Find the distance from the point (0, 4, 3) to the plane 5x +1y +2z

Answers

Answer 1

Answer:

distance =

[tex] \sqrt{ \frac{10}{3} } [/tex]

Step-by-step explanation:

Without going through and deriving this (my blackboard doesn't have space and a textbook, teacher, or online tutorial is probably better for that), the equation for the distance from some point on the plane to some point in space is as follows:

[tex]distance = \frac{ax + by + cz - d }{ \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } } [/tex]

•Note that the d in the equation should actually be D but Brainly doesn't allow me to do uppercase letters on mobile it seems... Anyway, d in the equation represents the value which the equation of the plane is equal to. You only gave the plane equation so I assumed d=0 in my calculations.

•x, y, and z all come from the point which you want to find the distance to. So (x,y,z)=(0,4,3) here.

•a, b, and c all come from the components of the vector normal to the surface. For planes, it simply somes to be the coefficients in front of each part. So (a,b,c)=(5,1,2) here.

With that you just need to plug the information in and simplify for your answer. My work is in the attachment, comment with questions or if anything seems off.

Find The Distance From The Point (0, 4, 3) To The Plane 5x +1y +2z

Related Questions

Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.

Answers

Answer:

well the length on both increases by x3 and the height increases by 2

Step-by-step explanation:

Which planet is an inner planet, and which one is an outer planet? Explain your answer.

Answers

The correct answers are Planet A 16 hours - Inner planet and planet B 1,408 hours - Outer planet.

What is a planet?

Large, circular celestial objects that are neither stars nor their remnants are known as planets. The inner planets are the ones that are much closer to the sun, thus they have much smaller orbits around it and it takes them much less time to circle around it. Also, these planets are much smaller, which enables them to spin around their axis much quicker too, so one day passes much quicker.

The outer planets are the total opposite. They are much further from the sun, so for them to be able to make a single circle around the sun it takes much more time, and also because they are much bigger, it takes them much more time to spin around their own axis, thus making one day much longer than the days of the inner planets.

The complete question is given below as:-

Which planet is an inner planet, and which one is an outer planet? Explain your answer. Planet A 16 hours planet B 1,408 hours

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A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: ; directrix: y = focus: (8,0); directrix: x = –8 focus: ; directrix: x =

Answers

Answer:

the coordinate of the focus is: (0, 1/2)

the equation of the directrix is: y=-1/2

Step-by-step explanation: The standard equation for a parabola that opens upward- parallel to the y-axis, is: x2=4ay. Meaning, a = distance from the vertex to focus and the vertex is at origin: (0,0).

4a is equal to 2

a is equal to 2/4

a is equal to 1/2 or 0.5

The parabola has

focus: (0,1/2)

directix: y=-1/2

What is the formula for focus and directrix of a parabola?

If the parabola is given by

y=a(x-h)²+k

then the focus of the parabola is given by

(h,k+1/4a)

and the directrix of the parabola is given by

y=k-a

How to solve the problem?

Given parabola is x²=2y

So, the parabola is y=(1/2)x², when compared with y=a(x-h)²+k  we have

a=1/2, h=0 and k=0

So, the focus of the parabola is

[tex](0,\frac{1}{4\frac{1}{2}})= (0,\frac{1}{2})[/tex]

and, the directrix of the parabola is

y= -1/2.

Hence, the parabola has

focus: (0,1/2)

directix: y=-1/2

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A train leaves Philadelphia at 3:00 PM. A second train leaves the same city in the same direction at 9:00 PM. The second train travels 120mph faster than the first. If the second train overtakes the first at 11:00 PM, what is the speed of each of the two trains?

Answers

Answer:

Step-by-step explanation:

2nd train DATA:

time = 2 hrs ; rate = x + 120 mph ; distance = 2(x+120) = 2x+240 miles

------

1st train DATA:

time = 8 hrs ; rate ; x mph ; distance = 8x miles

------------------

Equation:

distance = distance

8x = 2x+240

6x = 240

x = 40 mph (speed of the 1st train)

x+120 = 160 mph (speed of the 2nd train)

my regards #3Ss

Write an equation of the line passing through the points (3,7) and (-1,-13)

Answers

Answer:

Step-by-step explanation:

(-13 - 7)/(-1 + 3) = -20/2 = -10

y - 7 = -10(x - 3)

y - 7 = -10x + 30

y =  - 10x + 37

Write 18% as a fraction

Answers

Hi there!

