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3 years ago

Which ordered pair makes the equation true? 2x – 8y = –4

1 answer:

8 0

There aer infinite numbers
to make it easier we can solve for y

2x-8y=-4
x-4y=-2
-4y=-x-2
y=(1/4)x+(1/2)
some values aer
x=0, y=1/2
x=-2, y=0
etc

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Find the max and min values of f(x,y,z)=x+y-z on the sphere x^2+y^2+z^2=81

Anton [14]

Using Lagrange multipliers, we have the Lagrangian

$L(x,y,z,\lambda)=x+y-z+\lambda(x^2+y^2+z^2-81)$

with partial derivatives (set equal to 0)

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$
$L_y=1+2\lambda y=0\implies y=-\dfrac1{2\lambda}$
$L_z=-1+2\lambda z=0\implies z=\dfrac1{2\lambda}$
$L_\lambda=x^2+y^2+z^2-81=0\implies x^2+y^2+z^2=81$

Substituting the first three equations into the fourth allows us to solve for $\lambda$ :

$x^2+y^2+z^2=\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}=81\implies\lambda=\pm\dfrac1{6\sqrt3}$

For each possible value of $\lambda$ , we get two corresponding critical points at $(\mp3\sqrt3,\mp3\sqrt3,\pm3\sqrt3)$ .

At these points, respectively, we get a maximum value of $f(3\sqrt3,3\sqrt3,-3\sqrt3)=9\sqrt3$ and a minimum value of $f(-3\sqrt3,-3\sqrt3,3\sqrt3)=-9\sqrt3$ .

5 0

3 years ago

Is the function in the table linear or nonlinear and why? x y 0,−100 and 1,-50 and 2,0 and 3,100 and 4,150. (A)The function is n

Studentka2010 [4]

Answer:

The correct option is c.

Step-by-step explanation:

Linear function: The rate of change of a linear function is always constant.

Non-Linear function: The rate of change of a non-linear function is not constant.

From the given coordinate pairs it is noticed that the function is passing through the points (0,-100), (1,-50), (2,0), (3,100) and (4,150).

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope of function for points (0,-100) and (1,-50) is

$m_1=\frac{-50-(-100)}{1-0}=50$

The slope of function for points (2,0) and (3,100) is

$m_2=\frac{100-0}{3-2}=100$

Since the slopes of function are different, therefore the given function is non-linear.

The function is not linear because the rate of change is not constant and option c is correct.

7 0

3 years ago

Read 2 more answers

If you ran exactly one mile, how many feet did you run

elena-s [515]

Solution:

we have been asked to find

If you ran exactly one mile, how many feet did you run.

It mean , we will have to convert miles in feet.

As we know that

1 mile is equivalent to 5280 feet.

Hence , we can use this conversion to get the exact value of miles in feet.

If you ran exactly one mile,it mean you ran exactly for 5280 feet.

4 0

3 years ago

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In a right triangle, angle C measures 40. the hypotenuse of the triangle is 10 inches long. what is the approximate length of th

IrinaVladis [17]

Since angle C is not 90 degrees, it's one of the acute angles
in the right triangle.

   (The side adjacent to angle C ) divided by (hypotenuse)

is the cosine of angle C .

(adjacent) / (10 inches) = cos(40 degrees)

Multiply each side by (10 inches):

      Adjacent side = (10 inches) x cos(40) =

(10 inches) x 0.766 =

7.66 inches (rounded)

6 0

3 years ago

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8x - 5 > 13 - x<br> Solve inequalities

Archy [21]

Answer:

x>2

Step-by-step explanation:

3 0

2 years ago

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