A box with a square base and open top must have a volume of 97556 c m 3 cm3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x x .] Simplify your formula as much as possible.

Answers

Answer 1

Answer:

S(x)  =  x²  +  390224/x

Step-by-step explanation:

Volume of the open box  =   V  = 97556 cm³

Material needed:

Let´s call x the side of the square base then  the  area of the base is

A(b) = x²

For the sides of the box, we have 4 sides each one with area of x*h

where h is the height of the box

The volume of the box    V(b) = 97556 = x²*h   then    h  =  97556/x²

S(x,h) = x²  +  4*x*h*

The surface area of the box as function of x is:

S(x)  =  x²  + 4*x*97556/x²

S(x)  =  x²  +  390224/x


Related Questions

) A desk organizer sells for $35, which includes a markup rate of 60% based on the selling price.
a. Find the markup.
b. Find the cost.

Answers

Answer: a. $21

b. $14

Step-by-step explanation:

Selling price of desk organizer = $35

Markup rate = 60%

a. The markup will be:

= Markup rate × Selling price

= 60% × $35

= 0.6 × $35

= $21

Therefore, the markup is $21

b. The cost will then be:

Cost price = Selling price - Markup

= $35 - $21

= $14

Find the missing coordinates.

Answers

Answer:

1) (2, 1)

2) (2, -2)

3) (-1, -1)

4) (-5, -5)

Answer:

1. Pairs A(2, 5), B(6, 5), and C(6, 1)

missing coordinate is (2,1)

2. Pairs A(2, 3), B(7, 3), and C(7, -2)

missing coordinate is (2,-2)

3. Pairs A(-5, -1), B(1, -1), and C(1, -5)

missing coordinate is (-5,-5)

4. Pairs A(-1, 4), B(7, 4), and C(7, -1)

missing coordinate is (-1,-1)

Hope this is correct!! Have a nice day!!<3

lim x->1+( sin(1-x)-(e^(x-1))+1)/ lnx

Answers

We're given the one-sided limit,

[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}[/tex]

Evaluating the limand directly at x = 1 gives the indeterminate from

(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0

so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives

[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}[/tex]

kelly wants to make a box in the shape of a cube.How many pieces of wood does she need? In what shape should she cut them?

Answers

she will need 6 pieces and they must all be equal square shapes

According to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456. Use Appendix B.3. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,600 per year on reading and entertainment

Answers

Answer:

z = x-u/s

z = 2600 - 2020/456

z = 1.27

 = .897

1-.898 = .102

z > 1.27 = 10.2%

The percentage of adults spending more than $2,600 per year on reading and entertainment is 10.2%.

What is the z-score?

The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

Given that according to a government study, among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456.

The percentage will be calculated as,

z = x-u/s

z = 2600 - (2020/456)

z = 1.27

The value of z=1.27 in the table is 0.897. The percentage will be calculated as,

P = 1-.898 = .102

z > 1.27 = 10.2%

Therefore, the percentage of adults spending more than $2,600 per year on reading and entertainment is 10.2%.

To know more about z-score follow

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if a student is selected at random, find the probability that the student is 14 year old​

Answers

Answer:

If the student is selected at random the answer is if you put 14 years apart of the student selected at random means the answer are not apart.

Step-by-step explanation:

14 years selected the problem is that 14-9 is more then 9 and u add that up to get the right equation for the 14 years apart

how do you write .00057 1/2 in words​

Answers

Answer:

Step-by-step explanation:

visit the following;

https://sciencing.com/write-fractions-words-4443134.html

One difference between objects and data types is that it is usually not meaningful to compare the identities of separate instances of data types, but for objects it is valuable to compare separate object identities. Group of answer choices

Answers

Answer and explanation:

Question isn't complete but explanation is given below based on what you may be asking.

Answer and Explanation:

First, An object is a data type but is quite different from the usual or primitive data types such as string or integers. An object is based on object oriented programming(OOP) and is a sort of abstract data type which is usually defined by the programmer(some are inbuilt in the language). Objects are usually defined using classes and then become instances of those classes. Objects have identities(e.g- a dog has a name Zeus) and be compared to other objects of same class(other instances) while data types are not as well equipped to have identities, properties or methods that are user defined in order to make comparisons.

4/8 =?/2 please answer​

Answers

Answer:

? = 1

Step-by-step explanation:

4/8 = ?/2

Change the ? into a variable so it's easier to calculate:

Variable x = ?

4/8 = x/2

Cross multiply:

4 × 2 = 8 × x

8 = 8x

Divide both sides by 8 to isolate the variable:

1 = x

Check your work:

4/8 = 1/2

4 × 2 = 8 × 1

8 = 8

Correct!

1/2 Numerator and denominator are both divided by 4

Ordinary least squares estimation is subject to heterogeneity bias if _____. 答案选项组 the regression model exhibits heteroskedasticty the unobserved effect is correlated with the observed explanatory variables the regression model includes a lagged dependent variable the explanatory variables do not change over time

Answers

Answer:

Unobserved effect.

Step-by-step explanation:

The unobserved effect of heterogeneity is correlated with the observed explanatory variables. Population heterogeneity is bias in unobserved pre treatment factors which affect the outcome even without treatment.

