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sergey [27]
3 years ago
7

Which is the solution to –7x > 49?

Mathematics
1 answer:
mote1985 [20]3 years ago
6 0

Answer:

x<7

Step-by-step explanation:

Divide by -7 on both sides and when dividing by a negative you should flip the inequality sign.

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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
3 years ago
Discounts: there are 125,000 American soldiers in Iraq . 25% are infantry. From the rest 40% are reservist. How many reservist a
Bond [772]
 there are 87350 reservist

7 0
3 years ago
Determine value of k
Ipatiy [6.2K]
72+k is equal to 180. So if you set up a equation if looks like:

72+k=180

Subtract 72 from both sides

K=108°

Your answer is 108°
3 0
3 years ago
Determine+the+percentile+indicating+the+bottom+ranking+20%.+in+other+words,+what+is+the+dollar+number+that+defines+where+the+low
Aloiza [94]

The dollar number that defines where the lowest values falls is

20% percentile value =$20

This is further explained below.

<h3 /><h3>What is the dollar number that defines where the lowest value falls?</h3>

Generally,  Now we need to determine the 20th percentile ($20). It indicates that we need to locate a dollar amount that marks the point at which the 20 % data has a value lower than that number.

i=(p/100)*n

Where i is the position of p^th

percentile when the data is presented in ascending order.

i=20/100*50

i=1000/100

i=10

Therefore

n=50

p=20

In conclusion, the 10th position for given data is 20,

Therefore, 20% percentile value =$20

Read more about percentile

brainly.com/question/1594020

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Find the volume of the specified cone. Use 3.14 for Pi, and round your answer to the nearest whole number. Radius = 5 in., Heigh
Irina-Kira [14]

Answer:

The answer is 236 cu. In.

Step-by-step explanation:

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2 years ago
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