~

[tex]18[/tex]% [tex]= \frac{9}{50}[/tex]

Answer9/50:

Step-by-step explanation:

18/100

18÷2

100÷2

9/50

An apartment building has 11 floors in it. Each floor has 9 rooms on it. If each room has two people living there, how many people live in this apartment building?**

Answers

Answer: 198 total people

Step-by-step explanation:

so there are 11 floors and each obtain 9 rooms so if there are two people in each of the 9 rooms there will 18 total people in one floor and since there are 11 floors multiply it by 18 to find out how many people live in the apartment.

11 * 18 = 198

A toy company uses the linear model y=-2x+380 to predict the decline in sales of a toy after it has been on the market more than one year. If x is the number of months after the first year and y is the number of toys sold in hundreds during that month how many toys will be sold 11 months after the first year

Answers

Answer:

358 toys sold 11 months after the first year.

Step-by-step explanation:

y = - 2x + 380

x is number of months after release in this case x = 11

y is number of toy sold in the hundreds.

y = - 2 ( 11 ) + 380

y = - 22 + 380

y = 358

Number of toys sold 11 months after the first year =  358

What is linear equation?

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Given,

Linear equation

y = - 2x + 380

x is number of months after release

y is number of toy sold in the hundreds.

No. of months, x = 11

Putting value of x in above equation

y = - 2 ( 11 ) + 380

y = - 22 + 380

y = 358

Hence, 358 toys sold 11 months after the first year.

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Business: Discount Pricing A store sells refurbished
iPhones that cost 12% less than the original price. If the new price of a refurbished iPhone is $572, what was the original price? How much is saved by purchasing the refurbished

Answers

original price 640.64
saved: 68.64

The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile.

What is the percentage?

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

Let's say the original price of the mobile is x.

12% of x is 0.12x

The cost of refurbished mobile will be as x - 0.12x = 0.88x

0.88x = 572

x = $650

The amount saved = $650 - $572 = $78

Hence "The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile".

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The mean absolute deviation is best described as:



The value obtained when averaging the distances between each data point in the data set and the mean.


The value obtained when you add all the values in the data set and divide by the number of values.


The difference between the means of two similar data sets.


An approximation of the center of a data set.

Answers

Answer: It’s the second one

Step-by-step explanation:

Find height when diameter is 1.4m and its hold 770l water​

Answers

Answer:

≈ 0,5 m

≈ 50 cm

Step-by-step explanation:

d = 2r => r = d/2 = 1,4m/2 = 0,7 m

V = πr²·h => h = V/πr²

770 l = 0,77 m³

h = 0,77m³/3.14×0,49m²

= 0,77m³/1,5386m²

= 0,5004 m

≈ 0,5 m

≈ 50 cm

Simplify the expression: 42x3y6 6xy6 A) 7x2y12 B) 7x2y C) 36x2y12 D) 7x2

Answers

Answer:

D

Step-by-step explanation:

So first you simplify

Step 1: (2•3•7x3y6) (2•3xy6)

Step 2: you divide x3 by x1 = x (3-1) = x2

step 3: You cancel out y6 as it appears on both sides of the fraction line.

step 4: cancel out 2 as it appears on both sides.

step 5: cancel out 3 as it appears on both sides.

step 6: final result 7x2

what is the answer to 1.58x1.78=

Answers

The answer is 1.58x1.78= 2.8124

Define intersecting lines

Answers

Answer:

lines that meet at a point

How can you tell that 7. 630 and 7. 63 are equivalent decimals?

Answers

because if you add a zero onto something after the decimal point it doesn't increase or decrease the value of the number.

7.630 is literally just 7.63.

but if it was 76.3 and 760.3 it would be different.

An elm tree is 3 times as tall as an apple tree. The apple tree is 10 feet tall. How tall is the elm tree?

Answers

Answer:

LET ME GUESS hmmmm... OH WAIT 30

Step-by-step explanation:

Answer:

30 ft

Step-by-step explanation:

The elm tree is 3 times as tall as the apple tree.

The elm tree is 3 times as tall as 10 ft.

3 * 10 ft = 30 ft

PLEASE HELP QUICK what algebraic expression represents GK

Answers

Answer:

answer is 6x+4

mark it as branliest.

Answer:

GK = 6x + 4

Step-by-step explanation:

3x + 5 - x + 4x - 1 - x + x

3x -x + 4x - x + x + 5 -1

6x + 4

Suppose R is the solid bounded by the plane z=5x, the surface z=x2, and the planes y=0 and y=3. Write an iterated integral in the form below to find the volume of the solid R.

