1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lostsunrise [7]
3 years ago
9

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

coordinates of P and this minimum length
Mathematics
1 answer:
nirvana33 [79]3 years ago
8 0
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).
You might be interested in
What is 45 divided by 70?
Vesna [10]

Answer:

0.6428571429

=

9/14

this is the answer

8 0
2 years ago
Read 2 more answers
PLEASE HELP ASAP which equation of a like has a slope of -2/3 and passes thought point (-3,-1)
coldgirl [10]

Answer:

Skill Tests

With a partner, complete the Skill Tests for the six areas of skill-related fitness and record both your scores and your partner’s scores below. Answer the reflection questions.

My Scores:

Agility – Agility Square Test:

Speed – Stay on Your Toes Test:

Reaction Time – Ready, Set, Go Test:

Balance – Stork Stance Test:

Coordination – Off the Wall Test:

Power – Standing Long Jump Test:

Partner Scores:

Agility – Agility Square Test:

Speed – Stay on Your Toes Test:

Reaction Time – Ready, Set, Go Test:

Balance – Stork Stance Test:

Coordination – Off the Wall Test:

Power – Standing Long Jump Test:

Compare your scores to your partner’s scores. Explain the reason for any differences.

How can improving your balance and coordination affect your performance in sports or recreational activities?

What activity was the most difficult for you to perform? Why?

Describe an activity that could help improve your striking and your reaction time skills.

Select a physical activity or sport that you have never done but would like to try one day. Identify at least one element of skill-related fitness that is important to being successful in this activity.

What power-increasing activities do you need to perform regularly to improve your performance?

8 0
2 years ago
Which unit of measurement is part of the metirc system
Goryan [66]
Millimeter centimeter meter kilometer
7 0
3 years ago
The prism shown has a volume of 3,024 cm3.
Arlecino [84]

Answer:

14cm

Step-by-step explanation:

To find volume, you need to multiply the height width and length together. So when you have one missing measurement, to find it, you need to do the same steps except for put a variable for the missing measurement. And continue to do the problem as you would. Here is how I solved it.

V=12x18xH

3024=216xH (216 is 12x18)

Then to find the missing side, do 3024/216 which equals 14.

7 0
3 years ago
Read 2 more answers
Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helppppppppppppppppp me i do anyhting just help[
klemol [59]
Question A: 14

Question B: 30min
8 0
2 years ago
Other questions:
  • Will mark brainliest, please answer:)
    8·1 answer
  • How do you solve his
    12·1 answer
  • There are 35,000 McDonald's restaurants worldwide. There are 14,146 locations in the United States and 2,975 locations in Japan.
    13·1 answer
  • A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 f
    6·1 answer
  • Please help! Will mark you as BRAINLIEST!!!!!
    7·2 answers
  • HELP ASAP!!<br>The equation (blank) has no solution​
    5·1 answer
  • Help plz. I just need the answers.
    8·1 answer
  • Using transformation (x-2 y+3) find the new coordinates of (7 -5) brainly
    14·1 answer
  • How to divide a polygon into triangles?
    7·2 answers
  • You earn a salary of R6 000 per month. Your employer indicates that he will give you a 20% increase. How much will your salary b
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!