Write a coordinate proof of the Distance Formula in Space.Given: A has coordinates A(x, y, z) , and B has coordinates B(x, y, z) .Prove: A B = (x-x) + (y-y) + (z - z)

Write a coordinate proof of the Distance Formula in Space.

Given: A has coordinates A(x₁, y₁, z₁) , and B has coordinates B(x₂, y₂, z₂) .

Prove: A B = √(x₂-x₁)² + (y₂-y₁)² + (z₂ - z₁)²

Answers

Answer 1

Required coordinate proof of distance formula between two points in 3 dimension is:

[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]

As given,

Let points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) be referred to a system of rectangular axes OX , OY, OZ.

Through the points A and B, we draw planes parallel to rectangular coordinate plane as rectangular parallelepiped with AB as diagonal.

Pythagoras Theorem

[tex]AB^2 = AC^2 + CB^2....(1)[/tex]

[tex]AB^2=CD^2+DB^2...(2)[/tex]

From equation (1) and (2) we have,

[tex]AB^2=AC^2+DB^2+CD^2[/tex]

As coordinates of the points, A and B as known,

[tex]AC =y_{2}-y_{1}, CD = x_{2} -x_{1} and DB= z_{2}-z_{1}[/tex]

Distance formula :

[tex]AB^2=(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2[/tex]

Therefore, required coordinate proof of distance formula between two points in 3 dimension is ,

[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]

Learn more about distance formula here:

brainly.com/question/12864470

#SPJ4

Related Questions

The telephone company offers two billing plans for local calls. Plan 1 charges $23 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls. The answer is
(Type an inequality.)

Answers

a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23

b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1

c. the number of monthly calls x is x > 100

What is inequality ?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Plan 1: $23 per month for unlimited calls

Plan 2: $19 per month + $0.04 per call

Let the number of calls be x

a. 19 +0.04x >23

0.04x >4

x > 100

b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.

On solving the above inequality, we get over 100 calls should be made so that Plan 1 is more economical than Plan 2.

c. x > 100

Answers

Answer:

Negative

Step-by-step explanation:

Which of the following defines workplace politics?
O Choices made according to law
O Beliefs of a person or social group in which they have an emotional investment
O Games played in a workplace environment to achieve status, advancement and money
O Professional standards of conduct, based on moral principles and values, guilding decision-making and actions

Answers

Answer:

"Games played in a workplace environment to achieve status, advancement and money"

what is a non-repeating decimal, give examples of nom repeating decimals.

Answers

A non-repeating decimal is simply a decimal that goes on and on with no group of digits that repeat itself.

For example, pi = 3.14159265359...

Answer:

Recurring Decimal

Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).

Examples are

0.6666666666,

1.456456456

Step-by-step explanation:

Set as brainliest

Find the sum of pair of vectors. <6,-31> + (-22,3)

Answers

According to the given statement The sum of pair of vectors are = (-16 , -28).

What precisely is vector addition?

The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.

According to the given data:

Given two vectors are:

a =(6,-31)

b = (-22,3)

The vector sum is,

M = (a1 + b1, a2 + b2)

= (Mx, My).

Substitution of the value we get:

M = (6 + (-22), (-31) + (3))

= (-16 , -28)

The sum of pair of vectors are = (-16 , -28).

To know more about vector addition visit:

https://brainly.com/question/12937011

#SPJ4

Suppose a local office store has a press that can print 54,000 brochures per hour. How many brochures can be printed during a 3 1 4 hour run?

Answers

Answer:

Step-by-step explanation:

Rate: 54000 brochures per hour

Formula: D=RT Distance=Rate x Time (In this case distance is the amount)
(I’m not sure if you meant to type 3 1/4 or 314. I’ll include both)
D=54,000(3 1/4)

Two ways

1. 54,000(3 1/4)=175,500

2. 54,000x3 is 162,000, and 1/4 of 54,000 is 54,000/4=13,500. 162,000+13,500=175,500.

(54,000 x 314 = 16,956,000)

Hope this helps!

A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.

The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.
The largest angle is twice the smaller angle minus 30 degrees.
The sum of the triangle's interior angles is x + y + z = 180.

Which two equations represent the remaining angle relationships?

