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tresset_1 [31]
3 years ago
6

Find the inner product for (-4,9,8) . (3,2,-2) and state whether the vectors are perpendicular.

Mathematics
1 answer:
drek231 [11]3 years ago
6 0

Answer:

-10; no

Step-by-step explanation:

<h2>-4*3 + 9*2 + 8*-2 = -10</h2><h2></h2><h2>-10 does not equal 0 so it is not perpendicular</h2>

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Yes, no, yes

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The curve with equation y = x - 3x + 1 is reflected in the x-axis.
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Mona has 160 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed are
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3 years ago
The "cold start ignition time" of an automobile engine is being investigated by a gasoline manufacturer. The following times, in
Nezavi [6.7K]

Answer:

<em>1. Sample Mean = 2.50 </em>

<em>2. Sample Variance = 1.35</em>

<em>3. Standard Deviation = 1.16</em>

Step-by-step explanation:

Note: As this question is not complete, similar can be found on internet where following are asked to calculate and here I will calculate these as well.

1. Sample Mean.

2. Sample Variance.

3. Sample Standard Deviation.

So, for sample mean to calculate from the given data points. We need to apply to following formula to calculate sample mean.

Sample Mean = (X1 + X2 + .... + XN) divided by Total number of data points.

Sample Mean = (0.17 + 1.94 + 2.62 + 2.35 + 3.05 + 3.15 + 2.53 + 4.81 + 1.92) divided by (9).

<em>Sample Mean = 2.50</em>

Likewise, from the answer of sample mean we can calculate sample variance by following steps.

<u><em>Solution: </em></u>

1.      Subtract the obtained mean from each of the data point given.

       (0.17 - 2.50) = -2.33

       (1.94 - 2.50) = -0.56

       (2.62 - 2.50) = 0.12

       (2.35 - 2.50) = -0.15

       (3.05 - 2.50) = 0.55

       (3.15 - 2.50) = 0.65

       (2.53 - 2.50) = 0.03

       (4.81 - 2.50) =  2.31

       (1.92 - 2.50) = -0.58

2.      Square each of the differences obtained in step 1.

            -2.33^{2} = 5.43

            -0.56^{2} = 0.31

               0.12^{2} = 0.01

            -0.15^{2} = 0.02

              0.55^{2}  = 0.30

              0.65^{2}  = 0.42

              0.03^{2} = 0.01

              2.31^{2} = 5.34    

           -0.58^{2} = 0.34    

3.  Sum all of these squares.

(5.43 + 0.31 + 0.01 + 0.02 + 0.30 + 0.42 + 0.01 + 5.34 + 0.34) = 12.18

4. Divide 12.18 by (n-1), where n = 9.

<em>Sample Variance =  12.18/9 = 1.35</em>

Now, by using sample variance, we can calculate standard deviation with easy simple steps.

So, in order to find standard deviation, we just need to take the square root of sample variance that we have already calculated above.

<em>Standard Deviation = </em>\sqrt{1.35}<em> = 1.16 </em>

<em>Good Luck!</em>

6 0
3 years ago
The rectangular coordinates of a point are given. Find the polar coordinates ​(r,theta​) of this point with theta expressed in r
alexandr402 [8]

Answer:}

In polar coordinates P is

P  ( 12 ; 2.618 )  

Step-by-step explanation:

The point (ectangular coordinates)  

P ( -6√3  ;   6 )       P  (  x ; y )

Polar coordinates   P ( r  ;  θ )

x = r cos θ

y = r sin θ                  r > 0    and     0  ≤ θ ≤ 2π

Then

r  =  √ (x)² + (y)²        r  =  √(36)²*3 +( 36)²       r = √144

r  =  12   (hypothenuse module always positive)

The point   P  ( -6√3  ;   6 )   is in second cuadrant  between 90° and 180°

angle between  r  and horizontal axis x  is equal to θ

tan α =  l.opp/ l.adj.    tan θ =  y/x       tan θ = - 6 /6√3

tan α = - 1/√3

Then α  =  180⁰ - 150⁰  = 30⁰  or     θ =  150⁰

to express that value in radians we have :

1 π radian      =   180⁰         ⇒   3,1416   radians  =  180⁰

                                                      x ??                  =   150⁰

x =  radians

Finally the point is   P  ( 12 ; 2.618 )  

6 0
3 years ago
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