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Komok [63]
3 years ago
7

Plz help me!!! I need this answered correctly and with explanation!!! Solve z/−8 ≥ −0.25

Mathematics
2 answers:
eduard3 years ago
8 0

Answer:

z≥-2

Step-by-step explanation:

z/-8≥-0.25

In order to get the letter z by its self you have to do the same thing to each side of the greater or equal to symbol.

In order to get the z by its self you need to do the opposite as what is shown so you can get down to just the simpiest form: for example if you are multiplying you would end up deviding on both sides of you sign.

So insted of dividing z by -8 we will multiply -8 to each side and so on... I will write it out to show you:

z/-8≥-0.25

*-8        *-8

z≥-2

Svetlanka [38]3 years ago
6 0

Answer:

z≤2

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−1/8z≥−0.25

Step 2: Multiply both sides by 8/(-1).

(8/−1)*(−18z)≥(8−1)*(−0.25)

z≤2

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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
2 years ago
Which of the following is an example of VOLUME
zavuch27 [327]

I believe it would be 2, how much water is used to fill a cup

4 0
3 years ago
Show your work please!
timofeeve [1]

Answer:

C

Step-by-step explanation:

10^5=100,000

100,000*4.7=470,000  (Four Hundred Seventy Thousand)

10^8=100000000

100000000*3.9=390,000,000 (Three Hundred Ninty Million)

10^5=100,000

100,000*5.2=520,000 (Five Hundred Two Thousand)

Least to Greatest:

470,000     520,000   390,000,000

I                       III                     II

C

6 0
2 years ago
Read 2 more answers
Thank you so much for the answer in advance!
Aleonysh [2.5K]
A: 66 b:28 :))) have a good day
4 0
3 years ago
Algebra 1- 10 pts <br> Solve for t.<br><br> −4t≤48<br><br> Enter your answer as an inequality
iris [78.8K]
The answer for this problem is t ≥ - 12
7 0
3 years ago
Read 2 more answers
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