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
A skyscraper with 102 floors is 1,326 feet tall each floor is the same height how tall is each floor show your work
Alika [10]

Answer:

each floor is 13 feet tall

Step-by-step explanation:

1326/102 = 13 feet

4 0
3 years ago
Brad bought a piece of industrial real estate for $192,345. The value of the real estate appreciated at a constant rate per year
nevsk [136]

Answer:

look it up

Step-by-step explanation:

ez

7 0
3 years ago
a large storage container in the shape of a rectangular prism has the dimensions of the following: length 16.5m width 18.2m heig
Zielflug [23.3K]

Answer:

3603 boxes.

Step-by-step explanation:

Rectangular Prism is actually a cuboid.

Volume of cuboid = length * width * height.

It is given that length = 16.5 m,  width = 18.2 m, and height = 12 m. Therefore:

Volume = 16.5 * 18.2 * 12 = 3603.6 cubic meters.

Volume is actually the capacity of the shape. If the box has the volume of 1 cubic meters, then the number of boxes that can fit in the rectangular prism will be:

Number of boxes to be fit = Volume of Large container/Volume of Small Container.

Number of boxes = 3603.6/1 = 3603 boxes.

Therefore, 3603 boxes will fit the rectangular prism and 0.6 cubic meters will be the spare space!!!

4 0
3 years ago
Given the vectors w = <-5, 3> and z = <1, 4>, find the results of the vector subtractions. -w − z = z − w = w − z =
liq [111]

Answer:

-w − z = <4, -7>

z − w = <6, 1>

w − z = <-6, -1>

Step-by-step explanation:

6 0
2 years ago
2/9 of students in a school are in sixth grade how many sixth graders are in the school if the school has 27 students
Pani-rosa [81]

Answer:

The areas of the squares adjacent to two sides of a right triangle are shown below.

 

 

What is the area of the square adjacent to the third side of the triangle?

units^2  

2

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Solve for x. −23(3x−4)+3x=56
    8·2 answers
  • Plz help me with this
    10·2 answers
  • Solve the polynomial. <br><br> X^3 + 4x^3 - 11x - 30 = 0
    10·1 answer
  • Is there a math Theorem for a right triangle
    14·1 answer
  • En los numeros 4,5,8,10 y 11 cual es el numero que menos se repite
    5·1 answer
  • Timed test please answer ASAP
    10·1 answer
  • HELP PLEASE MAX POINTS
    8·2 answers
  • A pack of cinnamon scented pencils sell for $4.00 what is the sales tax rate if the total cost of the pencils is $4.32
    14·2 answers
  • What is the slope of<br> the line?<br><br> Give your answer as<br> a fraction in simplest<br> form.
    15·1 answer
  • Find the 96th term of the arithmetic sequence -16,-28,-40 (im stuck on this please help)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!