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).
Answer: 20%
Step-by-step explanation: The same number applies here. Think about it this way, let's say you have a friend named Sofia and she has 3 dollars more than you, how many dollars do you have less than Sofia? 3 dollars. That's the easiest way I can explain it.
Answer:
2+2=4
Step-by-step explanation:
1/2
Step-by-step explanation:
All outcomes of a single die= 6
Events less than 4 =3
probability=3/6
=1/2
Answer:
F is reduced by 31%
Step-by-step explanation:
F = 1/(d²)
now, we increase the distance by 20% (multiply by 1.2).
F new = 1/(1.2×d)² = 1/(1.44×d²) = (1/1.44) × (1/(d²)) =
= 1/1.44 × old F = 0.69 × old F
100 - 69 = 31%
