Step-by-step explanation:
Source: Desmos.
Graph represents the function: f(x)= -{x}
The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
<h3>What is the distance between the points (23,-33) and (4,9)?</h3>
The distance between two points on a graph can be determined using the equation;
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
Given that;
- x₁ = 23
- x₂ = 4
- y₁ = -33
- y₂ = 9
We substitute our values into the equation above.
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]
D = √[ ( -19 )² + ( 42 )² ]
D = √[ 361 + 1764 ]
D = √[ 2125 ]
D = 46.10
Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
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The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is 
which is an ellipse.
For given question,
We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.
We need to convert given parametric equations to a rectangular equation and sketch the curve.
Given parametric equations can be written as,
x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.
We know that the trigonometric identity,
sin²t + cos²t = 1
⇒ (x/2)² + (- y/3)² = 1
⇒
This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.
The rectangular equation is
The graph of the rectangular equation is as shown below.
Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is which is an ellipse.
Learn more about the parametric equations here:
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The mean absolute deviation is 10.52.
<h3>What is the mean absolute deviation?</h3>
The mean absolute deviation of a dataset is the average distance between each data point and the mean. It is a measure of variation of a data set.
MAD =1/n ∑ l x - m(x) l
Where:
n = total numbers in the data set
x = number
m(x) - median
The first step is to determine the mean of the data set: (42 + 31 + 1 + 1 + 2 4+ 5 + 6 + 7 + 3) / 10 = 10.2
Find the absolute value of the difference between the number and the mean. Add the result | (42 - 10.2) + (31 - 10.2) + (1 _ 10.2) + (1 - 10.2) + (2 - 10.2) + (4 - 10.2) + (5 - 10.2) + (6 - 10.2) + (7 - 10.2) + (3 - 10.2) = 105.2
Divide the sum by the total number in the dataset = 105.2 / 10 = 10.52
To learn more about mean absolute deviation, please check: brainly.com/question/27365177
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Answer:
x=1/2
Step-by-step explanation:
10-2x=14x+2
8/16=16x/16
x=1/2
