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:
They seem correct!
Step-by-step explanation:
Answer:
10 people lesser.
Step-by-step explanation:
Initially, it 15 people get off but 9 people get picked up, hence losing 6 people. If 4 more people get off, it has then lost 10 people total.
The original number of passengers on the bus decreased by 10 after the second stop
Assume that the total passengers on the bus before 2:30 was x
Now, at 2:30:
15 passengers got off and 9 got on.
This means that:
number of passengers = x - 15 + 9
number of passengers = x -6
10 minutes later:
4 passengers got off the bus
This means that:
number of passengers = (x-6) - 4
number of passengers = x - 10
The original number of passengers on the bus decreased by 10 after the second stop.
9^-2 = 1/81 or 0.0123
When there is a negative in front of the exponent it makes a fraction. It is usually just 1/the number it equals if it were positive.
Answer:
C. 1.75
Step-by-step explanation:
7 paved over 4 unpaved
7 divided by 4
1.75
