We have a right triangle $\triangle ABC$ where the legs $AB$ and $BC$ have lengths $6$ and $3\sqrt{3},$ respectively. Medians $AM$ and $CN$ meet at point $P.$ What is the length of $CP$

Answers

Answer 1

By using Pythagoras theorem and distance formula the length of CP is obtained as 3.43 units.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

To find the length of CP, first find the coordinates of point P, and then use the distance formula to calculate the length of CP.

Let A be at the origin (0, 0), and let B be on the positive x-axis at (6, 0). Then we can find the coordinates of C using the Pythagorean theorem -

AC² + BC² = AB²

AC² + (3√3)² = 6²

AC² = 9

AC = 3

So C is located at (3, 3√3). We can find the coordinates of M by taking the average of the coordinates of A and B, which gives -

M = ((0+6)/2, (0+0)/2) = (3, 0)

Similarly, find the coordinates of N by taking the average of the coordinates of B and C, which gives -

N = ((6+3)/2, (0+3√3)/2) = (4.5, 1.5√3)

Now find the equation of the line passing through M and C, which is the line containing median AM -

slope = (3√3 - 0)/(3 - 0) = √3

y - 0 = √3(x - 3)

y = √3x - 3√3

And find the equation of the line passing through N and A, which is the line containing median CN -

slope = (0 - 3√3)/(0 - 6) = √3/2

y - 0 = (√3/2)(x - 6)

y = (√3/2)x - 3√3

Now, find the intersection point of these two lines, which is point P -

√3x - 3√3 = (√3/2)x - 3√3

x = 6/3.5

x = 12/7

y = √3(12/7) - 3√3

y = 3√3/7

So P is located at (12/7, 3√3/7).

Now use the distance formula to find the length of CP:

CP² = (12/7 - 3)^2 + (3√3/7 - 3√3)²

CP² = (33/7)^2 + (6√3/7)^2

CP² = 1089/49 + 72/49

CP² = 1161/49

CP = √1161/7

Therefore, the length of CP is (approximately) 3.43.

To learn more about Pythagoras Theorem from the given link

https://brainly.com/question/21970437

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Related Questions

PLEASE HELPPPPPPPPPPPPPPPP!!!

Answers

Answer:

6 years

Step-by-step explanation:

5% of 1000 is 50

1. $1050

2. $1100

3. $1150

4. $1200

5. $1250

6. $1300

6 years because 5% of 1000 is 50

Find the perimeter. Simplify your answer.

Answers

Answer:

wild guess, 50

Step-by-step explanation:

10s+3+10s+3+3s+9+3s+9= 50

is 5,7,9 a pythagorem theorem? pls help me due rn

Answers

Answer:

No

Step-by-step explanation:

a^2+b^2=c^2

5^2= 25

7^2 = 49

25+49=74

square root of 74 does not equal 9

Answer:

No.

Step-by-step explanation:

Pythagorean Theorem: a²+b²=c²

5²+7²=9²

5²=25, 7²=49, 9²=81

25+49 does not equal 81.

A circle is divided into equal parts. An angle turns through one of the parts, as
shown below. Which equation shows a way to find the measure of the angle?

Answers

Answer:

1/6 = 60/360

Step-by-step explanation:

The circle is split into 6 parts and a circle equals 360°

1/6 = x/360

Cross Multiply...

6x = 360

Divide to isolate x...

x = 60

The equation measures the angle that will be 1 / 6 = x / 360. Then the correct option is D.

What is a circle?

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

A circle is divided into equal parts. An angle turns through one of the parts, as shown below.

Then the equation shows a way to get the measure of the angle that will be

The arc of the circle makes 360°. And the circle is divided into six equal parts, and then the angle of each section will be equal.

Let x be the angle of each section.

Then the ratio of the area of the complete circle and one-sixth circle. Then we have

A₁ = 6A₂

Then we have

A₂ / A₁ = [(x/360) πr²] / [πr²]

A₂ / 6A₂ = x / 360

1 / 6 = x / 360

Then the value of x will be

x = 60°

More about the circle link is given below.

https://brainly.com/question/11833983

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Select the function that is odd.