76. In the diagram below, lines land mare
parallel. Both are intersected by
transversal t.
What is the value of x?

Answers

4x = 2x + 30 Alternate angles in parallel lines are equal
2x = 30
x = 15


Two and three fifths plus one and three fifths

Answers

Answer:

2 3 + 1 3 = 3/5 + 3/5 = 1 1/5 + 2+1 = 3 + 1 !/5 = 4 1/5

5 5

Step-by-step explanation: The Slashes mean The number bellow

Please make this answer Brainlist...

Find the area
10
7
12
4
5
5

Answers

Answer:

[tex]{ \tt{area = (7 \times 10) + (12 \times 4) + (5 \times 5)}} \\ { \tt{ = 70 + 48 + 25}} \\ { \tt{ = 143 \: {in}^{2} }}[/tex]

Answer: break into 2 rect and 1 sqr the sum areas of each

Step-by-step explanation: square = 5x5

Rectangle 1 = 10x7

Rectangle 2 = 12x4

Sum each shape area = total area

Ethan is 1.6 metres tall, Uzma is 154 cm tall.
Work out how much taller Ethan is than Uzma.

Answers

Answer:

1.6 metres is 160 centimetres

Ethan is 6 centimetres taller than Uzma

There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)

Answers

Answer:

3 1/3 each

Step-by-step explanation:

10/3=3 1/3

0.3 liters each student

3 liters = 3.000 ml so 3.000(ml) : 10(students) =300 ml which is 0.3 liters

was the expression a^2-b^2 = (a+b)(a-b) invented or discovered?

Answers

Answer:

the expression is invented

I would say it was discovered.
Expanding (a + b)(a - b)
= a(a - b) + b(a - b)
= a^2 - ab + ba - b^2
= a^2 - b^2
So factorising the difference between two squares simply reverses the equation

Based on the areas of the squares, determine whether the triangle shown is a right triangle.

Answers

It is not a right triangle

Explanation:
Pythagorean Theorem ONLY for right triangles: a^2+b^2=c^2
If a^2=58 and b^2=10
Then 58+10 does not equal 64

The given triangle is not a right-angle triangle as the sides don't form a Pythagorean triplet.

What is the Pythagoras theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the le right triangle is equal to the square on the hypotenuse (the Pythagoras the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given her:  Three squares whose sides form one Pythagoreans of a triangle .

Now a²=58

b²=10

b=√10

c²=64

c=8

Clearly √10<√58<8

Thus c must be the hypotenuse of the triangle.

Using Pythagoras' theorem we get

√10²+√58²=68≠64

Hence, The given triangle is not a right angle triangle as the sides don't form a Pythagorean triplet.

Learn more about the Pythagoras theorem here:

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Find the area and circumference of a circle with a radius of 13cm. ::note:: answers can be written in decimal form to the nearest hundredth (for example, 9.42) or in terms of pi (for example if you wanted to say 3π
you could write 3 pi--the pi symbol is not available to Area=

Circumference=

Answers

Answer:

14cm

Step-by-step explanation:

Answer:

28 cm2

14 cm

Step-by-step explanation:

Give the answer in its simplest form

Answers

Answer:

1/52

Step-by-step explanation:

as there is only one of the three of clubs,

total possible outcomes= 52

favourable outcome= 1

P(getting a three of clubs) = total outcome/ favourable outcome

= 1/52

hope this helps

Use the diagram to estimate the perimeter, rounding each number to the nearest hundred.

A parallelogram is shown. Two sides are labeled 5,534 feet. The other two sides are labeled 1,566 feet.


14,200 feet


16,000 feet


14,400 feet


14,000 feet

Answers

Answer:

14,000 feet.

Step-by-step explanation:

A parallelogram has 4 total sides and the opposite sides are characterized as having the same length. Therefore, If we are provided the lengths of two adjacent sides we can easily calculate the perimeter by multiplying these provided lengths by 2 and then adding them together. Since we are asked to round each number to the nearest hundred, it would be the following...

(5,500 * 2) + (1,500 * 2) = x

11,000 + 3000 = x

14,000 = x

Finally, we can estimate that the perimeter of the parallelogram is 14,000 feet.

Which expression represents the product of (3x+5) with (2x-3)

Answers

Answer:

[tex]6x^2-x+15[/tex]

Step-by-step explanation:

(3x + 5)(2x - 3) = [tex]6x^2-9x+10x-15=6x^2+x-15[/tex]

Activity IB. FIND ME!
Find the area of each circle. Use = 3.14
3.
1.
2.
om
13cm
19in.
5.
33cm
25cm
yan paki sagot​

Answers

1 “113.04m²”
2 “530.66m²”
3 “1133.54in²”
4 “854.865cm²”
5 “1962.5cm²”
Hope it helps :)

CGB=79 the what is DGB

Answers

Answer:

101

Step-by-step explanation:

Angles 1 and 2 together equal 180, Angle 1 is 79 therefore

180 = Angle 1 + Angle 2

180 = 79 + Angle 2

180 - 79 = Angle 2

101 = Angle 2

How to solve the inequality 8x + 10 ≤ 60

Answers

Answer:

x ≤ 6.25

Step-by-step explanation:

8x + 10  ≤  60

Subtract 10 from both sides

8x ≤ 50

Divide both side by 8

x ≤ 6.25

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

write an equation of the line below ​

Answers

I think the equation is y= -x - 4

Explanation:

The two given coordinates are (0,-4) and (4,-7).

