examples of one solution

A rectangular container with a square base, an open top, and a volume of 4,000 cm³. The minimum surface for the container is 1,200 cm².

The result is obtained by using the derivative.

These are the specified parameters:

Volume container is 4,000 cm³.

Let side of square base = a, and height of the container = h, so:

Volume = a × a × h

4,000 = a² h

       h = [tex]\displaystyle \frac{4000}{a^2}[/tex]     ... (1)

Surface area with a square base, an open top is area of a square + 4 times the vertical side.

Surface area (A) = a² + 4ah

Substitute the value of h = [tex]\displaystyle \frac{4000}{a^2}[/tex] into surface area.

A = a² + 4ah

A = a² + 4a ([tex]\displaystyle \frac{4000}{a^2}[/tex])

A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]

So that the surface area is minimal, when the derivative and equate to 0.

A = a² + 16000 a⁻¹

A' = 0

2 a²⁻¹ + (-1) 16000 a⁻¹⁻¹

2a - 16000 a⁻²  = 0

2a - [tex]\displaystyle \frac{16000}{a^2}[/tex] = 0

2a = [tex]\displaystyle \frac{16000}{a^2}[/tex]

2a³ = 16000

 a³ = [tex]\displaystyle \frac{16000}{2}[/tex]

 a³ = 8000

 a = ∛8000

 a = 20

Surface area with a square base, an open top.

Substitute the value of a = 20

A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]

A = 20² + [tex]\displaystyle \frac{16000}{20}[/tex]

A = 400 + 800

A = 1200

The minimum surface for the container is 1,200 cm².

Learn more about other the derivative here:

brainly.com/question/200158

#SPJ4

If there are four consecutive odd integers such that five times the second number minus twice the fourth number is the third number subtracted by 252 then the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.

What are consecutive integers?

Whole numbers that follow each other without gaps are known as consecutive integers.

For example, the numbers 15, 16, and 17 are all consecutive integers.

If 'n' is an integer, then the following consecutive integers begin at n, n+1, n+2, n+3, and so on.

Let x be the 1st of the four consecutive integers.

the other three consecutive integers could be

(x + 1) , (x + 2), and (x + 3).

By using the given conditions, we get

From the question,

(x + 1) = (5 * (x + 2)) - (x + 3)

Expand, and subtract like terms:

x + 1 = 5x + 10 - x - 3.

Simplifying the above expression, we get

x + 1 = 4x + 7.

3x = -6.

x = -2.

Hence, the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.

To learn more about the consecutive integers, visit:

https://brainly.com/question/24415977

#SPJ1

Percentage discount is 11.36%

Given in question,

Marked price = MP = $2200

Selling price = SP = $1950

Discount = D

               = MP - SP

               = 2200 - 1950

               = 250

Discount % = (D/MP)*100

                   = (250/2200)*100

                   = 250/22

                   = 11.36

Hence, discount percent is 11.36%.

To learn more about discount here:

https://brainly.com/question/3541148

#SPJ1  

Answer:

24

Step-by-step explanation:

let the starting number be x

she sold 1/2 x and has 1/2 x remaining with her

she bought 13 and has 25 now

so, 1/2x + 13 = 25

1/2 x= 25-13 = 12

hence x= 24

Answer:

    24

Step-by-step explanation:

now Mei has 25 stamp collections after adding 13 more to what she remained with after selling; this means that after selling she was left with (25_13)=12

this is the half of what she had initially

this means that she initially had (12*2)=24

this gives means that she started with 24 as a stamp of her collection

The coordinates (4, 0) and (3, -1) represents the solution of the function f(x).

According to the question -

y = f(x) = x - 4

Case 1 : P(4, 0)

0 = 4 - 4 = 0

P (4, 0) represents a solution

Case 2: P (3, -1)

-1 = 3 - 4 = -1

P (3, -1) represents a solution

Answer: $350

Reason: 10% of $350 is $35.

[tex]\frac{5}{2}x+\frac{1}{4} +\frac{3}{4} x=\frac{1}{8} \\\\\frac{5}{2}(8)x+\frac{1}{4} (8)+\frac{3}{4}(8) x=\frac{1}{8}(8)\\20x+2+6x=1\\20x+6x=1-2\\26x=-1\\\frac{26x}{26} =\frac{-1}{26} \\x=-\frac{1}{26}[/tex]

The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation rule,

(x,y) → (x+8,y+7)

The next translation is (x,y) → (x-5,y+5)

The resultant translation will be,

(x,y) → (x+8,y+7) to (x+8-5,y+7+5)

⇒ (x+3,y+12)

Hence "The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12)".

To learn more about the transformation of graphs,

brainly.com/question/3099136

#SPJ1

Answer:the geometric mean is the product of all the numbers in a set, with the root of how many numbers there are.

here, there are two numbers, so a square root is used.

geometric mean of

3

and

12

:

√

3

⋅

12

3

⋅

12

=

36

√

36

=

6

the value of the geometric mean of

3

and

12

is

6

.

