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
Ainat [17]
2 years ago
8

Consider the line which passes through the point P(−1,-3,5), and which is parallel to the line x=1+7t, y=2+2t, z=3+4t Find the p

oint of intersection of this new line with each of the coordinate planes:
Mathematics
1 answer:
bija089 [108]2 years ago
8 0

The given line is parameterized by

x(t) = 1 + 7t

y(t) = 2 + 2t

z(t) = 3 + 4t

and points in the same direction as the vector

d/dt (x(t), y(t), z(t)) = (7, 2, 4)

So, the line we want has parameteric equations

x(t) = -1 + 7t

y(t) = -3 + 2t

z(t) = 5 + 4t

Solve for t when one of x, y, or z is equal to 0 - this will tell you for which value of t the line cross a given plane. Then determine the other coordinates of these intersections.

• x = 0, which corresponds to the y-z plane:

0 = -1 + 7t   ⇒   7t = 1   ⇒   t = 1/7

y(1/7) = -3 + 2/7 = -19/7

z(1/7) = 5 + 4/7 = 39/7

⇒   intersection = (0, -19/7, 39/7)

• y = 0 (x-z plane):

0 = -3 + 2t   ⇒   2t = 3   ⇒   t = 3/2

x(3/2) = -1 + 21/2 = 19/2

z(3/2) = 5 + 12/2 = 11

⇒   intersection = (19/2, 0, 11)

• z = 0 (x-y plane):

0 = 5 + 4t   ⇒   4t = -5   ⇒   t = -5/4

x(-5/4) = -1 - 35/4 = -39/4

y(-5/4) = -3 - 10/4 = -11/2

⇒   intersection = (-39/4, -11/2, 0)

You might be interested in
Each face of a number cube is a square with a side length of 16 millimeters. What is the total area of all of the faces of the n
luda_lava [24]
I think that is a total area
5 0
2 years ago
What is the absolute value of the following complex number?<br> -4 + 4
snow_lady [41]

Answer:

Itz 0 if I am not wrong

hope it helps

3 0
3 years ago
Read 2 more answers
Slove the inequality 8(1/2x-1/4)&gt;12-2x
HACTEHA [7]

8(1/2x-1/4)>12-2x

4x-2>12-2x

6x>14

x>7/3

Hope this helps! ;)

6 0
4 years ago
The fare for an Uber is $5 per trip plus $0.50 per mile. The fare for the trip from the airport to the school center was $11.50.
Vinvika [58]

Answer:

13 miles

Step-by-step explanation:

The fare for the Uber

Cost= 5+ .5 m  

where m is the number of miles

We spent 11.50

11.50 = 5 + .5 m

Subtract 5 from each side

11.5 -5 = 5+.5m -5

6.50 = .5 m

Divide by .5 on each side

6.5/.5 = .5m/.5

13 = m

We went 13 miles

6 0
3 years ago
Help ASAP plssssssssss
mr_godi [17]

Answer:

Length of three dimensions of the cube is

<u>6</u>cm.

What is the area of the base of a cube of sides 2.5m?

<u>37.5m²</u>

5 0
3 years ago
Other questions:
  • For accounting purposes, the value of assets (land, buildings, equipment) in a business depreciates at a set rate per year. The
    5·2 answers
  • 10 POINTS<br> Find the surface area of the regular pyramid. Round to the nearest tenth if necessary.
    12·2 answers
  • What is the measure of angle A to the nearest degree?
    11·1 answer
  • Maggie bought a total of 30 pounds of three different types of produce to feed her hungry hippopotamus.
    9·1 answer
  • Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
    8·1 answer
  • 4) Jacqueline, Hanry, and Stanley bought a pizza pie to share for dinner. Harry ate
    13·1 answer
  • Please help photo attached
    13·1 answer
  • A tree grows at a rate of 4 feet per year. Which graph has a slope that best represents this rate?
    7·1 answer
  • What is a country that starts with an V
    14·2 answers
  • Please help. No links or else I will report you.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!