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il63 [147K]
2 years ago
6

Find a set of scalar parametric equations for the line formed by the two intersecting planes. 3x+3y+2z+2=0 2x−3y+2z−2=0

Mathematics
1 answer:
vivado [14]2 years ago
8 0

The normal vectors to the two planes are (3, 3, 2) and (2, -3, 2). The cross product of these will be the direction vector of the line of intersection, (12, -2, -15).

Using x=0, we can find a point on this line by solving the simultaneous equations that remain:

... 3y +2z = -2

... -3y +2z = 2

Adding these, we get

... 4z = 0

... z = 0

so the point we're looking for is (x, y, z) = (0, -2/3, 0). This gives rise to the parametric equations ...

  • x = 12t
  • y = -2/3 -2t
  • z = -15t

By letting t=2/3, we can find a point on the line that has integer coefficients. That will be (x, y, z) = (8, -2, -10).

Then our parametric equations can be written as

  • x = 8 +12t
  • y = -2 -2t
  • z = -10 -15t
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A . r^(3-1) = 18
a . r^2 = 18...... (i)

a . r^(6-1) = 486
a . r^5 = 486 ...... (ii)

dengan membuat perbandingan dari kedua persamaan diperoleh:
r^2/r^5 = 18/486
1/r^3 = 1/27 
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dari persamaan <span>a . r^2 = 18...... (i)
                          a . 3^2 = 18
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3 0
1 year ago
Josiah owns a food truck that sells tacos and burritos. He only has
bogdanovich [222]

Answer:

Therefore Josiah must sell 68 or 69 or 70 tacos in order to meet the requirement.

Step-by-step explanation:

Given , Josiah owns a food truck that sells tacos and burritos.

He sells each burritos for $7.50. If 79 burritos were sold.

Then the price of 79 burritos is $(7.50×79) =$592.50

Let x tacos were sold.

He sells each tacos for $5.

Then the price of x tacos is = $(x × 5)=$5x

Also given that Josiah must sell a minimum of $930 worth of tacos and burritos.

Therefore,

5x+592.50≥ 930

⇔5x≥930-592.50

⇔5x≥337.5

⇔x≥67.5

But he only has enough supplies to make 149 tacos or burrito.

He already sold 79 burrito.

So, remain space for tacos is = (149-79) = 70

So,67.5≤x≤70

∴x = 68 or 69 or 70

Therefore Josiah must sell 68 or 69 or 70 tacos in order to meet the requirement.

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1 year ago
Samantha is wall papering her bedroom and wants to make sure that she bought enough wall paper. Each wall in her room measures 1
Gala2k [10]

Answer:

17.60

Step-by-step explanation:

Look at the room carefully, the length of the room is 11 feet

And the height = 10 feet

The area of the 4 walls of the room = 4( 11×10) = 440 sq ft

Area covered by each roll = 25 sq ft

= 440/25 = 17.60 rolls

Therefore we require 17.60 rolls to cover a rectangular room on all four sides.

7 0
2 years ago
Explain how one whole, one tenth, and one hundredth are related
Oduvanchick [21]
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GRAHAM CORPORATION
astra-53 [7]

Answer:

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Step-by-step explanation:

Given that the shares cost $d

n shares will be =$dn

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Her net proceeds algebraically will be

Net proceed= s-nd-11-0.02nd

collect like terms

Net proceed= s-(nd-0.02nd)-11

Net proceed= s-0.98nd-11

5 0
1 year ago
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