Answer:
10
Step-by-step explanation:
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The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
The one who walked 1.2 miles would have made $72 and the one who walked 0.8 miles would have made $48.
Rate of change of line that passes through the given points is 1
Step-by-step explanation:
The ratio of vertical and horiontal changes is called the rate of change of a line. It is called slope which is denoted by m.
The formula for slope when (x1,y1) and (x2,y2) are the points on line is given by:
Given
(x1,y1) = (-6,-6)
(x2,y2) = (-2,-2)
Putting the values in the formula
Rate of change of line that passes through the given points is 1
Keywords: Slope, rate of change
Learn more about rate of change at:
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