Select each correct answer.
1) x=y−z+40
2) x=2z−30
3) x=y+z−40
4) x=30−2z
5) x = y + z + 40

Answers

The correct answer would be option 2 and 3:

2) x=2z−303) x=y+z−40

How to solve for the angles

We have to sove the problem by carefully trying to understand the statements

x = largest angle

y = next largest angle

z = smallest.

1. For the first statement: The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.

largest angle < y + z

This would be represented as

x = y + z - 40

2. The largest angle is twice the smaller angle minus 30 degrees.

This is represented as

2 times of smallest = 2 * z = 2z

minus 30 degrees = 2z - 30

Hence the solutions to the question from the option that we have would be the options

2) x=2z−303) x=y+z−40

Answers

Answer:

Just graph, first one Y int: 2 and X is rise over run 1 and 2

Step-by-step explanation:

the sum of 12 and twice y

Answers

Answer:12+2y

Step-by-step explanation:

Answer:

12 + 2y

Hope this helps :)

Step-by-step explanation:

When it says "sum," this means the answer to 2 numbers you add. The first number would be 12, and the other number will be y 2 times. So y plus y equals 2y. The final equation is 12 + 2y.

(12+6) divided by 3 squared simplified :p

Answers

Answer:

The answer is 36

Step-by-step explanation:

12+6=18

18/3=6

6 squared is 36

36 simplified is still 36

Eddie used 9.6 cups of flour to bake 3 cakes. How much flour, on average, did he put in each cake?

Answers

Answer: i believe its 3.2 cups per cake

Step-by-step explanation:

9.6 / 3 = 3.2

Complete the congruence statements for each pair of congruent figures below

Answers

Triangles are congruent if their matching interior angles and sides are all congruent.

What is congruence in math?

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Congruent figures: what are they?

Congruent figures have sides that are the same length and angles that are the same measurement. In other terms, two figures are said to be congruent when they are superimposed upon one another. Even when they are flipped or rotated, they perfectly fit on top of one another.

What is congruent shapes?

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Learn more about congruent

brainly.com/question/12413243

#SPJ9

What types of things have you measured before?

Answers

Answer:

1. Room size (length * width) for carpet

2. From window top to floor for curtains

Step-by-step explanation:

Find the distance between each pair of parallel lines with the given equations.
y=-2 x+1 y=-2 x+16

Answers

The distance between each pair of parallel lines with the given equations y = -2x+1 and y = -2x+16 is 15 units.

We can find the points passing through the lines.

Hence,

The points passing through the line y = x - 11 are:-

Let x = 0

y = -2(0) +1

(0,1)

and;

Let x = 1/2

y = -2(1/2) + 1 = -1 +1

(-1/2,0)

The points passing through the line y = -2x + 16 are:-

Let x = 0

y = -2(0) + 16 =16

(0,16)

and;

Let x = 8

y = -2(8) + 16 = -16 + 16

(8,0)

Hence, using distance formula, the distance between the parallel lines will be:-

[tex]\sqrt{(16-1)^2+(0-0)^2} = \sqrt{15^2+0}=\sqrt{225} = 15[/tex] units.

To learn more about distance formula, here:-

brainly.com/question/8283882

#SPJ4

PLEASE PLEASE PLEASE HELP!! ASAP!! BRAINLIEST FOR WORK THAT SHOWS ALL STEPS AND CORRECT ANSWERS!! :)

1. Factor the expression: x^6–729. Show your work for full credit.

2. Solve the equation 2x^2+16x–11= -7 by completing the square. Show your work for full credit.

3. Factor over the complex numbers. Show your work for full credit. x^4–5x^2–36

Answers

1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18

3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)

How to factorize expressions?

1) We are given the expression; x⁶ - 729

It can also be written as;

(x²)³ - 9³

Now, from factorization of algebra, we know that;

a³ - b³ = (a - b)(a² + ab + b²)

Thus;

(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)

= (x² - 9)(x⁴ + 9x² + 81)

= (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.

