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OlgaM077 [116]
3 years ago
11

Please help!! ; Evaluate the expression. 6 ÷ −3 A. -2 B. -3 C. 3 D. 2

Mathematics
2 answers:
Licemer1 [7]3 years ago
5 0

Answer:

A

Step-by-step explanation:

6 \div  - 3 =  - 2

Serggg [28]3 years ago
4 0

Answer:

-2

Step-by-step explanation:

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. Use Lagrange multipliers to find the maximum and minimum values of the function, f, subject to the given constraint, g. (Place
zzz [600]

Answer:

Minimum value of f(x, y, z) = (1/3)

Step-by-step explanation:

f(x, y, z) = x⁴ + y⁴ + z⁴

We're to maximize and minimize this function subject to the constraint that

g(x, y, z) = x² + y² + z² = 1

The constraint can be rewritten as

x² + y² + z² - 1 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = x⁴ + y⁴ + z⁴ - λ(x² + y² + z² - 1)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 4x³ - λx = 0

λ = 4x² (eqn 1)

(∂L/∂y) = 4y³ - λy = 0

λ = 4y² (eqn 2)

(∂L/∂z) = 4z³ - λz = 0

λ = 4z² (eqn 3)

(∂L/∂λ) = x² + y² + z² - 1 = 0 (eqn 4)

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

4x² = 4y²

4x² - 4y² = 0

(2x - 2y)(2x + 2y) = 0

x = y or x = -y

Also,

4x² = 4z²

4x² - 4z² = 0

(2x - 2z) (2x + 2z) = 0

x = z or x = -z

when x = y, x = z

when x = -y, x = -z

Hence, at the point where the box has maximum and minimal area,

x = y = z

And

x = -y = -z

Putting these into the constraint equation or the solution of the fourth partial derivative,

x² + y² + z² = 1

x = y = z

x² + x² + x² = 1

3x² = 1

x = √(1/3)

x = y = z = √(1/3)

when x = -y = -z

x² + y² + z² = 1

x² + x² + x² = 1

3x² = 1

x = √(1/3)

y = z = -√(1/3)

Inserting these into the function f(x,y,z)

f(x, y, z) = x⁴ + y⁴ + z⁴

We know that the two types of answers for x, y and z both resulting the same quantity

√(1/3)

f(x, y, z) = x⁴ + y⁴ + z⁴

f(x, y, z) = (√(1/3)⁴ + (√(1/3)⁴ + (√(1/3)⁴

f(x, y, z) = 3 × (1/9) = (1/3).

We know this point is a minimum point because when the values of x, y and z at turning points are inserted into the second derivatives, all the answers are positive! Indicating that this points obtained are

S = (1/3)

Hope this Helps!!!

6 0
3 years ago
Write the equation of the line that passes through (-2,0) and (0, -7)
MakcuM [25]

Answer:

Step-by-step explanation:

1.

(-2,0) (0,-7)                y2-y1

                            -----------------

                                 x2-x1

-7-0= -7

0- (-2)= 2             ------>>> -7/2 =m or slope

2.

y= -7/2x+b          to find b u plug in one pair of coordinates for example (-2,0)

                          and use inverse properties to find b

0 = -7/2(-2) + b

       14/2 = 7

0= 7+b

-7 -7

-----------

-7=b

3.

y=-7/2x-7    

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To complete the square (x+2/5)^2 it would be x^2+(4/5)x+4/25
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4.7 x 10^4
or 5 x 10^4

<span>The scientific notation of 70, 030, 000. To find the scientific notation of this value </span><span><span>
1.  </span>We first move the period which separates the whole number from the decimal number which is located after the numbers of the given value.</span> 
<span><span>2.  </span>We move it in the very recent order number which is seventy million, seven and zero.</span> <span><span>
3.  </span>It becomes 7.003</span>
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5.  </span>7.003 x 10^7 </span>


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3 years ago
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