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:
300
Step-by-step explanation:
you just divide the number of parts by minutes. In this case, 3600/12=300. There's your answer
Answer:
A. 2 (0)=0
B. 2 (2)=4
Step-by-step explanation:
You have to multiply the X numbers by 2 for example 2x , x=2 , 2x2=4
Answer:
D
Step-by-step explanation:
The question says 6 is greater than x. That means that 5 is the highest it can go and it can not get any higher so you have to go backwards.
Answer:
B
Step-by-step explanation:
x/5 + 2/3x
first you multiply both denominator.
this will be you denominator unless you can simplify it.
denominator=5 x 3X = 15X
now you times both denominator with the opposite numerator.
e.g. 5 x 2 and X x 3X.
=10 and 3X^2
now you and both numerators which is 3X^2 + 10
so the answer is b