A. f (x) = sin (x)
B. f (x) = cos (x) + sin (x)
C. f (x) = cos^3 (x)
D. f (x) = sin^2 (x)

Answers

The answer is A. F(x)= sin(x)

the price of a pair of shoes increases from $58 to $61 What is the percent increase to the nearest percent?
please help I will mark brainliest​

Answers

Answer:

23.08

Step-by-step explanation:

5x-4=9x+6 please put explanation

Answers

1- first more the all the variables to the left side and change the sign.
So: 5x-9x=6+4
2- add/ subtract the terms. So: -4x=10
3- divide both sides by -4 to find x
So: -4x/-4 =10/-4
The answer will be: x= -2.5

Simplify 38 - 32
-
A. 34
B. 36
c. 310
D. 3-6

Answers

Answer:

38 - 32 = 6

Step-by-step explanation:

subtract the question

i have to explained it in words pls help

Answers

9514 1404 393

Answer:

slope: cost per miley-intercept: fixed base cost

Step-by-step explanation:

The y-intercept is the value of y when x=0. The problem statement tells you that x is the number of miles driven, and y is the rental cost.

When the number of miles driven is zero, the rental cost is ...

  y = 2.25×0 +70

  y = 70

The cost of renting the truck is $70 when it isn't driven anywhere. The y-intercept ($70) is the basic, fixed cost of truck rental.

__

If x=1 (1 mile driven), then 2.25 is added to the cost of the truck rental. The slope (2.25) is the cost per mile driven. (That mileage cost is added to the basic rental cost.)

Please man, I need this answer as fast as possible. Thank You!!!!

Answers

Answer:

-5f

and

2g

Step-by-step explanation:

what is rt5 x rt3
yeah do that plz

Answers

Answer:

3(2r+1)

Step-by-step explanation:

5r+1 is 6

Then you factor out 3 and get 3(2r+1)

8x -2 + (4x - 1)(4x+1) = 0

Answers

Answer:

8x - 1 + 16x²

Step-by-step explanation:

8x - 2 + (4x - 1)(4x+1) = 0

=> 8x - 2 + 16x² + 4x - 4x - 1

=> 8x - 2 + 16x² - 1

=> 8x - 1 + 16x²

Therefore, 8x - 1 + 16x² is our answer

HELP 25 POINTS LIKE HELP SOLVE THIS ASAP!!!

Answers

Answer:

nahhhh why did you report me I did nun wrong

Step-by-step explanation:

easy one for you folks.​

Answers

Answer:

if its easy do it

Step-by-step explanation:

Answer:

7.5/15 or something because yes

Complete the recursive formula of the arithmetic sequence -1, -13, -25, -37
a ( 1 ) =
a ( n ) = a ( n-1 ) +

Answers

Answer:

see explanation

Step-by-step explanation:

A recursive formula allows the next term in a sequence by adding the common difference d to the previous term.

d = a₂ - a₁ = - 13 - (- 1) = - 13 + 1 = - 12 , then

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 12 with a₁ = - 1

What is the greatest common factor of 48, 72 and 52? A.2 B.4 C.8 D.16

Answers

the answer is 4 since 4 is common in all the three digits

B).4

HELP ASAP!!!
What are the exact solutions of x2 − 3x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b squared minus 4 times a times c all over 2 times a?

x = the quantity of 3 plus or minus the square root of 5 all over 2
x = the quantity of negative 3 plus or minus the square root of 5 all over 2
x = the quantity of 3 plus or minus the square root of 13 all over 2
x = the quantity of negative 3 plus or minus the square root of 13 all over 2

Answers

Answer:  Choice C

Explanation:

The given equation is in the form [tex]ax^2+bx+c=0[/tex], where,

a = 1b = -3c = -1

Use the quadratic formula to get the following

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-1)}}{2(1)}\\\\x = \frac{3\pm\sqrt{9+4}}{2}\\\\x = \frac{3\pm\sqrt{13}}{2}\\\\[/tex]

The last equation matches with choice C.

phân tích đa thức x^3 - x thành phân tử

Answers

Answer:

1

Step-by-step explanation:

Please help. Been stuck on this for days.

