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Vera_Pavlovna [14]
3 years ago
13

2a.Solve the quadratic equation with completing the square method 5x2 - 4x + 125 = 0 ​

Mathematics
1 answer:
EastWind [94]3 years ago
4 0

Answer:

There is No real solutions.

Step-by-step explanation:

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Use Lagrange multipliers to find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Enter the dimens
Dima020 [189]

Answer:

(x,y,z) = (12,12,12) cm

Step-by-step explanation:

The box is assumed to be a closed box.

The surface area of a box of dimension x, y and z is given by

S = 2xy + 2xz + 2yz

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

xyz = 1728

The constraint can be rewritten as

xyz - 1728 = 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) = 2xy + 2xz + 2yz - λ(xyz - 1728)

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) = 2y + 2z - λyz = 0

λ = (2y + 2z)/yz = (2/z) + (2/y)

(∂L/∂y) = 2x + 2z - λxz = 0

λ = (2x + 2z)/xz = (2/z) + (2/x)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x)

(∂L/∂λ) = xyz - 1728 = 0

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

(2/z) + (2/y) = (2/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(2/z) + (2/x) = (2/y) + (2/x)

(2/z) = (2/y)

z = y

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

x = y = z

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

xyz - 1728 = 0

x³ = 1728

x = 12 cm

x = y = z = 12 cm.

7 0
2 years ago
If a train travels at the speed of 100 km how far will it travel in half an hour
choli [55]

Answer:

50 kilometers

Step-by-step explanation:

If it travels 100 in an hour, it would travel 50 in half

4 0
2 years ago
Read 2 more answers
Value of ratio 3/4 to 2
MrMuchimi

Answer:

3/8 or 0.375

Step-by-step explanation:

0.75/2 = 3/8

4 0
3 years ago
Show all work. <br><br>PLEASE HELP!!!!
34kurt
(a) Using the table, give the values fo rthe inverse


1) original table of values:


x      1     2     3    4    5

f(x)   0     1     1    5    3


2) The inverse of the function is obtained by exchanging x and f(x), this is:


                   ( x, f(x) ) → ( f(x), x)


3) So, the table of values of the inverse of the given function is:


x          0    1     1      5     3

f⁻¹ (x)   0     1     2     3     4


(b) Is the inverse a function?


No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.


This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.
7 0
3 years ago
No sé cómo hacerlo. Y me gustaría que me ayudaran con él proceso?
In-s [12.5K]

Answer:

BC=11

Step-by-step explanation:

we need to find BC

and we  know that

AB= x+2

AC=13

BC=2x+11

A, B and C are collinear

that means that

AB+BC=AC

x+2+2x+11=13

3x+13=13

3x=0

x=0

so BC=2(0)+11

BC=11

7 0
2 years ago
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