Add 7 to both sides to get;

2x² + 16x – 11 + 7 = -7 + 7

2x² + 16x – 4 = 0

Divide through by 2 to get;

x² + 8x – 2 = 0

Add 2 to both sides to get;

x² + 8x = 2

Take half of the x term and square it and then add the result to both sides to get;

x² + 8x + 16 = 2 + 16

Rewrite the perfect square on the left to get;

(x + 4)² = 18

Take square root of both sides to get;

x + 4 = ±√18

Subtract 4 from both sides to get;

x = -4 ± √18

x = -4 + √18 or -4 - √18

3) We want to factorize x⁴ – 5x² – 36

Using the difference of squares identity, we know that;

a² - b² = (a + b)(a - b)

Thus;

x⁴ – 5x² – 36 = (x² + 9)(x² - 4)

Now, (x² + 9) factored over the complex numbers gives;

(x² + 9) = (x + 3i)(x - 3i)

Thus;

x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)

Read more about factorization at; https://brainly.com/question/723406

#SPJ1

what is the area of the triangle below

Answers

The area of triangle is 12 square units.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

The given points are

A=(1,2)

B=(1,8)

C=(5,2)

According to given question we have

By the use of distance formula , we get

[tex]AC=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AC=\sqrt{(5-1)^{2} +(2-2)^{2} }\\\\AC=\sqrt{(4)^{2} +(0)^{2} }\\\\AC=4 units\\\\\\AB=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AB=\sqrt{(1-1)^{2} +(8-2)^{2} }\\\\AB=\sqrt{(0)^{2} +(6)^{2} }\\\\AB= 6 units[/tex]

Area of right triangle(A) is given by:

[tex]Area =\frac{1}{2} base *height[/tex]

where,

base of the triangle =4 units

height of the triangle =6 units.

[tex]Area =\frac{1}{2} base *height\\\\Area =\frac{1}{2}* 4 *6\\\\Area =12 square units[/tex]

Therefore, the area of triangle is 12 square units.

Learn more details about triangle here:

https://brainly.com/question/2773823

#SPJ1

Which statements prove that m || n?

Answers

Answer:

The first 2 and the 2nd to last equations

Step-by-step explanation:

Angles 8 and 10 are alternate interiors, which would only work if m and n are parallel.

Angles 1 and 9 are congruent angles, which would only work if m and n are parallel.

Angle 1 and 3 are on the same line, so that can't prove it.

m8 and m9 could only add up to 180 if m and n are parallel, which makes this also true.

Angles 7 and 10 add up to 180, but can't be congruent.

STRUCTURE The students in Mrs. Mangione’s class attempt to guess the number of marbles in a jar to earn 2 extra credit points on their next exam. Suppose there are 1206 marbles in a jar and a student makes a guess of m marbles. Which expression represents the difference between the student's guess and the actual number of marbles. Select all that apply.

Answers

The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.

How to illustrate the information?

When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:

= 2 × m

= 2m

The expression that represents the difference between the student's guess and the actual number of marbles will be:

= 1206 - 2m

= 2(603 - m)

Learn more about expressions on:

brainly.com/question/1280754

#SPJ1

Two shops are selling the same DVD. In Tesco the DVD cost £11.49. In Asda the DVD
costs £13.99. Asda have an offer- "20% off all DVDs". Which shop should you buy the DVD
from?

Answers

100 -20= 80% = 0.8

0.8 x 13.99= £11.19 (Asda)

£11.49 (Tesco)

Therefore Asda is cheaper.
Buy from Asda
Ans: Asda

Multiply the numbers.

Answers

The result of multiplying the numbers 234 x 0.35 is 81.9

How to multiply the numbers?

The numbers are given as:

234 and 0.35

Express the numbers in a product expression

So, we have

234 x 0.35

Express 234 as 200 + 34

So, we have

234 x 0.35 = (200 + 34) x 0.35

Expand the bracket

So, we have

234 x 0.35 = 200 x 0.35 + 34 x 0.35

Evaluate the product

So, we have

234 x 0.35 = 70 + 11.9

Evaluate the sum

So, we have

234 x 0.35 = 81.9

Hence, the result of multiplying the numbers 234 x 0.35 is 81.9

Answers

Answer:

why did the teacher give an exam

A group of friends were working on a student film that had a budget of $1400. They
used 67% of their budget on props. How much money did they spend on props?

Answers

They spent $938 on the props.

