Answer:
this is the answer
Step-by-step explanation:
42.7893
Step-by-step explanation:
you would start by replacing the "x" with the 9
subtract the 15 and 9
then that would equal 6 which in this case it would be equal to
I'm pretty sure (sorry if it is wrong)
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).
<h3>
Answer: 12 square units</h3>
Explanation:
Rectangle ABDE is 4 units across the horizontal, and 2 units tall.
The area of this rectangle is length*width = 4*2 = 8 square units.
Triangle BCD has a base of 4 and height 2. The area of which is base*height/2 = 4*2/2 = 4 square units.
The total area is
rectangle + triangle = 8 + 4 = 12 square units
