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lesantik [10]
2 years ago
10

Help me please I will give u 100 points and brainliest

Mathematics
1 answer:
Sonja [21]2 years ago
3 0

The correct answer is -2

<em>Sure hope this helps you :D</em>

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P is the point on the line 2x+y-10=0 such that the length of OP, the line segment from the origin O to P, is a minimum. Find the
nirvana33 [79]
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).
8 0
3 years ago
Pat's income is 20 % more than Adam. How much percent is Adam's income less than Pat's?
pantera1 [17]

Answer: 20%

Step-by-step explanation: The same number applies here. Think about it this way, let's say you have a friend named Sofia and she has 3 dollars more than you, how many dollars do you have less than Sofia? 3 dollars. That's the easiest way I can explain it.

4 0
3 years ago
What is two plus two
Olenka [21]

Answer:

2+2=4

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A 6-sided die is rolled. what is the probability of rolling a number less than 4?
ohaa [14]

1/2

Step-by-step explanation:

All outcomes of a single die= 6

Events less than 4 =3

probability=3/6

=1/2

7 0
1 year ago
(b) The force, F, between two objects is inversely proportional to the square of the distance, d, between
LiRa [457]

Answer:

F is reduced by 31%

Step-by-step explanation:

F = 1/(d²)

now, we increase the distance by 20% (multiply by 1.2).

F new = 1/(1.2×d)² = 1/(1.44×d²) = (1/1.44) × (1/(d²)) =

= 1/1.44 × old F = 0.69 × old F

100 - 69 = 31%

6 0
3 years ago
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