Answer:

That is wrong it is not $938 its $322

Step-by-step explanation:

1. Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x-2y = -16
Ographing
substitution
O elimination
distributive
(1 point)

Answers

Are they together or separate

Which equation below combines with the equation -4 x+6 y=3 to form a system with an infinite number of solutions?
A. 0.5+x=1.5 y
B. 0.75+2 x=1.5 y
C. 0.5+2 x=1.5 y
D. 0.75+x=1.5 y

Answers

To form a system with an infinite number of solutions, the equation -4x + 6y = 3 must be combined with D. 0.75 + x = 1.5 y.

A system of equations is a set of two or more equations which includes common variables.

To form a system with an infinite number of solutions, the lines should be the same or overlapping. These lines must have the same slope and y-intercept. The equations of these lines must be the multiple of one another.

Given the equation -4x + 6y = 3, rewrite this in the form c + ax = by(same as the form of the choices).

-4x + 6y = 3 ⇒ 3 + 4x = 6y

To make 6y into 1.5y, divide both sides by 4.

3 + 4x = 6y ⇒ 0.75 + x = 1.5 y

Hence, the equation -4x + 6y = 3 must be combined with 0.75 + x = 1.5 y to form a system with an infinite number of solutions.

To learn more about solving systems of equations: brainly.com/question/13729904

#SPJ4

Help wanted! Im I’m desperate need of assistance!

Answers

Answer:

-2/5

Step-by-step explanation:

Hi there!

We find slope by using rise over run.

For this problem, identify two points on the line. I'll use (0, 3) and (5, 1).

[tex] m = \frac{{y} - {y} }{ {x} - {x}}[/tex]

You can plug the coordinates into this formula, making sure they stay in the right order. Subtract the first y coordinate from the second y coordinate, and the first x coordinate from the second x coordinate. (Just make sure one point is on the left, and the other on the right).

[tex] \frac{3 - 1}{0 - 5} = \frac{2}{ - 5} [/tex]

2/-5 is the same as -2/5, so that is your answer

what is multiples of 30 and 45?

Answers

It’s 1,3, and 5 I think

The vasquez family visits their grandmother every 3 weeks and hosts a neighborhood party every 8 weeks. every 16th week, the vasquez family takes a day to go hiking. a. after how many weeks will the vasquez family both visit their grandmother and host the neighbor hood party? b. after how many weeks will all three events occur?

Answers

Using least common multiple (LCM), the Vasquez family both visit their grandmother and host the neighbor hood party after 24 weeks. After 48 weeks, all three events will occur at the same time.

A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.

If the Vasquez family visit their grandmother every 3 weeks and host a neighbor hood party every 8 weeks, to know when will these event will occur at the same time, solve for the LCM of 3 and 8.

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . .

8 : 8, 16, 24, 32, 40, . . .

LCM = 24

Hence, after 24 weeks, both will occur at the same time.

To know when will the three events will occur at the same time, solve for their LCM.

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, . . .

8 : 8, 16, 24, 32, 40, 48, . . .

16 : 16, 32, 48, . . .

LCM = 48

Hence, after 48 weeks, all three events will occur at the same time.

Learn more about LCM here: brainly.com/question/16054958

#SPJ4

with the steps as well please

Answers

Answer:

Step-by-step explanation:

(i)

[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]

(ii)

[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]

(iii)

[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]

Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?

Answers

We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

Given,

The quantity of medicine added to the original mixture = 15 ounces

New quantity of medicine in the mixture = 18 ounces

Quantity of water in the mixture = 7 ounces

Total new quantity of mixture = 18 + 7 = 25 ounces

Original quantity of medicine in the mixture = 18 - 15 = 3 ounces

Original quantity of water in the mixture = 7 ounces

Total original quantity of mixture = 3 + 7 = 10 ounces

We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.

Here,

Proportion of medicine and water in original mixture = 3:7

Quantity of medicine and water in new mixture = 18:7

Now,

18 ÷ 3 = 6

Then, 7 × 6 = 42

So, 42 - 7 = 35

Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

Learn more about proportion here:

https://brainly.com/question/28292396

#SPJ1

Solve $2+\frac{1}{6}y=3x+4$

Answers

Answer:

[tex]y=18x+ 12[/tex]

Step-by-step explanation:

Given equation:

[tex]2+\dfrac{1}{6}y=3x+4[/tex]

Solve for y

Subtract 2 from both sides:

[tex]\implies 2+\dfrac{1}{6}y-2=3x+4-2[/tex]