Step-by-step explanation:

Answer:y=mxb

Step-by-step explanation:

Answer:

The equation is: y = 5x - 268

The conditional relative frequency that a female prefers running is 0.36

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data

The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :

all females

all people preferring cycling

the way it was phrased I would say the reference is all females.

the conditional relative frequency is then

0.15 / 0.46 = 0.326

Hence the conditional relative frequency that a female prefers running is 0.36

To learn more on Statistics click:

https://brainly.com/question/14259577

#SPJ1

Answer:

Step-by-step explanation:

Dont listen to the above the answer is acually 58

The representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

In this question, we have been given an equation y = 3x + 1

We need to find the correct representation  of given equation.

For x = 0,

y = 3(0) + 1

y = 1

For x = 2,

y = 3(2) + 1

y = 7

for x = -1,

y = 3(-1) + 1

y = -2

This means, the options A, B and C are incorrect.

Therefore, the representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ1

If  they were 70 more cheeseburgers sold than hamburgers. The number of hamburgers  that were sold on Tuesday​ is 225.

Total of 603 hamburgers and cheeseburgers = x+y= 520

70 more cheeseburgers than hamburgers = y=x+70

Hence,

x+y= 502

y=x+70

Substitution

x+(x+70)= 520

2x+70 = 520

  -70    -70

2x= 450

2    2

x=225 hamburgers

Number of cheeseburgers

Substitute  x in either equation.

y=x+ 70

y=225 +70

y=295 cheeseburgers

Therefore 225  hamburgers was sold.

Learn more about number of hamburgers sold here:https://brainly.com/question/28355089

#SPJ1

Answer:

statement 1 is true

statement 2 is true

statement 3 is false

statement 4 is false

statement 5 is also false cause parallelogram has 2 pair of congruent sides

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

The given coordinate points are {(1, 2), (-2, 2), (5, 2), (4, 2)}.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A) {(1, 2), (-2, 2), (5, 2), (4, 2)}

It is a function as every input has a single output.

So, 1, -2, 5 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 5, 4} and range ={2}

B) {(7, 8), (7, 9), (7, 10), (7, 11)}

Since the element 7 corresponds to four different images i.e., 8, 9, 10 and 11. So, this relation is not a function.

C) {(0,0)}

It is a function as every input has a single output.

So, 0 is the element of the domain of the given relation.

Here domain ={0} and range ={0}

D) {(1, 4), (-2, 8), (2, 2), (4, 9)}

It is a function as every input has a unique output.

So, 1, -2, 2 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 2, 4} and range ={4, 8, 2, 9}

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ1

The measure of one of its angle is 150°

A Polygon is a two-dimensional closed figure made up of line segments (not curves). Polygon is a combination of two words, poly (which means many) and gon (which means shape) (means sides). To create a closed figure, at least three line segments must be connected end to end.

Given that

12 sided regular polygon

We can use the following formula to calculate the total number of degrees in any shape:

(n−2)⋅180

[Where n = number of sides]

(12−2)⋅180

(10)⋅180

=1800

So a 12-sided polygon has 1800 degrees. To calculate the measure of one angle, divide the total number of degrees (1800) by the number of sides, n.

(1800/12) = 150°

Therefore the measure of one of its angle is 150°

To learn more about polygons visit

https://brainly.com/question/10441863

#SPJ1

Answer:

a) [tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]

b) [tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]

Step-by-step explanation:

From the given equations to find, we are differentiating function G with respect to V out. Therefore, we will be only using the equation (6):

[tex]\displaystyle{G=20\log (10V_{\text out})}[/tex]

Here’s a fresh-up reminders for logarithmic differentiation formula:

[tex]\displaystyle{f(V)=a\log_b V \to f'(x)=\dfrac{a\cdot V'}{V\ln b}}[/tex]

Note that V' means to derive or differentiate the V-term

Therefore, in this scenario, our values of term are:

Therefore, we can apply differentiation formula:

[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot \dfrac{d(10V_{\text out})}{dV_{\text out}}}{10V_{\text out}\ln 10}}[/tex]

Simplify:

[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot 10}{10V_{\text out}\ln 10}}\\\\\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]

And we have finished the part a. On part b, we just differentiate the answer from part a again, the second part is to obtain the second derivative which is to derive the first derivative. Therefore:

[tex]\displaystyle{\dfrac{d^2G}{dV_{\text out}^2} = \dfrac{d\left(\dfrac{20}{V_{\text out}\ln 10}\right)}{dV_{\text out}}}[/tex]

First, separate the constant every time when you have to differentiate a function:

[tex]\displaystyle{\dfrac{20}{\ln 10}\cdot \dfrac{1}{V_{\text out}}}[/tex]

Differentiate 1/V out: recall the formula of fraction:

[tex]\displaystyle{f(V)=\dfrac{1}{V} =V^{-1} \to f'(x)=-V^{-2} = -\dfrac{1}{V^2}[/tex]

The formula above is derived from power rules formula where:

[tex]\displaystyle{f(V)=V^n = nV^{n-1}}[/tex]

Therefore, from the function of V out:

[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(\dfrac{1}{V_\text{out}}\right)'}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (V_\text{out})^{-1}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (-V_\text{out})^{-2}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(-\dfrac{1}{V_\text{out}^2}\right)}[/tex]

Simplify to latest as we get:

[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]

Please let me know if you have any questions!

aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters

this is an arithmetic sequence whose n th term ( explicit formula) is

aₙ = a + (n - 1 )d

where d is the common difference and  a the first term

The given sequence is 12,10,8,6

twelve comma ten comma eight comma six

d=10-12=-2

a=12

Apply in explicit formula

aₙ = 12+ (n - 1 )(-2)

aₙ = 12-2n +2

aₙ = 14- 2n

Hence aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

As given in the question,

For the given rectangular playpen,

Perimeter of rectangular playpen is equal to 150 feet .

