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SVEN [57.7K]
3 years ago
5

Find a vector i normal to the plane 2x + y + 2z = 4

Mathematics
1 answer:
m_a_m_a [10]3 years ago
4 0

Answer: <em>i</em> =2i+1j+2k

Step-by-step explanation:

The parametric equation of a plane is Ax+By+Cz=D and by definition the normal vector of the plane is n=Ai+Bj+Ck, where i,j,k are the canonic vectors

Then, in this case a normal vector to the given plane is i=2i+1j+2k

To prove that a vector defined as n=Ai+Bj+Ck is normal to the plane, let V1 and V2 be two vectors that are in the plane

If V1 ∈ Ax+By+Cz=D then Aa1+Bb1+Cc1=D

If V2 ∈ Ax+By+Cz=D then Aa2+Bb2+Cc2=D

The vector V1V2=V2-V1=(a2-a1)i+(b2-b1)j+(c2-c1)k

Two vectors are normal or perpendicular if the dot product is zero.

V2V1_{o}n=0

(a2-a1)i+(b2-b1)j+(c2-c1)k_{o}Ai+Bj+Cj=0\\(a2-a1)A+(b2-b1)B+(c2-c1)C=0\\Aa2+Bb2+Cc2-(Aa1+Bb1+Cc1)=0\\D-D=0

So, n is a normal vector to the plane.

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In a certain​ country, the mean birth weight for boys is 3.27 ​kg, with a standard deviation of 0.51 kg. Assuming that the distr
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Answer:

0.066

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ, where

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σ is the population standard deviation

For the question

mean birth weight for boys is 3.27 ​kg, with a standard deviation of 0.51 kg.

x = 2.5

Hence:

z = 2.5 - 3.27/0.51

z = -1.5098

Probability value from Z-Table:

P(x ≤ 2.5) =P(x < 2.5) = P(x = 2.5) =

=0.065547

Therefore, the proportion of baby boys that are born with a low birth weight is 0.066

5 0
3 years ago
Find the slope of the line that contains the following pair of points. (3, 4) (3, -7)
mojhsa [17]
Negative 3 is the answer
8 0
3 years ago
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Evaluate (4p)3 when p = (-1)
Leona [35]

Answer:

-12

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plug in -1 into the equation which is going to be (4*-1)3

you multiply what is in the parenthesis first and after is going to be (-4)3

lastly your going to multiply -4*3 and it is going to equal to -12.

3 0
3 years ago
Somebody help me out please
Digiron [165]

Answer:

Boys : girls

5:6

Step-by-step explanation:

Boys : girls

20:24


We can divide each  of these numbers by 4

20/4 =5

24/4 =6

Boys : girls

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5 0
3 years ago
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