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
belka [17]
3 years ago
7

"Parameterize the plane through the point (−1,−3,1) with the normal vector ⟨−4,4,3⟩

Mathematics
1 answer:
Makovka662 [10]3 years ago
3 0
The equation of the required plane can be obtained thus:
-4(x + 1) + 4(y + 3) + 3(z - 1) = 0
-4x - 4 + 4y + 12 + 3z - 3 = 0
4x - 4y - 3z = 5

Let x = 1, y = 2, then 4(1) - 4(2) - 3z = 5
z = (4 - 8 - 5)/3 = -9/3 = -3
Thus, point (1, 2, -3) is a point on the plane.

Let a = (a1, a2, a3) and b = (b1, b2, b3) be vectors parallel to the plane.
Then, -4a1 + 4a2 + 3a3 = 0 and -4b1 + 4b2 + 3b3 = 0
Let a1 = 2, a2 = -1, then a3 = (4(2) - 4(-1))/3 = (8 + 4)/3 = 12/3 = 4 and let b1 = -1 and b2 = 2, then b3 = (4(-1) - 4(2))/3 = (-4 - 8)/3 = -12/3 = -4
Thus a = (2, -1, 4) and b = (-1, 2, -4)

Therefore, the required parametric equation is r(s, t) = s(2, -1, 4) + t(-1, 2, -4) + (1, 2, -3) = (2s, -s, 4s) + (-t, 2t, -4t) + (1, 2, -3) = (2s - t + 1, -s + 2t + 2, 4s - 4t - 3)


You might be interested in
If you multiply the four-digit number abcd by 4, the order of digits will be reversed. That is, abcd x 4=dcba. The digits a, b,
Arisa [49]
The given is that A B C D <span>x 4 = D C B A
</span><span>
Possible values of A are 1 or 2. It can't be 1 since the </span><span> </span><span>final result A is in unit place and 1 is not possible when we multiply any number by 4
</span><span>
2 B C D x </span><span>4 = </span><span>D C B 2</span>
It is clear above, that D = 8
2 B C 8 x <span>4 = </span><span>8 C B 2</span>
Possible values of B should be 1 or 2
We try B=1

2 1 C 8 x <span>4 = </span><span>8 C 1 2

</span>To find for C, you can use the equation:

(2000+100+10C+8) x 4 = 8000+100C+10+240C = 432-12 = 420
Therefore,

C = 7
So, the number is 2178.
5 0
3 years ago
Read 2 more answers
What is the value of in e^4?
True [87]
54.5981500331 is the answer
7 0
3 years ago
Read 2 more answers
If you get a sneak peak at the salary list of your job and realize you are in the lowest bracket, which is the lowest 1%, what i
hoa [83]

Answer:

z=-2.33

And if we solve for a we got

a=48000 -2.33*5500=35185

And for this case the answer would be 35185 the lowest 1% for the salary

Step-by-step explanation:

Let X the random variable that represent the salary, and for this case we can assume that the distribution for X is given by:

X \sim N(48000,5500)  

Where \mu=48000 and \sigma=5500

And we want to find a value a, such that we satisfy this condition:

P(X>a)=0.99   (a)

P(X   (b)

We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.01 of the area on the left and 0.99 of the area on the right it's z=-2.33. On this case P(Z<-2.33)=0.01 and P(z>-2.33)=0.99

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-2.33

And if we solve for a we got

a=48000 -2.33*5500=35185

And for this case the answer would be 35185 the lowest 1% for the salary

7 0
3 years ago
Look at this function:
Rom4ik [11]
X values are increasing by 2
y values are increasing by 4
Mark is correct
5 0
3 years ago
Read 2 more answers
1 peso = $ .075. How many pesos (whole number) do you get for $100 ?
olga55 [171]

Answer:

133

Step-by-step explanation:

100/.75 = 133.33 = 133

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following represents "a number less ten is twenty-two"?
    13·1 answer
  • Use the substitution method to solve the system of equations. Choose the correct ordered pair.
    9·2 answers
  • -Solve the system of equations.<br>- 10y + 9x = -9<br>10y + 5x = -5​
    14·2 answers
  • Simplify (4х – б) + (5х + 1)
    10·2 answers
  • What is arc BC equal to?
    11·1 answer
  • Multiply. Reduce the answer to lowest terms.<br><br> 2\3 times 3\4
    11·1 answer
  • What is the slope for y=3x+6
    12·2 answers
  • Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating
    15·1 answer
  • Suppose you are conducting a study about how the average US worker spends time over the course of a workday. You are interested
    9·1 answer
  • If x = 9 units and h = 4 units, then what is the area of the triangle shown above?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!