-10/40 = y / -5
cross multiply
(40)(y) = (-5)(-10)
40y = 50
y = 50/40
y = 5/4 <===
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).
That will be easy. It could be 12/56+3/56 or, 7/56+8/56 or, 10/56+5/56.
The probability that the red balls can be drawn before the green ball is drawn is 3/8.
<h3>What is Probability?</h3>
The probability is the measure of the likelihood of an event to happen.
Given:
red balls= 3
white balls = 4
green balls = 1
So, Probability of red balls
=3/8
Probability of green balls
=1/7
Learn more about probability here:
brainly.com/question/14546377
#SPJ1
Use the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 15^2 = 25^2
a^2 + 225 = 625
a^2 = 400
a = 20
Answer: 20 cm
Hope this helps!!
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