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aliina [53]
3 years ago
10

) find a vector parallel to the line of intersection of the planes 5x − y − 6z = 0 and x + y + z = 1.

Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.

Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>

We calculate the cross product as a determinant of (i,j,k) and the normal products

    i   j   k
   5 -1 -6
   1  1  1

=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>

Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0

Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
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A inversely as x, and y=23 when x=8, find when x=4
Feliz [49]

Answer:

  • y=1/x
  • y=k/x
  • k=yx
  • given y=23,x=8
  • k=23×8=184
  • when x=4
  • y=184/4=46ans

6 0
2 years ago
Find the difference 5 1/3 - 3 2/3
ollegr [7]
5/3 or 1 2/3 the first one is the answer but the second answer is just simplified :)

3 0
3 years ago
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baherus [9]
I think it is 81 but I'm not sure
8 0
2 years ago
OFFERING 50 POINTS!!! The army reports that the distribution of waist sizes among female soldiers is approximately normal, with
hammer [34]

Answer:

Step-by-step explanation:

1)

Percentile is related to the area under the standard normal curve to the LEFT of a certain data value (which in this case would be 26.1 inches).

On my Texas Instruments TI-83 Plus calculator, I found this area as follows:

normcdf(-100, 26.1, 28.4,1.2), where the range -100 to 26.1 represents the area (as a decimal fraction) to the left of 26.1 inches.  My result was 0.028, which corresponds to the 3rd percentile (0.028 rounds off to 0.03, which would be 3rd percentile).

2)  The mean waist size is 28.4 inches, represented by a vertical line through the standard normal curve lying between 24 and 32.  We use the same function on the calculator:  normcdf(24, 32, 28.4, 1.2).

The result is 0.9985.  Subtracting this from 1.0000, we get 0.001, or 0.1%, which is the percentage of female soldiers requiring custom uniforms.

4 0
2 years ago
solve this problem as a quadratic equation. The difference between two positive numbers is 5. Their product is 104 find the numb
Karolina [17]
Let's call the smaller number x:

y-x=5
xy=104

y-x=5 can be rewritten as y=x+5

Substituting this into the second equation gives:

x(x+5)=104
x^2+5x=104
x^2+5x-104=0

Then simply solve as a quadratic:

x^2+13x-8x-104=0
x(x+13) -8(x+13)=0
(x-8)(x+13) = 0

x=8,-13

the question said the numbers are positive, so x=8

if x=8,

y=x+5
y=13

So the two numbers are 8 and 13.
8 0
3 years ago
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