁺³ = 3 is matched with graph B.
2 The expression 3ˣ⁺¹=3 is matched with graph C.
3) The expression 4ˣ = 3 is matched with graph
4 ) The expression 1ˣ/4 = 3 is matched with graph
What is the explanation for the above?1) The graph of the expression 2⁻ˣ⁺³ = 3 represents an exponential function where the y-coordinate is 3 when the base 2 raised to the power of (-x+3).
2) The graph of the expression 3ˣ⁺¹=3represents an exponential function where the y-coordinate is 3 when the base 3 raised to the power of (x+1). This graph is a straight line with a slope of 1.
3) The graph of the equation 4ˣ = 3 represents an exponential function where the base 4 raised to the power of x is equal to 3. This equation has a single solution, which can be determined using logarithms.
4) The graph of the expression 1ˣ/4 = 3 represents an exponential function where the base 1 raised to the power of (x/4) is equal to 3.
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A rectangular room is
1.5
times as long as it is wide, and its perimeter is
35
meters. Find the dimension of the room.
The length is :
meters and the width is
meters.
The dimensions of the room are approximately 7 meters by 10.5 meters.
The length is 10.5 meters and the width is 7 meters.What are dimensions?In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.
Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.
The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:
\(\text{Perimeter} = 2(\text{length} + \text{width})\)
Substituting the values we have for length and width, we get:
\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)
Simplifying the equation, we get:
\(\rightarrow35 = 2(2.5\text{x})\)
\(\rightarrow35 = 5\text{x}\)
\(\rightarrow\text{x}=\dfrac{35}{5}\)
\(\rightarrow\bold{x\thickapprox7}\)
So the width of the room is 7 meters.
To find the length, we can substitute x into the expression we have for the length:
\(\rightarrow\text{Length} = 1.5\text{x}\)
\(\rightarrow\text{Length} = 1.5(7)\)
\(\rightarrow\bold{Length=10.5}\)
So the length of the room is 10.5 meters.
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Please help!!
look at the picture for the question
Answer:
Quadrant: each of the four quarters of a plane, as it is divided by the number lines
y-axis: the vertical number line
Origin: the place at which the horizontal and vertical number lines cross
x-axis: the horizontal number line
Step-by-step explanation:
5 3/4 x 2 1/6 ayuda por favor
Some triangles can have more than one right angle true or false
Answer:
False
Step-by-step explanation:
Since a triangle must contain 3 interior angles all adding to 180°, then there can't be more than one right angle since 2 right angles would add up to 180°.
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 QUESTION 1 [24] Gavin Pillay is employed at Maritzburg Engineering, a Steel manufacturing company in Pietermaritzburg. Below is a copy of his Payslip. 1. 3201 Company Maritzburg Engineering cc 21 Halsted Road Pietermaritzburg Employment No 105 Id Number Income Basic Salary Overtime M Gross Salary Maritzburg Engineering cc Employee Name Gavin Pillay Period 31/05/2023 Sex Male 790128514088 R8700 R1200 A Status Married Deductions PAYE UIF Total Deductions Net Pay 1200 87 B C Name the Employee? What does UIF stand for? Show by calculation that the UIF paid by Gavin is calculated correctly Which month is this Payslip for? Calculate the missing values A to C How old is Gavin this year? Give the address of Gavin's work place. Gavin would like to contribute towards a Pension fund (7,5% of his Basic Salary). H would this affect his net salary?
If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.
1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.
Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.
Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.
31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6
Total deductions of Gavin includes PAYE, UIF and pension fund contribution.
Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7
Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?
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in triangle QRS, the measure of angle RSQ is 48.2 degrees, and the SQR is 75 degrees. what is the QRS?
The measure of angle QRS in triangle QRS is 56.8 degrees.
To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
We know that:
- The measure of angle RSQ is 48.2 degrees
- The measure of angle SQR is 75 degrees
Let x be the measure of angle QRS. Then, we can write:
RSQ + SQR + QRS = 180
Substituting the known values, we get:
48.2 + 75 + x = 180
Simplifying and solving for x, we get:
x = 180 - 48.2 - 75x = 56.8
Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.
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ANSWER THE QUESTION FOR BRAINLIEST
Answer:
c -1 and 2
Step-by-step explanation:
can i have BRAINLIEST?
What is the y-intercept of this graph?
Answer:
The Y-intercept is 0.
Step-by-step explanation:
Use the following information to answer the next question. In the process, what is the total distance that Jeremy covers?Use the following information to answer the next question.
In the process, what is the total distance that Jeremy covers?
The total distance covered by Jeremy is 1320 m
What is a line segment ?
A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.
For sapling 1 = No distance is covered.
For sapling 2, distance covered = 10 m
Return distance=10 m
For sapling 3, distance covered =20 m
Return distance=20 m and so on
Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...
Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12
Total distance covered = 122 [2(0) + (12 − 1) 20 ]
Total distance covered = 6 (11)(20) = 1320 m
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Complete question:
There are 12 saplings to be planted in a straight line at an interval of 10 m between
two consecutive saplings. Jeremy can carry only one sapling at a time and he has to
come back to the original point to take the next sapling. He plants 12 saplings in this
manner, planting the first sapling at the original point. After planting all the saplings,
he comes back at the original point,
In the process, what is the total distance that Jeremy covers?
Translate this sentence into an equation.
The sum of 21 and Delia's height is 70 .
Answer:
21 + x = 70
Step-by-step explanation:
Since we do not know delia's height, you would mark it as x! sum means add, so 21 + x = 70!
This question was a little simple, so I'm sorry for the lack of an explanation, but I'm here if you need more help!!
Malia invests $975 in a savings account with a fixed annual interest rate 3% compounded continuously. What
will her account balance after 12 years?
Malia will have [a] in her bank account.
Answer: The answer is 600 years
Step-by-step explanation:
Solve the expression 4(5a + 10b)
Answer:
20a + 40b
Step-by-step explanation:
Solve the expression 4(5a + 10b)
4(5a + 10b) =
20a + 40b
Answer: The answer is 20a + 40b
Step-by-step explanation:
First, you distributed the 5 and a to the 4
4(5a + 10b)
20a
Then, you distributed the 10 and b toward the 4
4(10b)
which it's 40b.
find a basis and the dimension of the solution space of the given homogeneous systems g x - y z - w
x − 78 = 6(2x + 3) − 8
I need help with this.
Answer:
8
Step-by-step explanation:
you use the 45-45-90 method and get 8
Answer:8
Step-by-step explanation:
20% of 50. Mathmethics
Answer:
1000%
Step-by-step explanation:
just multiply both
brainliest pls
Answer:
10
Step-by-step explanation:
20 x 50
100
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
Tommy can paint a fence in 6 hours. If his friend Huck helps they can paint the fence in 1 hour. How fast could Huck paint the fence by himself?
Answer:
Step-by-step explanation:
Answer:
it would take Huck 5 hours to paint the fence by himself
Step-by-step explanation:
its simple really, if it takes 6 hours for tommy to do it but if huck helps it would be 1 hour and thats 5 hours less so if huck does it by himself then it would take at least 5 hours.
(24 points) Need some help please !
Answer:
39°
Step-by-step explanation:
3x+15+1+10x+60=180
13x+76=180
13x=180-76
13x=104
x=8
A=3x+15
A=3(8)+15
A=24+15
A=39
Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following. Give answers as integers or rounded to 2 decimal places as appropriate.
Answer:
A = 22.62°
B = 67.38°
c = 26
Step-by-step explanation:
\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)
\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios
\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)
There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.