<span>Let time taken by Luke to cover the distance = x hours
Speed of Luke = 6 miles per hour
Therefore, Distance covered by Luke = 6x ------(1)
Speed of Micah = 4 miles per hour
Since Micah walked 2 miles before Luke started running, Luke started 1/2 an hour after Micah started.
Therefore time taken by Micah to cover the distance = x+1/2
Distance covered by Micah = 4(x + 1/2) -------(2)
Equating (1) and (2)
6x = 4(x+1/2)
6x = 4x +2
2x = 2
x= 1
Therefore Luke would take 1 hour to cover the distance covered by Micah.</span>
Answer:
15
Step-by-step explanation:
Let the smallest integer be x. The integers will be x, x+1, x+2, all the way up to x+6.
119 = 7x + (1+2+3+4+5+6)
119 = 7x + 21
7x = 98
x = 14
The second smallest integer will be x+1, so x+1 = 15.
and 
are the <em>farthest</em> from the origin and 
is the <em>closest</em> from the origin.
Let be a curve of the form 
. The distance with respect to origin is found by using the following Pythagorean identity:
(1)
Where 
is the square distance function.
We can modify (1) as following:
![r = [27-3\cdot (y-2)^{2}]+y^{2}](https://tex.z-dn.net/?f=r%20%3D%20%5B27-3%5Ccdot%20%28y-2%29%5E%7B2%7D%5D%2By%5E%7B2%7D)
(1b)
Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:
First derivative test
Second derivative test
The y-component represents a maximum.
Now we graph the function with the ressource of a graphing tool, we find the following points:
Farthest points: , .
Closest points: .
and are the <em>farthest</em> from the origin and is the <em>closest</em> from the origin.
To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943
I think that X = -2 and Y = 1
I hope my answer will serve you.
