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:
<h2>x = -17</h2>
Step-by-step explanation:
Answer:
i think its C
Step-by-step explanation:
Answer:
137
Step-by-step explanation:
2(-9)^2+5(-9)+20
2(81)-45+20
162-45+20
117+20
137
Answer:
Step 2
Step-by-step explanation:
Meredith made a fatal mistake or error in step 2;
Any quadratic problem will always have two solutions. Therefore since, we only have one solution here, it is wrong. The mistake was incurred in step 2;
From the given problem ;
<u> Wrong right</u>
2(x + 4)² = 242
(x + 4)² = 121 Step 1
x+4=11 Step 2 x + 4 = ± 11
x = 7 Step 3 x + 4 = 11 or x + 4 = -11
x = 11- 4 or x = -11 - 4
x = 7 or -15
