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Vinil7 [7]
2 years ago
14

Does -8 have a greater absolute value than 6

Mathematics
2 answers:
r-ruslan [8.4K]2 years ago
7 0

Answer:

yes.

Step-by-step explanation:

because -8 absolute value is 8

m_a_m_a [10]2 years ago
5 0

Answer:

yes beacuse -8 have a greater absolute value than 6

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Simplify the following expression: 3m-5n+6m-8n
vichka [17]

3m - 5n + 6m - 8n \\ 3m + 6m - 5n - 8n \\ 9 m- 13n

5 0
2 years ago
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Which point on the scatter plot is an outlier?
dlinn [17]

Answer:

The point 9,50

Step-by-step explanation:

All the other ones are within a reasonable distance of each other.

7 0
1 year ago
Priya has completed 9 eczema questions.THis is 60% of the questions on the exam? how many questions are on the exam?
qwelly [4]

Answer:

15 questions

Step-by-step explanation:

9x100=900

900/60=15

9/15=60%

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7 0
3 years ago
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
The dimensions of a triangular prism are shown in the diagram. What is the
goldfiish [28.3K]

Answer:

D

Step-by-step explanation:

SA = bh + (s1 + s2 + s3)H is the formula to find out the surface area

b is base, h is height (small height), s's are the sides, H is the height (longer one)

SA = 12(9) + (10 + 10 + 12)32

SA = 108 + (32)32

SA = 108 + 1024

SA = 1132

5 0
3 years ago
Read 2 more answers
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