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:
Graph A is correct
Step-by-step explanation:
p(x)= x/10
x= 1, 2, 3, 4
Plug in x values in p(x)
when x=1 , then P(1) = 1/10
When x=2 , then P(2) = 2/10
When x=3 , then P(3) = 3/10
When x=4 , then P(4) = 4/10
In the graph y axis has 2/10 , 4/10 , 6/10...
1/10 lies between 0 and 2/10
3/10 lies between 2/10 and 4/10
Graph A is correct
Answer:
Expression: 2.89+(1.28x3) Answer: 6.73
Step-by-step explanation:
Number 1
In mathematical analysis, Clairaut's equation is a differential equation of the form where f is continuously differentiable. It is a particular case of the Lagrange differential equation
Answer:
67°
Step-by-step explanation:
Angles on a straight line add to 180, so:
A + D = 180
D = 180 - A
D = 180 - 113
D = 67