Area of the rectangular playpen is equal to at least 1,000 squared feet .

Area = length × width

Let x be the length of the rectangular playpen .

Then its width is equal to 1000 / x.

Substitute the value of length and width in perimeter we get,

Perimeter of rectangular playpen = 2 ( length + width )

⇒ 150 = 2 [ x + (1,000/x)]

⇒ 150 / 2 = ( x² + 1,000 ) / x

⇒ x² + 1000 = 75x

⇒ x² -75x + 1,000 =0

Simplify quadratic equation using discriminant we get,

x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)

⇒ x = (  75 ± √5625 - 4000) /2

⇒ x = (75 ± 40.31) / 2

⇒ x = 57.66 or 17.35

Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

Learn more about perimeter here

brainly.com/question/6465134

#SPJ4

Answer:

Step-by-step explanation:

The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.

A salad dressing is made by mixing yoghurt and mayonnaise in the ratio

3:5. For 800 ml of salad:

Amount of yoghurt = (3 / (3 + 5)) * 800 ml = 300 ml

The amount of yoghurt that Karolina used when making 800 ml of salad is 300 ml.

The slope is 6.25, it means that her day pay increases by $6.25 for each computer sold

A general linear equation in the point-slope form is written as:

y = a*x + b

Where y and x are the two variables, a is the slope, and b is the y-intercept.

In this case, the linear equation is:

P(x) = 6.25*x + 75

We know that P(x) represents her pay, and x represents the amount of computers she sold.

Here we can see that the slope is 6.25, it means says how much her pay increases per computer sold.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

 (a)

  [tex]\left[\begin{array}{cc}20&80\\32&3\end{array}\right][/tex]

Step-by-step explanation:

You want the product of the given 2×2 matrices.

The value at any given (row, column) of the result matrix is the dot product of the corresponding row of the first matrix with the corresponding column of the second matrix.

For example, row 2 column 1 of the result will be the dot product of row 2 of the left matrix with column 1 of the right matrix:

  [-2, 3]·[-4, 8] = (-2)(-4) +(3)(8) = 8 +24  = 32

This is sufficient to identify the first answer choice as the correct one.

__

Additional comment

A suitable calculator can compute the entire product for you, as in the attachment.

Answer:

the amount of birdseed leftover is 32

Step-by-step explanation:

Form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.

As given in the question,

Probability distribution established by baker :

    x :       1               2                3              4

P(x) :       0.10        0.30         0.40          0.20

As it is give that number of batches made by baker to sell muffins .

For selling 1 batch x = 1.

For selling 2 batch x = 2.

For selling 3batch x = 3.

For selling 4 batch x = 4

Probability of selling exactly one batch by baker is given by when x =1

Probability of x  = 1 is given by :

P( x = 1 )  = 0.10

Therefore, form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.

The complete question is :

A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.10 2 0.30 3 0.40 4 0.20 What is the probability the baker will sell exactly one batch.

Learn more about probability here

brainly.com/question/11234923

#SPJ1

one example of terminating decimal and one repeating decimal between -1/2and -1/3

terminating decimal = -2/5

repeating decimal = -3/11

A decimal with an end digit is referred to as a terminating decimal. It is a decimal with a limited number of digits.

examples of terminating decimal are

When a number's digits are periodic and its indefinitely repeated portion is not zero, the representation of that number as a decimal is said to be repeating or recurring.

Examples of a repeating decimal are

Learn more about decimal here:

https://brainly.com/question/29401139

#SPJ1

Answer:

1) 112°

3) 55°

4) 51°, complementary angles

Step-by-step explanation (question one):

3x +10 +2x = 180

3x +10 +2x -10 = 180 -10

3x + 2x = 170

5x = 170

x = 34

3(x)+10 = angle ABD

3(34)+10 = angle ABD

102+10 = angle ABD

angle ABD = 112°

Step-by-step explanation (question two):

180 -70 = 2x

110 = 2x

55 = x

angle SQT = 55°

Step-by-step explanation (question three):

Since it's a right angle, we can simply subtract.

90 -39 = 51

angle b = 51°

I wish you luck on your homework!

Explanation: Please give brainly if it's right!

First move all the x and y values on one side, and the constants on the other:

-x² + y = − 1

-x² - y = -7

Multiply -1 to the 2nd equation to change signs and then solve:

-x² + y = − 1

+x² + y = +7

2y = 6

y = 3

Plug in y to either equation (I plug into the first one)

-x² + 3 = − 1

-x² = -4

x = 2

Answer: Neither

Step-by-step explanation: