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:On a scale drawing of a steel I-beam , the height of the beam is 2 1/2 in. The scale is 1/4 in = 6 feet. What is the actual height of the I-beam. \(12\)
Step-by-step explanation:
$13.68 because you do [.18+.06=.24] [18•.24=4.32] [18-4.32=13.68]
Y=1/4x+3 i think is the right answer because your y-intercept is 3 and you go up one and over 4
If the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.
Given that the arc of a circle measures 250 degrees.
We are required to find the range of the central angle.
Range of a variable exhibits the lower value and highest value in which the value of particular variable exists. It can be find of a function.
We have 250 degrees which belongs to the third quadrant.
If 2π=360
x=250
x=250*2π/360
=1.39 π radians
Then the radian measure of the central angle is 1.39π radians.
Hence if the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.
Learn more about range at brainly.com/question/26098895
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