[tex]\implies \dfrac{1}{6}y=3x+2[/tex]

Multiply both sides by 6:

[tex]\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2[/tex]

[tex]\implies y=18x+ 12[/tex]

Other Questions

I need help with 1-5 Solve the system. 5x+y=4x+6y=9.5 Challenge activity 1. 2. 2: math with engineering prefixed numbers. 431044. 2084776. Qx3zqy7 complete the following calculation and select the appropriate engineering notation prefix: (note: watts Three personal watercraft vehicles launch from the same dock. The first vehicle leaves the dock traveling due northeast, while the second vehicle travels due northwest. Meanwhile, the third vehicle leaves the dock traveling due north.The first and second vehicles stop about 300 yards from the dock, while the third stops about 212 yards from the dock.(b) Write a coordinate proof to prove that the dock, the first vehicle, and the second vehicle form an isosceles right triangle. How did Rosalind Franklins work change the way we think about DNA? 3-4 sentences Determine whether each infinite geometric series diverges or converges. If the series converges, state the sum. 1+2+4+ . . . The perimeter of an equilateral triangle is 10 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle. What was the perspective of many American colonists following the French and Indian War?- Some wondered why they had risked their lives to capture Caribbean islands for Britain.- They resented British martial law and found British officers arrogant.- They claimed credit for having won the war.- They began to see themselves as Americans and sought to distance themselves from Great Britain. show work, please!!! What is 30y 15 if y is 7? (I NEED THIS ASAP)A: 225B: 195C: 52D: 36 4. Katelyn is struggling in school and fighting frequently with herparents. She is not sure about her future and what she wants to study incollege. With which of the following statements about Katelyn would ahumanistic psychologist most likely agree?(A) Katelyn will work to the best of her ability to get her life back onmalding animazom5W (3)track.(B) Katelyn has been shaped by her parents' dysfunctional relation-ship and will have a difficult time forming deep relationships in thefuture.dow abeced(C) Katelyn is overthinking her problems, which are minor, andher misperception of the scope of the problems is inflating theirimportance.(D) Katelyn has learned from her peers to treat her parents badly andto not put forth her best effort in school. Because this behavior isrewarded by her friends, it will continue in the future.51 Douragi2 (A)(E) Katelyn's problem is the result of changing hormones; oncethese level out, she will be able to concentrate on her goals andrelationships. The number of radioactive nuclei in a particular sample decreases to one-eighth of its original number in 9 days. what is the half-life of these nuclei? Which is a terminating decimal? Question 8-Evaluate the expression if g = 2, r = 3, and t = 11.g + 6t Refer to F .Identify a chord that is not a diameter. Part B. of Bul-go!-giWhich sentence from the text best develops the central idea of identified in part A?A. She was American, just as much as she was Korean, and even though her mother wouldnt have wanted her to do it, starting the food truck was Ji-Suks way of honoring her mother and showing that she valued what her mother had taught her.B. Even though shed made Ji-Suk take Korean lessons every Saturday morning followed by violin lessons in the afternoonand cooked kimchi and other Korean delicacies with her at least once a weekJi-Suks Mother had wanted her to succeed by American standards.C. If her own mother had still been alive, she would have been quite upset with Ji-Suk for that.D. Her mother had spent years. Learning to speak relatively good English, and shed been determined to make sure Ji-Suk graduated from respectable college and become a lawyer.To see part A : https://brainly.com/question/24809394?referrer=searchResults Many animals are thought to navigate using the position of the Sun. Explain why these animals need to have an internal 'clock' that they also know what time of the day it is.Pls answer, will give 30 points Identify a pattern in this list of numbers 3,4,6,9,13,18 Probability and statistics question any help is appreciated! Brianliest if answer I really need help

Write a coordinate proof of the Distance Formula in Space. Given: A has coordinates A(x₁, y₁, z₁) , and B has coordinates B(x₂, y₂, z₂) . Prove: A B = √(x₂-x₁)² + (y₂-y₁)² + (z₂ - z₁)²

Answers

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Write a coordinate proof of the Distance Formula in Space.

Given: A has coordinates A(x₁, y₁, z₁) , and B has coordinates B(x₂, y₂, z₂) .

Prove: A B = √(x₂-x₁)² + (y₂-y₁)² + (z₂ - z₁)²