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Alex73 [517]
3 years ago
5

Use the graph of the line to answer each question.

Mathematics
1 answer:
Mariulka [41]3 years ago
8 0

The y intercept (b) is where is crosses the y axis = 5

The x intercept is where is crosses the x axis = 4

The slope is rise over run  or y2 - y1/x2 - x1

m = 0 - 5/4 - 0

m = -5/4

y = mx +b

y = -5/4x + 5

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Graph y = -1/4x + 6. Please help!!
OverLord2011 [107]

Answer:

6  1/4

Step-by-step explanation:

6 0
2 years ago
Describe the end behavior of the following function: F(x)=2x^4+x^3
Anika [276]

Answer:

Rises to the left and rises to the right.

Step-by-step explanation:

Since, the given function is f(x)=2x^{4}+x^{3}, and the end behavior of the given function is determined as:

Consider the given function f(x)=2x^{4}+x^{3}, identify the degree of the function:

The degree of the function is : 4 which is even

And then identify the leading coefficient of the given function that is +2 which is positive in nature.

Hence, the function is positive and even in nature, therefore, the end behavior of the function will be rising to the left and rising to the right.

3 0
2 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
Graph y=-2x+5<br> Plz hurry
Vedmedyk [2.9K]

Answer:

Here's a picture of the answer.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Tomas wrote the equation y = 3x +3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutio
mamaluj [8]
–6x + 2y = 3/2

or, 2y= 6x + 3/2
or, y= (6x + 3/2)/2
or, y = 6x/2 + 3/4
or, y = 3x + 3/4

Therefore, –6x + 2y = 3/2 is Sandra's equation.  


4 0
2 years ago
Read 2 more answers
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