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fgiga [73]
3 years ago
12

Order these numbers from least to greatest. 6.374, 6 4/9, 127/20, 6.39

Mathematics
1 answer:
In-s [12.5K]3 years ago
8 0
To compare, you have to make the fraction/mixed number into decimals
6&4/9=6.4444444444444
127/20=6.35
every decimal has a whole of 6, so you need to look at the tenth's place, 4 is obviously larger than 3, so 6&4/9 is the largest.
the other three numbers all have a 3 in its tenth's place, so look at the hundredth's place, 9 is larger than 7, and 7 is larger than 5
so from the least to the largest:
127/20, 6.375, 6.39. 6&4/9
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find the parametric equations for the line of intersection of the two planes z = x + y and 5x - y + 2z = 2. Use your equations t
Kaylis [27]

Answer:

You didn't give the points in which you want the parametric equations be filled, but I have obtained the parametric equations, and they are:

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

Step-by-step explanation:

If two planes intersect each other, the intersection will always be a line.

The vector equation for the line of intersection is given by

r = r_0 + tv

where r_0 is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = ax, y = by, and z = cz

where a, b and c are the coefficients from the vector equation

r = ai + bj + ck

To find the parametric equations for the line of intersection of the planes.

x + y - z = 0

5x - y + 2z = 2

We need to find the vector equation of the line of intersection. In order to get it, we’ll need to first find v, the cross product of the normal vectors of the given planes.

The normal vectors for the planes are:

For the plane x + y - z = 0, the normal vector is a⟨1, 1, -1⟩

For the plane 5x - y + 2z = 2, the normal vector is b⟨5, -1, 2⟩

The cross product of the normal vectors is

v = a × b =

|i j k|

|1 1 -1|

|5 -1 2|

= i(2 - 1) - j(2 + 5) + k(-1 - 5)

= i - 7j - 6k

v = ⟨1, -7, -6⟩

We also need a point on the line of intersection. To get it, we’ll use the equations of the given planes as a system of linear equations. If we set z = 0 in both equations, we get

x + y = 0

5x - y = 2

Adding these equations

5x + x + y - y = 2 + 0

6x = 2

x = 1/3

Substituting x = 1/3 back into

x + y = 0

y = -1/3

Putting these values together, the point on the line of intersection is

(1/3, -1/3, 0)

r_0= (1/3) i - (1/3) j + 0 k

r_0​​ = ⟨1/3, -1/3, 0⟩

Now we’ll plug v and r_0​​ into the vector equation.

r = r_0​​ + tv

r = (1/3)i - (1/3)j + 0k + t(i - 7j - 6k)

= (1/3 + t) i - (1/3 + 7t) j - 6t k

With the vector equation for the line of intersection in hand, we can find the parametric equations for the same line. Matching up r = ai + bj + ck with our vector equation,

r = (1/3 + t) i + (-1/3 - 7t) j + (-6t) k

a = (1/3 + t)

b = (-1/3 - 7t)

c = -6t

Therefore, the parametric equations for the line of intersection are

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

3 0
3 years ago
How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9?
Wittaler [7]

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

5 0
3 years ago
Mr. Abyad used 3 2/3 square feet of material for his first bulletin board, 6 3/4 square feet of material for his second bulletin
mylen [45]
I hope this helps you

6 0
3 years ago
Read 2 more answers
I NEED HELP??? with this math problem?
7nadin3 [17]

Answer:


Step-by-step explanation:

35x + 30 = 22x + 69

<u>-22x  -30    -22x  -30</u>

13x = 39

x=3

6 0
3 years ago
Please can I check with you the answer for nbr 12?<br> Is it correct?
Crank

Answer:

B and C

Step-by-step explanation:

  • B = 2,4,6
  • =3,6
  • C= 2,4,6,8,10,12
  • = 6,12
8 0
2 years ago
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