Which compound inequality is represented by the graph?

The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]

The given parameters are:

Assume the dimensions of the container are: x, y and z.

The volume (V) would be:

[tex]V = xyz[/tex]

Substitute 480 for V

[tex]xyz =480[/tex]

And the objective cost function would be:

[tex]C =8xy + 6xz + 6yz[/tex]

Differentiate the cost function using Lagrange multipliers

[tex]8x + 6z = \lambda xz[/tex]

[tex]8y + 6z = \lambda yz[/tex]

[tex]6x + 6y = \lambda xy[/tex]

Divide equation (1) by (2)

[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]

[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]

Factor out 2

[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]

Cross multiply

[tex]4xy + 3yz = 4xy + 3xz[/tex]

Evaluate the like terms

[tex]3yz = 3xz[/tex]

Divide both sides by 3z

[tex]y = x[/tex]

Divide the first equation by the third

[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]

[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]

Factor out 2

[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]

Cross multiply

[tex]4xy+3xz = 3xz + 3yz[/tex]

Cancel out the common terms

[tex]4xy = 3yz[/tex]

Divide both sides by y

[tex]4x = 3z[/tex]

Make z the subject

[tex]z =\frac{4}{3}x\\[/tex]

So, we have:

[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]

Recall that:

[tex]xyz =480[/tex]

Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]

[tex]x \times x \times \frac 43x = 480[/tex]

So, we have:

[tex]\frac 43x^3 = 480[/tex]

Multiply both sides by 3/4

[tex]x^3 = 360[/tex]

Take the cube roots of both sides

[tex]x = \sqrt[3]{360}[/tex]

Recall that:

[tex]y = x[/tex]

So, we have:

[tex]y = \sqrt[3]{360}[/tex]

Also, we have:

[tex]z =\frac{4}{3}x\\[/tex]

So, we have:

[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]

Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]

Read more about Lagrange multipliers at:

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Answer:

64 in 2 is it the answers im not shure

Answer:

I have no any ideas

Step-by-step explanation:

sorry

I did the math in the link below  

Answer:

no I'm pretty sure it's wrong

Step-by-step explanation:

the y intercept for that to right us -4

Answer:

8.48

Step-by-step explanation:

36 + 36 = 72

t^2 = 72

t = 6[tex]\sqrt{2}[/tex] = 8.48

Answer: 6

Step-by-step explanation:

Answer:

m / 6/7 = 5/6

m = 35

Step-by-step explanation:

Answer:

Step-by-step explanation:

The quotient of m and 6/7 is 5/6:

Answer:

1100

Step-by-step explanation:

Answer:

A = 55.15

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos A = adj side / hypotenuse

cos A = 4/7

Taking the inverse cos of each side

cos ^-1 ( cos A) = cos ^-1( 4/7)

A =55.15009542

To the nearest hundredth

A = 55.15

Answer:

83.1219512195

Step-by-step explanation:

Hope this helps!

Answer:

y = 6

Step-by-step explanation:

A line with a slope of zero is a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (- 5, 6 ) with y- coordinate 6 , then

y = 6 ← equation of line

Answer: A. they will have too much butter

Step-by-step explanation: to much

Answer:

13

Step-by-step explanation:

Have a great day!! :)

Answer:

ok so first take a way 100 from 350

250 then divide by 20

12

Hope This Helps!!!

Answer:uh 2 divide 1.19 and add 12 i think

Step-by-step explanation:

The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to  [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex]  and it can be determined by using LCM and fraction.

[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]

If no denominator equals zero,

Which expression is equivalent to the given expression?

Expression;

[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]

If no denominator equals zero,

To determine the equivalent relation of the given equation following all the steps given below.

                   [tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]

                   [tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]

Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to  [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .

For more details about Expression refer to the link given below.

https://brainly.com/question/14610993

A) Length is 82 m

B) Width is 58 cm

Hope this is helpful!

Answer:   a=(3,-4)

                B=(3,-1)

                C=(5,-2)

Step-by-step explanation:

Answer:

supplementary angles - two angles are supplementary when they add up to 180 degrees (a straight line)

complementary angles - two angles are complementary when they add up to 90 degrees (a right angle)

hopefully this helps! :)

Answer:

1. complementary

2. neither

3. supplementary

4. complementary (x = 6)

10x + 30 = 90         x + 3 = 9          x = 6

5. supplementary (x = 20)

4x + 40 + 3x = 180       7x = 140       x = 20

6. x = 50.5

2x + 79 = 180     2x = 101       x = 50.5

Step-by-step explanation:

When the measurement of the angles adds up to 90 degrees, the angles are complementary. When the sum of the angles is 180 degrees, then they are supplementary.

The common denominator is 1

Given the expression:

Find the LCM of the numerator to have:

Simplify both the numerator and the denominator to have:

[tex]= \dfrac{\frac{b-a}{ab} }{\frac{1}{ab} }\\= \frac{b-a}{ab} \times ab\\=\frac{b-a}{1} \times 1 \\=\frac{b-a}{1}[/tex]

From the result, we can see that the common denominator is 1

Learn more about fractions here: https://brainly.com/question/17743912

Answer:

here is the correct answer for edge2022

Step-by-step explanation:

Answer:

infinitely many solutions

Step-by-step explanation:

The lines over lap

Answer:

(5, -4)

Step-by-step explanation:

Answer:

(5,-4)

Step-by-step explanation:

((0+10/2),(-2-6/2))

(10/2, -8/2)

(5,-4)

Answer:

D)

Step-by-step explanation:

The answer would be D. The slope of a line is how fast it climbs. Height divided by base. Up divided by over. Thus, if it goes across 3 and up 1, its slope would be 1/3. If it goes across 1 and up 2, the slope is 2. If it goes across 1 and up -1, the slope is -1.

HOPE THAT HELP YOU MARK ME BRINILYLIST

Using conditional probability, it is found that there is a 0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

In this problem:

According to the chain given, the percentages associated with not getting into their first-choice college are:

Hence:

[tex]P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605[/tex]

The probability of both not getting into their first-choice college and taking chemistry is 0.1375, hence [tex]P(A \cap B) = 0.1375[/tex]

Then, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273[/tex]

0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.

To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287

Answer: 0.2273

Step-by-step explanation: because it says so <3

Answer: Do the math, the positive solution

t = 5.0495 seconds (If it's wrong sorry, I havent done a problem like this one in awhile!)

Step-by-step explanation:

Answer:

I would say not valid

Step-by-step explanation:

well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject

Answer:

62.96%

Step-by-step explanation:

do this

51/81 ×100%

Answer:62.953%

Step-by-step explanation:

81 * (%) = 51

% = 51 / 81

% = 62.953

Answer:

59.3ft³

Step-by-step explanation:

The formula for the volume of a cylinder is V= πr²h, where r is radius and h height.

So in our case, we have r= 3ft and h=2.1 ft and π≅3.14

So from the formula for the volume of a cylinder, we get 3.14*3²*2.1 = 59.3 ft³

The volume of the cylinder is about 59.3 ft³