We have 2 equations to specify the location of the object and we desire the velocity. In order to get that, we simply need to calculate the first derivative of each location equation. So: X = 2 cos(t) X' = 2 (-sin(t)) X' = -2 sin(t) Y = sin(t) Y' = cos(t) So the velocity vector at time t is (-2sin(t), cos(t)). But you want the velocity. So using the Pythagorean theorem we can get that by calculating the square root of the sum of the squares. So: V = sqrt((-2sin(t))^2 + cos^2(t)) V = sqrt(4sin^2(t) + cos^2(t)) Speed at t = 1, is V = sqrt(4sin^2(1) + cos^2(1)) V = sqrt(2.832293673 + 0.291926582) V = sqrt(3.124220255) V = 1.767546394 And t=3: V = sqrt(4sin^2(3) + cos^2(3)) V = sqrt(0.079659427 + 0.980085143) V = sqrt(1.05974457) V = 1.029438959 Now asking for velocity as a function of P, we have a bit of a complication. As shown above, it's trivial to calculate velocity as a function of t. But if all you're given is the X and Y coordinates of the object, we have a bit more work to do. The below equations will be using the trigonometric identity of cos^2(a) + sin^2(a) = 1 for any angle a. X = 2 cos(t) X' = -2 sin(t) We want to get from X which is 2cos(t) to X'^2 which is 4sin^2(t). So: X/2; We now have cos(t) (X/2)^2: We now have cos^2(t) 1-(X/2)^2: We now have sin^2(t) 4(1-(X/2)^2): We now have 4sin^2(t) which is what we want. Time to simplify 4(1 - (X/2)^2) 4(1 - (X^2/4)) 4 - 4(X^2/4) 4 - X^2 Now we need to get from Y to Y'^2. Will do the same as for X to X'^2, but without all the comments. Y = sin(t) Y' = cos(t) Y'^2 = 1 - Y^2 So the equation for the velocity as a function of X,Y we get V = sqrt(4 - X^2 + 1 - Y^2) V = sqrt(5 - X^2 - Y^2) In summary: Position at time t = (2cos(t), sin(t)) Velocity vector at time t = (-2 sin(t), cos(t)) Velocity as function of t is: V = sqrt(4sin^2(t) + cos^2(t)) Velocity as function of P is: V = sqrt(5 - X^2 - Y^2) Is object traveling at constant speed? NO Velocity at t = 1 is: V = 1.767546394 Velocity at t = 2 is: V = 1.029438959
Answer:
According to my evaluations this equation is very petty and most likely has an answer. There are variables and numbers "3x". This part of the equation makes me feel special because 3 is a prime number. It is also mysterious because we dont know for sure what x is. This equation teaches the mathematician the true meaning of life. As it demonstrates the complexity, the information you know for sure and the information that you will learn in the future. The reader will also learn that not all problems can be solved and the ones that can be solved should be solved with varying difficulty. Finally the individual will realize that everyone has their own method to solve problems and go about life. In conclusion, this pretty equation teaches the mathematician about the importance of hard work and acceptance of everyone in their community.
The group of measures which would lead to the provided conclusion is the range is 7, the mean of the data is 12, the median is 12 and the mode is 11.
Given that, the data is around 12. If another measurement were taken, it would probably be around 12.
We need to find which group of measures would lead to this conclusion.
<h3>What are the mean, median and mode of the data set?</h3>
The mean of the data is the average value of the given data. The mean of the data is the ratio of the sum of all the values of data to the total number of values of data.
The median of the data is the middle value of the data set when it arrange in ascending or descending order. The data is around 12 which suggests that the median is 12.
Median=12
The mode of a data set is the value, which occurs most times for that data set. The value which has the highest frequency in the given set of data is known as the mode of that data set.
Mean and mode is around the median. For this case, the mean of the data is 12 and the mode is 11.
Mode=11
Mean=12
Thus, the group of measures which would lead to the provided conclusion is the range is 7, the mean of the data is 12, the median is 12 and the mode is 11.
Learn more about the mean, median and mode here;
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Answer:
Step-by-step explanation:
x/4 - y/3 = 1..multiply everything by the LCD....which is 12
3x - 4y = 12 <== standard form
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if it makes it easier for u, x/4 is the same as (1/4)x and y/3 is the same as (1/3)y
so ur problem can be written as : (1/4)x - (1/3)y = 1....multiply by 12
12(1/4)x - 12(1/3)y = 12(1)
(12/4)x - (12/3)y = 12.....reduce
3x - 4y = 12
