My Notes Ask Your Teacher (a) Find parametric equations for the line through (1, 3, 4) that is perpendicular to the plane x-y + 2z 4, (Use the parameter t.) )13-12-4 (b) In what points does this line intersect the coordinate planes? xy-plane (x, y, z)-((-1,5,0)|x ) yz-plane (x, y, z)- xz-plane x, 9+ Need Help? Read it Talk to a Tutor Submit Answer Save Progress Practice Another Version

Answers

Answer 1

Parametric equations for the line through (1, 3, 4) that is perpendicular to the plane x-y+2z=4 are:

x = 1 + 2t

y = 3 - t

z = t

We know that the direction vector of the line should be perpendicular to the normal vector of the plane. The normal vector of the plane x-y+2z=4 is <1, -1, 2>. Thus, the direction vector of our line should be parallel to the vector <1, -1, 2>.

Let the line pass through the point (1, 3, 4) and have the direction vector <1, -1, 2>. We can write the parametric equations of the line as:

x = 1 + at

y = 3 - bt

z = 4 + c*t

where (a, b, c) is the direction vector of the line. Since the line is perpendicular to the plane, we can set up the following equation:

1a - 1b + 2*c = 0

which gives us a = 2, b = -1, and c = 1.

Substituting these values in the parametric equations, we get:

x = 1 + 2t

y = 3 - t

z = t

To find the intersection of the line with the xy-plane, we set z=0 in the parametric equations, which gives us x=1+2t and y=3-t. Solving for t, we get (1/2, 5/2, 0). Therefore, the line intersects the xy-plane at the point (1/2, 5/2, 0).

Similarly, we can find the intersection points with the yz-plane and xz-plane by setting x=0 and y=0 in the parametric equations, respectively. We get the intersection points as (-1, 5, 0) and (9, 0, 3), respectively.

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Related Questions

I need help with this question!

Answers

Answer:

sorry but don't know this answer

A spherical balloon has a diameter of 4 feet. Approximate how many cubic feet of air this balloon holds. Use 3.14 as an approximation for pie, and give a numerical answer.

Answers

Answer:

3.764

Step-by-step explanation:

just try matgs is a tough de partoe

EDGE20 ASSIGNMENT, WILL MARK BRAINLIEST FOR WHOLE ASSIGNMENT Quadratic in Form Polynomials
Assignment
Active
Practice writing as a quadratic.
ASSIGNMENT

Answers

Answer:

[tex] \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]

Step-by-step explanation:

[tex] {(3x + 2)}^{2} + 7 {(3x + 2)} - 8 = 0 \\ \\ plug \: (3x + 2 )= y \\ \\ so \: above \: quadratic \: equation \: \\transforms \: to \\ \\ \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]

In comparing the two written forms of a sequence, which is easier to find a50, the explicit form or the recursive form?

Answers

Answer:

Explicit

Step-by-step explanation:

Given

[tex]Term: a_{50[/tex]

Required

Explicit or Recursive; which is easier

The explicit form is easier.

Take for instance, the explicit form of the sequence is:

[tex]a_n = 2n + 1[/tex]

And the recursive form is:

[tex]a_n = a_{n-1} + 2[/tex]

To find [tex]a_{50}[/tex] in [tex]a_n = 2n + 1[/tex]

You simply substitute 50 for n and then solve for [tex]a_n[/tex]

Which gives:

[tex]a_{50} = 2*50 + 1 = 101[/tex]

The case is different in: [tex]a_n = a_{n-1} + 2[/tex]

First, you substitute 50 for n

[tex]a_{50} = a_{50-1} + 2[/tex]

[tex]a_{50} = a_{49} + 2[/tex]

Next, you need to calculate a49.

This action continues until you get to a1

Then you evaluate the corresponding expressions from a1 to a49 before you get a50.

Hence, the explicit form is easier.

One half of a watermelon is shared among 6 people what is the fraction of how much each will get?

Answers

Answer:

1/12

Step-by-step explanation:

please help me I will give brainlist

Answers

Answer:

3 + 2n

Step-by-step explanation:

2 + 1 = 3.

2n cannot be added into this because it has a letter in front of it. Therefore, it stays on its own.

2n + 3

1 and 3 are like terms, and because there are no more variables, the 2n will stay alone :)

hi can u please help solve this. something with conjugnates.