Answers

I have attached the complete question.

Answer:

See 2nd attachment

Step-by-step explanation:

We are told that R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y = 3.

Thus, the region in the xz plane would be defined as;

0 ≤ x ≤ 3 and x² ≤ z ≤ 5x

For the iterated integral for the volume of the solid R, see 2nd attachment.


You want to share 1000 dollars between you and 5 friends,

Can you share the money evenly

What is the maximum amount that can be shared evenly

What is then the leftover as a fraction

Answers

Answer:

the answer is 200

Step-by-step explanation:it's because

you have to divide 1000 in to 5 and 1000 divided by 5 is 200

What is the image of (-5, -8) after a reflection over the y-axis?

Answers

Answer:

[tex](5,-8)[/tex]

Step-by-step explanation:

The rule for a reflection over the y-axis is

[tex](x,y) -> (-x,y)[/tex]

In this situation, we have to change the sign of x.

[tex](-5,-8) -> (5,-8)[/tex]

Rewrite as a logarithmic equation.
*=8

Answers

Answer:

yes in the steps

Step-by-step explanation:

conclusive

If Mikayla rides for 2 hours on a bicycle, what is her rate if she rides for 22 miles?

Answers

We will need to know the mph, please feel free to comment when u provide the full i fob

Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer.

Point (9,−11); Slope=−8

Answers

Answer:

Step-by-step explanation:

y + 11 = -8(x - 9)

y + 11 = -8x + 72

y = -8x + 61

The equation of the line in slope-intercept form having the given point and slope is: y = -8x + 61.

How to Find the Equation of a Line in Slope-intercept Form?

Slope-intercept formis expressed as y = mx + b.

Given the following:

A point = (9, -11) = (a, b)

Slope = -8 = m

Substitute m = -8 and (a, b) = (9, - 11) into y - b = m(x - a)

y - (-11) = -8(x - 9)

Rewrite in slope-intercept form

y + 11 = -8x + 72

y = -8x + 72 - 11

y = -8x + 61

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42 is 64% of what number

Answers

Answer: x = 65.63
Explanation:
We have, 64% × x = 42 or, 64/100 × x = 42
Multiplying both sides by 100 and dividing both sides by 64, we have x = 42 × 100 64
x = 65.63

Answer:

the answer is 65.625, 42 is 64% of 65.625

Find the nth term of this quadratic sequence 7,16,25,34,43

Answers

Answer:

52

Step-by-step explanation:

everytime it adds by 9:

7+9=16

16+9=25

25+9=34

34+9=43

43+9=52


Find the distance between points P and Q.

Answers

Answer:

4;3 might be the answer

I believe it is -3/4

(3 + 5i) + (11 -7i) Write answer in standard form a +bi

Answers

Answer:

14-2i

Step-by-step explanation:

[tex]\left(3+5i\right)+\left(11-7i\right)\\\\Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number\\\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3+11\right)+\left(5-7\right)i\\3+11=14\\5-7=-2\\\\=14-2i[/tex]

What percent of 150 is 900

Answers

Answer:

600 %

Step-by-step explanation:

x · 150 ÷ 100 = 900

150x = 90000

x = 600

Evaluate the given expression if x= -3 and y=6.

x+3y / 6+3y

Answers

Answer:

5/8

Step-by-step explanation:

The given expression is [tex]\dfrac{x+3y}{6+3y}[/tex]

We need to find of above expression when x = -3 and y = 6

Put x = -3 and y = 6 in given expression such that,

[tex]\dfrac{x+3y}{6+3y}=\dfrac{(-3)+3(6)}{6+3(6)}\\\\=\dfrac{-3+18}{6+18}\\\\=\dfrac{15}{24}\\\\=\dfrac{5}{8}[/tex]

So, the value of given expression is 5/8.

2 ( x - 6 ) = 3 ( x + 9 )

Answers

Steps to solve:

2(x - 6) = 3(x + 9)

~Distribute both sides

2x - 12 = 3x + 27

~Add 12 to both sides

2x = 3x + 39

~Subtract 3x to both sides

-x = 39

~Divide both sides by -1

x = -39

Best of Luck!

Answer:

2×-12=3×+27

2×-3×=27+12

-×=39

Step-by-step explanation:

Grouping like terms

then simplify to get x

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