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
lbvjy [14]
3 years ago
8

Find the point P on the line yequals=66x that is closest to the point (74 comma 0 )(74,0). What is the least distance between P

and (74 comma 0 )(74,0)​?
Mathematics
1 answer:
tekilochka [14]3 years ago
4 0

Answer:

The point P that is closest to the point (74, 0) is P(7.4, 22.2), and the least distance between P and (74, 0) is 70.2

Step-by-step explanation:

Given

y = 66x

And a point A(74, 0)

We are required to find the point on the line that is closest to A, and then find the distance between these points.

Let the point be P(s, t)

Because it's coordinate satisfies the given equation

y = 3x

Let t = 3s, then we have

p(s, t) = P(s, 3s)

Next, we find the distance between P and A

Let the distance be

D = √[(x1 - y1)² + (x2 - y2)²]

Here x1 = 74, x2 = 0, y1 = s, y2 = 3s.

D = √[(74 - s)² + (0 - 3s)²]

= √(s² - 148s + 5476 + 9s²)

= √(10s² - 148s + 5479)

To maximize the distance, we find the derivative of D with respect to s, and set it to 0.

That is dD/ds = 0

dD/ds =

(20s - 148)/2√(10s² - 148s 5479) = 0

=> 20s - 148 = 0

20s = 148

s = 148/20

s = 7.4

Since t = 3s, we have

t = 22.2

So, the point is P(7.4, 22.2)

Finally, we find the distance D.

D = √[(74 - s)² + (0 - 3s)²]

D = √[(74 - 7.4)² + (0 - 3×7.4)²]

D = √(4435.56 + 492.84)

= √4928.4

D = 70.2

Therefore, the distance is 70.2

You might be interested in
How many hundredths are in one tenth? Explain using pennies and dimes.
Umnica [9.8K]

Answer:

11 ways

100 Pennies & 0 Dimes

90 Pennies & 1 Dimes

80 Pennies & 2 Dimes

70 Pennies & 3 Dimes

60 Pennies & 4 Dimes

50 Pennies & 5 Dimes

40 Pennies & 6 Dimes

30 Pennies & 7 Dimes

Step-by-step explanation:

6 0
3 years ago
Help please! Not sure what this is
Lesechka [4]
B. Rotation
I’m assuming the question is not asking about placement but just the way the shape is.
Hope this helps!
3 0
3 years ago
Read 2 more answers
The of choice are ways epress 0.4 which is not
Ann [662]

Answer:

NO IT IS 4

Step-by-step explanation:

6 0
3 years ago
What pair of factors will add together and give you 0
lbvjy [14]

Answer:

the type of factor would be 4,4 I just figured it out

Step-by-step explanation:

3 0
3 years ago
Please answer correctly !!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Liula [17]

Answer:

  8 5 5

Step-by-step explanation:

Line 3 sets t = 5

Line 5 sets n = t = 5

Line 6 sets c = n+3 = 8

The displayed values for c, n, are

  8 5 5

6 0
3 years ago
Other questions:
  • On Tuesday, Allison earned $39.25 for watching the smith twins for 5 hours. How much does Allison get paid per hour to watch the
    7·2 answers
  • A box filled with 2 red cards , 2 green cards , and 14 yellow cards. A card is chosen at random from the box. What is the probab
    6·2 answers
  • What is the slope of the line that contains the points -2,7 and 2,3
    14·1 answer
  • HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    14·1 answer
  • Select all values that make the equation true.
    9·1 answer
  • Slove for 1.2 x 3 = V ​
    7·1 answer
  • Please help me and explain thank you so much I appreciate it
    13·1 answer
  • Factorise the following expression :​
    11·1 answer
  • Roberta has $50 in her purse. The money she has left over after buying two boxes of cookies is given by the equation 50 − x = 38
    7·1 answer
  • Write an equation in slope-intercept form of the line that passes through (7, 2) and (2, 12)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!