Answers

Answer:

At least 8.333 km/hr

Step-by-step explanation:

Using the inequality setup, we have

5/r + 1.25 + .75 + .9 ≤ 3.5

5/r ≤ .6

5 ≤ .6r

r ≥ 25/3 = 8.333

points (4, 3) and (0, 6) Mid point

Answers

Answer:

(3.5,3)

Step-by-step explanation:

Midpoint= (x¹+x²/2, y¹+y²/2)

x¹=4

x²=3

y¹=0

y²=6

Put your values into the formula

(4+3/2,0+6/2)

(7/2, 6/2)

(3.5,3)

Find the range of the following group of numbers: 1, -8, -10, 11, 19

Answers

it should be 29. range is taking the biggest number and subtracting the smallest number. biggest is 19 and smallest is -10. 19 minus -10 equals 29 :D

Megan spent half of her paycheck on an iPad. Over the weekend she earned $12 from babysitting. If she has $514.50 now. Write and equation and solve to find out how much was her paycheck

Answers

A: $1,005
Explanation:
514.50 = -12 + 502.50(2)
She had twice as much money before buying the iPad. 514.5 - 12 = 502.5
502.5 is half of her paycheck, so multiply by 2.

If the perimeter of a rectangle is 6x^2-2x+14 and the length is x^2-x+8 what is the measure of the width?

Please help!!

Answers

Answer:

w = 2x^2-2x+15

Step-by-step explanation:

Since the formula to find the perimeter is P=2l+2w, use this to set up your equation:

6x^2-2x+14 = 2(x^2-x+8) + 2w

Then, distribute the 2 to everything inside the parentheses.

6x^2-2x+14 = 2x^2-2x+16 + 2w

Subtract 2x^2-2x+16 from both sides, leaving you:

4x^2-4x+30 = 2w

Divide 2 from both sides.

2x^2-2x+15

The answer is 2x^2-2x+15

For each gallon of gas Sean puts in his truck, the truck will go $\frac{8}{3}$ miles. Suppose Sean's tank is empty, and he puts in $\frac{7}{5}$ gallons. How far can Sean go with his truck?

Answers

Answer:

56/15

Step-by-step explanation:

All we have to do is 8/3 x 7/5 and 8x7 is 56,5x3 is 15

So the answer is 56/15.

Answer:

56/15

Step-by-step explanation:

simplify the expression.

20a^4 × (1/2 a^3 )^2

Answers

Answer:

5a^10

Step-by-step explanation:

Help me urgently i have to submit a t today

Answers

Answer:

6/5

Step-by-step explanation:

He reads 1.2 page every 1 minute, 1.2X15(mins)=18 page.

What is Arithmetic ?

Answers

Answer:

Arithmetic is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them - addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Answer:

The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

Step-by-step explanation:

1,2
2,6
3,12
4, 20

Is the function Linear or Nonlinear, and explain why

Answers

Answer: Nonlinear

Explanation:

The variable x increases by 1 each time we move down the rows. This increase is constant or the same jump each time.

However, the variable y increases by different amounts. From y = 2 to y = 6, we have +4. Then from y = 6 to y = 12 is +6. This mismatch of increases is sufficient to prove we don't have a linear function. The function is nonlinear.

Visually, we can plot all of the points on the same xy grid. Notice that a straight line does not go through all four points. Rather, a parabola does, and the equation of the parabola is y = x^2+x which is the same as y = x(x+1).

a man earn $6 in two hours. how much does he earn in 5 hours​

Answers

Answer:

$15

Step-by-step explanation:

6 divided by 2 is 3

3 multiplied by 5 is 15

A recipe calls for

23

cup of sugar for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cup of sugar?

Answers

Answer:

.....

Step-by-step explanation:

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