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bekas [8.4K]
3 years ago
9

Evaluate arcsec(2)?. . a) (pi/6, plus/minus 2pin, 5pi/6 plus/minus, 2pin. b) (pie/3). c) (pie/6, 5pie/6). d) (pie/3 plus or min

us 2pien, 5pie/3 plus or minus 2pien). .
Mathematics
2 answers:
Gennadij [26K]3 years ago
5 0
The value of arc sec of any number is equal to an angle in unit degrees or radians. In this case, sec is the inverse of cos, so as we input in the calculator, we write (1/cos)^-1 (2) or simply (cos)^-1 (0.5).  The answer is  pi/ 3. cosine of an angle located in the first and fourth quadrant is positive . Hence the answer that is applicable is b. pi/3/ 
enot [183]3 years ago
3 0

Answer:

(pie/3 plus or minus 2pien, 5pie/3 plus or minus 2pien)

Step-by-step explanation:

Done on Apex

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John has about 1.09 m of rope.
31 cm is 0.31 m
soo 0.33 + 0.45 + 0.31 = 1.09 
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Is -2.7 an integer??????????
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What is the difference between a relation and function? Classify each of the following as a function, or not a function. State t
Levart [38]

Answer:

A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.

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2 years ago
A bowl contains 11 white stones and 3 black stones. One stone is chosen and not replaced, then another stone is chosen. What is
Nataly [62]

Answer:

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Step-by-step explanation:

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2 years ago
Read 2 more answers
The plane x+y+2z=8 intersects the paraboloid z=x2+y2 in an ellipse. Find the points on this ellipse that are nearest to and fart
DiKsa [7]

Answer:

The minimum distance of   √((195-19√33)/8)  occurs at  ((-1+√33)/4; (-1+√33)/4; (17-√33)/4)  and the maximum distance of  √((195+19√33)/8)  occurs at (-(1+√33)/4; - (1+√33)/4; (17+√33)/4)

Step-by-step explanation:

Here, the two constraints are

g (x, y, z) = x + y + 2z − 8  

and  

h (x, y, z) = x ² + y² − z.

Any critical  point that we find during the Lagrange multiplier process will satisfy both of these constraints, so we  actually don’t need to find an explicit equation for the ellipse that is their intersection.

Suppose that (x, y, z) is any point that satisfies both of the constraints (and hence is on the ellipse.)

Then the distance from (x, y, z) to the origin is given by

√((x − 0)² + (y − 0)² + (z − 0)² ).

This expression (and its partial derivatives) would be cumbersome to work with, so we will find the the extrema  of the square of the distance. Thus, our objective function is

f(x, y, z) = x ² + y ² + z ²

and

∇f = (2x, 2y, 2z )

λ∇g = (λ, λ, 2λ)

µ∇h = (2µx, 2µy, −µ)

Thus the system we need to solve for (x, y, z) is

                           2x = λ + 2µx                         (1)

                           2y = λ + 2µy                       (2)

                           2z = 2λ − µ                          (3)

                           x + y + 2z = 8                      (4)

                           x ² + y ² − z = 0                     (5)

Subtracting (2) from (1) and factoring gives

                     2 (x − y) = 2µ (x − y)

so µ = 1  whenever x ≠ y. Substituting µ = 1 into (1) gives us λ = 0 and substituting µ = 1 and λ = 0  into (3) gives us  2z = −1  and thus z = − 1 /2 . Subtituting z = − 1 /2  into (4) and (5) gives us

                            x + y − 9 = 0

                         x ² + y ² +  1 /2  = 0

however, x ² + y ² +  1 /2  = 0  has no solution. Thus we must have x = y.

Since we now know x = y, (4) and (5) become

2x + 2z = 8

2x  ² − z = 0

so

z = 4 − x

z = 2x²

Combining these together gives us  2x²  = 4 − x , so

2x²  + x − 4 = 0 which has solutions

x =  (-1+√33)/4

and

x = -(1+√33)/4.

Further substitution yeilds the critical points  

((-1+√33)/4; (-1+√33)/4; (17-√33)/4)   and

(-(1+√33)/4; - (1+√33)/4; (17+√33)/4).

Substituting these into our  objective function gives us

f((-1+√33)/4; (-1+√33)/4; (17-√33)/4) = (195-19√33)/8

f(-(1+√33)/4; - (1+√33)/4; (17+√33)/4) = (195+19√33)/8

Thus minimum distance of   √((195-19√33)/8)  occurs at  ((-1+√33)/4; (-1+√33)/4; (17-√33)/4)  and the maximum distance of  √((195+19√33)/8)  occurs at (-(1+√33)/4; - (1+√33)/4; (17+√33)/4)

4 0
3 years ago
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