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il63 [147K]
3 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]3 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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jasenka [17]

Answer:

10+20=30

10 is what percent of 30?

10 is 1/3 of 30

Step-by-step explanation:

10 is 33.33% of 30

so 33% of the shirts sold were blue

6 0
3 years ago
Cookies are sold singly or in packages of 3 or 9. With this packaging, how many ways can you buy 18 cookies?
tresset_1 [31]
I believe 5 different ways. The options being two packs of 9-one pack of 9 and 3 packs of 3- 1 pack of 9, 2 packs of 3 and 3 singles- one pack of 9, one pack of 3, and 6 singles- and then one pack of 9 and 9 singles.
Hope this helped!

8 0
3 years ago
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as
Lesechka [4]

The correct question is;

You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth. Find the probability of spinning an odd number, flipping heads, then spinning another odd number? Write your answer as a fraction in simplest form.

Answer:

If the spinner has an even number of spaces, the probability of spinning an odd number, flipping heads, then spinning a yellow is = 1/8

Whereas, if the spinner has an odd number of spaces, more information is needed

Step-by-step explanation:

The answer will depend on whether the spinner has an odd or even number of spaces.

Now, if we suppose that the spinner has an even amount of numbers on it, there will be an equal number of odd and even numbers.

Thus the probability of spinning an odd number is ½.

Also, the probability of flipping heads on a coin is ½.

Thus, the probability of spinning an odd number, flipping heads, then spinning another odd number is;

= ½ × ½ × ½ = ⅛

Similarly,

If the spinner has an odd amount of numbers on it, the probability of spinning an odd number will vary. For instance, if there are 5 spaces on the spinner, the probability of spinning an odd number will be

3

However, if there are 9 spaces, the probability will be 5/9

So,we can conclude that;

If the spinner has an even number of spaces, the probability of spinning an odd number, flipping heads, then spinning a yellow is = 1/8

Whereas, if the spinner has an odd number of spaces, more information is needed.

6 0
3 years ago
Need help with this problem​
Arisa [49]

Answer:

1/4

Step-by-step explanation:

take the negative reciprocal when finding the slope of a perpendicular line.

So, -4 can be written as -4/1

flip it to make -1/4

and remove the negative to make 1/4

6 0
3 years ago
6 points and brainliest answer
kati45 [8]
Well, the angle looks like it is an obtuse angle, right? And we know that obtuse angles are greater than 90 degrees, so wouldn't the answer be A. 115 degree?
I think the answer is 115 degrees. Hope this helps!
4 0
3 years ago
Read 2 more answers
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