Use those to find the slope which is -1

Then use the slope intercept form and substitute the answers where they belong.

y - y1 = m(x - x1)

y - (-4) = -1 (x - 0)

y = -x - 4

Find the perimeter of the triangle whose vertices are the following specified (0,3), (-10,-4) (-9,-7) points in the plane.

Answers

Answer:

The perimeter of the triangle is 28.82

Step-by-step explanation:

Please check the image uploaded for the diagram.

Perimeter = d₁ + d₂ + d₃

[tex]d_1 = \sqrt{(-10-0)^2 + (-4-3)^2} = \sqrt{100+49} =\sqrt{149} = 12.21\\\\d_2 = \sqrt{(-9-0)^2 + (-7-3)^2} = \sqrt{81+100} =\sqrt{181} = 13.45\\\\d_3 = \sqrt{(-10+9)^2 + (-4+7)^2} = \sqrt{1+9} =\sqrt{10} = 3.16\\\\Perimeter = 12.21 + 13.45 + 3.16 = 28.82[/tex]

Three rectangular prisms each have a height of 1 cm.
. Prism A has a base that is 1 cm by 11 cm
* Prism B has a base that is 2 cm by 7 cm SA +V
Prism C has a base that is 3 cm by 5 cm.
1. Find the surface area and volume of each prism. Use the dot paper to draw the prisms, if needed.

Answers

Answer:

A: SA = 46 cm^2; V = 11 cm^3

B: SA = 46 cm^2; V = 14 cm^3

C: SA = 46 cm^2; V = 15 cm^3

Step-by-step explanation:

SA = 2B + PH = 2LW + PH

where SA = total surface area,

B = area of a base

P = perimeter of the base

H = height of the prism

L = length of the base

W = width of the base

V = LWH

Prism A:

SA = 2(11 cm)(1 cm) + 2(11 cm + 1 cm)(1 cm)

SA = 46 cm^2

V = (11 cm)(1 cm)(1 cm) = 11 cm^3

Prism B:

SA = 2(7 cm)(2 cm) + 2(7 cm + 2 cm)(1 cm)

SA = 46 cm^2

V = (7 cm)(2 cm)(1 cm) = 14 cm^3

Prism C:

SA = 2(5 cm)(3 cm) + 2(5 cm + 3 cm)(1 cm)

SA = 46 cm^2

V = (5 cm)(3 cm)(1 cm) = 15 cm^3

please help step by step, please

Answers

9514 1404 393

Answer:

title: 300%payday: 650%check cashing: 214%

Step-by-step explanation:

The formula for simple interest is ...

  I = Prt

where P is the principal amount loaned, r is the annual rate, and t is the time in years. Solving for interest rate, we get ...

  r = I/(Pt)

We assume 12 months or 52 weeks in a year.

__

Car title loan

  r = 125/(500×1/12) = 3 × 100% = 300%

The APR is 300%.

__

Payday loan

  r = 125/(500×2/52) = 6.5 × 100% = 650%

The APR is 650%.

__

Check cashing

  r = 19.66/(478.41×1/52) ≈ 2.1369 × 100% ≈ 214%

The APR is about 214%.

Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.


sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction

Answers

Answer:

Sin(E) = 7/25

Sin(D) = 24/25

Tan(D)= 24/7

Step-by-step explanation:

Sin=opp/hyp

Tan=opp/adj

Cos=adj/hyp

The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

How to determine the trigonometric ratios?

The given parameters are:

EF = 24

DF = 7

Start by calculating the length DE using:

DE²= EF² + DF²

So, we have:

DE²= 24² + 7²

Take the square root of both sides

DE= 25

The sine of the angles is calculated using:

sin(Ф) = opp/hyp

So, we have:

sin(E) = 7/25

sin(D) = 24/25

The tangent of the angles is calculated using:

tan(Ф) = opp/adj

So, we have:

tan(D)= 24/7

Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

Read more about trigonometric ratios at:

https://brainly.com/question/11967894

According to a survey, 57% of all workers read e-mail while they are in a meeting. Suppose that 19% of those who read e-mail while they are in a meeting write down important notes. Assuming that these figures are true for all workers, if a worker is randomly selected, what is the probability the worker reads e-mail while in meeting and writes important notes

Answers

Answer:

The probability will be "10.83%".

Step-by-step explanation:

According to the question,

Workers read e-mail,

= 57%

= 0.57

Write down important notes,

= 19%

= 0.19

Now,

The probability of worker who reads e-mail while in meeting and writes important notes will be:

= [tex]P[email \ reading \ during \ meeting]\times P[writes \ important \ notes][/tex]

By putting the values, we get

= [tex]0.57\times 0.19[/tex]

= [tex]0.1083[/tex]

= [tex]10.83[/tex] %

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