Answers

Answer:

Use mathcway its 2 ez with that page trust me bro

Step-by-step explanation:

No cap

5 10 okey espero te sirva

a worded math problem that = 5

Answers

Answer:

Seven take away two is equals to five

Step-by-step explanation:

Because,

Seven take away two is equals to five

is the same to

7 - 2 = 5

6/3 + -1/6 reduce this equation to the simplest form

Answers

Answer:

12/6-1/6=11/6 simplified to 1 5/6

Step-by-step explanation:

to make this easier make sure all fractions have the same denominator 6/3x2/2=12/6 since they now have the same denominator add 12/6+-1/6=11/6

adding a negative(6/3+-1/6) is the same as subtracting a positive(6/3-1/6)

Answer:

1 5/6

hope this helps :)........

Find (-5x + 6) - (-2x - 7)

Answers

The answer is: -3x +13

the square of a number is 16 do you know the number

Answers

Answer:

4

Step-by-step explanation:

4 squared, which is the same thing as 4 times 4, is 16.

[tex]4^2=16[/tex]  or [tex]4 * 4 = 16[/tex]

you can check your answer by finding the square root of 16.

[tex]\sqrt{16}=4[/tex]

i hope this helps! have a nice day <3

a) Andrés construye cajas de diferente base. Utiliza poligonos regulares, la longitud de sus lados es la misma Adomna
1. Analiza la siguiente situación y realiza lo que se te pide:
el contorno de las tapas con liston dorado.
• Completa la siguiente tabla que elaboró para su presupuesto de materiales:
- Polígono
5
8
(lados)
Perimetro
24
30
36
(cm)
4
50
¿Cuántos centimetros mide cada lado de la tapa?
* Como encontraste el valor anterior?
¿Qué relación tiene el número de lados con el perimetro?
¿Cuál seria el perimetro de una figura de tres lados? amigos me pueden ayudar es importante ​

Answers

Respuesta:

la tapa mide 6 centimetros,sobre la tabla aumenta de 6 en 6

Explicación paso a paso:vas dividir 24 que es el valor de el perimetro entre 4 porque es la cantidad de lados al dividirlo te va a dar 6 que indica que aumenta de 6 en 6 tambien en la tabla cuando son 4 lados son 24 de perimetro y en el siguiente viene que 5 son 30 :)

ojala te ayude friend :-}

Can someone solve these for me I have no idea what to do and it has to be turns in within an hour

Answers

Answer:

Step-by-step explanation:

Subtract second equation from first equation to eliminate x

2x+6y-2x+10y=17-9

16y=8

y=1/2, use either original equation to solve for x

2x+6y=17 becomes

2x+6(1/2)=17

2x+3=17

2x=14

x=7 so the solution is the point (7, 1/2)

We can multiply the first by -2 and add it to second equation to eliminate x.

-2(3x-4y)+6x+3y=-2(-10)-42

-6x+8y+6x+3y=20-42

11y=-22

y=-2 using 3x-4y=-10 becomes

3x-4(-2)=-10

3x+8=-10

3x=-18

x=-6 so the solution is the point (-6,-2)

So you should be able to see how to solve the other two.

Answer:

Question 1: x = 7, y = [tex]\frac{1}{2}[/tex]

Question 2: x = -6, y = -2

Question 3: x = -1, y = 9

Question 4: There is no solution.

what is
(7x3)-2(5+1)+4

Answers

Answer:

13

Step-by-step explanation:

(7x3)-2(5+1)+4=13

An ordinary dice is rolled. What is the probability that the number
of dots on the upper face is -
(a) 3
(c) an even no
(b) less than 3
(d) 7​

Answers

Answer:

A) 1/6

B) 1/3

C)1/2

D) 1/6

Answer:

1/6 , 1/3 , 1/2 , 0

Step by Step Explanation:

An ordinary die has numbers from 1 to 6

Number of dots on the face = number that face represent

Dots on face can be 1 , 2 , 3 , 4 , 5 , 6

1. Number of 3 Dots

Probaility = 1/6

2. Number of Dots less than 3 = 1 or 2 Dots

Probability = 2/6 = 1/3

3 . An even number = 2 , 4 , 6

Probability = 3/6 = 1/2

4 7 Dots not possible Hence

Probability = 0

Learn more:

A die is rolled. What is the probability that the number appearing on ...

brainly.in/question/4334466

An unbiased die is thrown .what is the probability of getting a ...

brainly.in/question/7707663

circumference and area of radius 42

Answers

Answer:

Area = 5542.488 unit^2

Circumference= 263.9 units

Step-by-step explanation:=

Given data

Radius= 42 units

Circumference= 2πr

C= 2*3.142*42

C=263.9 units

Area= πr^2

A= 3.142* 42^2

A= 3.142* 1764

A= 5542.488 unit^2

Write your answer in scientific notation.
(5.1x10^7)+(1.3 x 10^6)

Answers

the answer is 5.23*10^7

Hey please help me please

Answers

Answer:

c

Step-by-step explanation:

360 is a full rotation and 90 is a quarter

Answer: C

Step-by-step explanation:

A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost, in dollars, for a passholder to watch n movies.
Is function C a piecewise function? Explain your reasoning.

Answers

probably it's 8 or 4. and as $8 is the initial fee, that sounds like the starting value. :-)

the line equation you need is the slope intercept form y = mx + b where m = gradient and b = y intercept.

in this case, y = 4x + 8 where x = number of movies seen, and y = total cost in $

for this line m = 4 and b = 8. hence, indeed, the y intercept is 8

Mark as brainlist

Answer:

Step-by-step explanation:

C is a piecewise function because it represents more than one type of deal.

¿ Cómo surge la estadística?

Answers

Answer:

surgiendo dah

jjhhjjklnt7ikkkkvvh

Answer:

Los métodos matemáticos de la estadística surgieron de la teoría de probabilidades, la cual tiene sus raíces en la correspondencia entre Pierre de Fermat y Blaise Pascal (1654). ... En su libro, Bernoulli introdujo la idea de representar certeza completa como el número 1 y la probabilidad como un número entre cero y uno.

What is the ratio of the length of the rectangle to its width. 24 and 20

Answers

6:5 is the ratio
Hope this helps!

answer Pls Gyys Options i ​

Answers

Answer:

Step-by-step explanation:

1301/100 is the correct answer

How many solutions does this is have
6(x - 6)+ 26=6x - 10
Show all work please!

Answers

Answer:

All numbers are solutions. You can try this yourself by inserting numbers in.

Step-by-step explanation:

Find the slope of the line represented by the table of values.
A)
12
5
B)
D)

Answers

Answer:

B 4456448444424346464646464664646464

hey can u answer my math question look atbthe picture to see
the pic.​

Answers

Answer:

4 3/4 yards

Step-by-step explanation:

5 1/4 + 2 1/2 = 7 3/4

(1/2 is equal to 2/4)

12 1/2 - 7 3/4 = 4 3/4

Hope this helps, mark me brainliest if it does! :)

Answer:

[tex]4\frac{3}{4} [/tex]

Jotted Solution:

Could you help me please ?

Answers

Answer:

she messed up on the part where u need to cube root the solution she should of gotten 6 from the 4.

5 consecutive odd number between 40 and 60​

Answers

Answer:

47 49 51 53 55

Step-by-step explanation:

Consecutive: following one another in uninterrupted succession or order; successive: six consecutive numbers, such as 5, 6, 7, 8, 9, 10. marked by logical sequence. Grammar. expressing consequence or result: a consecutive clause.

Odd number between 40 and 60​: 41, 43, 45, 47, 49, 51, 53, 55, 57, 59

Answer:

The answer is 41, 43, 47, 49 and 51

What are the answers
2x = 10; x=?

-3x = 21;x=?

1/3x=6; x=?

-1/2x = -7;x?

Answers

Answer:

1) 5 2)7 3)18 4) 14

Step-by-step explanation:

Wallace has 1/2 gallon of milk. He wants to pour it into 4 smaller containers putting the same amount in each container

Answers

Answer: c. 1/2 /4

Step-by-step explanation:

There is a 1/2 gallon of milk.

This 1/2 gallon is pour in equal amounts into 4 small containers which means the 1/2 gallon was divided into 4 places.

Formula is therefore:

= 1/2 ÷ 4

= 1/2 /4

When solved you will get a result of:

= 1/8 gallons

Discussion Topic You have used the Distributive Property to transform numerical expressions such as (5)(3) + (2)(3) to (5 + 2)(3). How would you transform 5x + 2x into a single term? Substitute five different values into the expressions 5x + 2x and 7x - 1. What do you notice about the values of the expressions? Is there any value that would make the two expressions equal? Why or why not?

Answers

Answer:

b

Step-by-step explanation:

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