Find a formula for the described function. An open rectangular box with volume 3 m3 has a square base. Express the surface area SA of the box as a function of the length of a side of the base, x.

Answers

Answer 1

Answer:

[tex]SA(x) = x^2 + \frac{12}{x}[/tex]

Step-by-step explanation:

Given

[tex]V = 3m^3[/tex] --- volume

[tex]x \to base\ length[/tex]

[tex]y \to height[/tex]

Required

The surface area as a function of base length

The volume (V) is calculated as:

[tex]V = Base\ Area * Height[/tex]

[tex]V = x*x*y[/tex]

[tex]V = x^2*y[/tex]

Make y the subject

[tex]y = \frac{V}{x^2}[/tex]

Substitute 3 for V

[tex]y = \frac{3}{x^2}[/tex]

The surface area of the open box is:

[tex]SA = x^2 + 2xy+2xy[/tex]

[tex]SA = x^2 + 4xy[/tex]

Substitute: [tex]y = \frac{3}{x^2}[/tex]

[tex]SA = x^2 + 4x*\frac{3}{x^2}[/tex]

[tex]SA = x^2 + 4*\frac{3}{x}[/tex]

[tex]SA = x^2 + \frac{12}{x}[/tex]

Hence, the function is:

[tex]SA(x) = x^2 + \frac{12}{x}[/tex]


Related Questions

Struggling with these

Answers

Answer 5.5
I hope this helps

PLEASE PLEASE HELP!!!!

Find the volume of the triangular pyramid to the nearest whole number

A) 170in³
B) 340in³
C) 680in³
D) 1,020³

Answers

V=(l x w x h) / 3 ———> (10 x 12 x 17) / 3 ———> 2040/3 = 680 in^3, it’s C

Need help with this equation if anyone can respond

Answers

Answer:

120 yards is the answer to the equation

will give brainly please help now <3

Answers

Answer:

16 ounces/minute

Step-by-step explanation:

1 pound = 16 ounce

60 pound = 960 ounce

1 hour = 60 minute

960/60 = 16

Tony is building a new silo to store corn as animal feed. It will be a cylinder topped with a half-sphere, and must store 21 000 t of corn. The entire silo can be filled with corn. Tony wants to minimize the surface area of the silo to reduce materials and paint costs. He has the following information:
• 1 cubic m of corn has a mass of 700 kg.
• Building costs are $8/m2, taxes included.
• Paint comes in 3.8 L cans.
Each can covers 40 sq m and costs $35,
taxes included.
• Corn costs $140 per tonne ($140/t), taxes
included.
What is the total cost to build, paint, and fill a silo with the least surface area?

Answers

Answer:

The total bill is $6900 because 69 is a man which hair is multi colour

Please answer this will give brainliest

Answers

Answer:

A. -8

B. 23

C. 3

D. 5

Step-by-step explanation:

Mrs Gren baked a cake on her son's birthday and divided it into 12 pieces.
Serah
ate 1/3 of the cake and her son ate 1/4 of the cake.
2. How many pieces of the cake did Serah eat?
- How many pieces of the cake did her son eat?
What fraction of the cake was eaten?
What fraction of the cake was left?

Answers

Answer:

2

Step-by-step explanation:

it has 2 in the equation

1/3 of the cake = 12/3 = 4 pieces for
Serah

1/4 of the cake = 12/4 = 3 pieces for her son

Fraction of cake eaten, 4 + 3 = 7/12

Fraction left, 12 - 7 = 5/12

Help plz I’m so confused

Answers

answer is 6/7
u never multiply the bottoms only the top so it will give u 6 since theyre both negatives
-
answer = 6/7

Answer and Step-by-step explanation:

Simply multiply the numerator by the numerator, and the denominator by the denominator.

[tex]-\frac{2}{7}[/tex] × [tex]-\frac{3}{7}[/tex] = [tex]\frac{6}{49}[/tex]

#teamtrees #PAW (Plant And Water)

Easy question 34.8 + 6.879 =?

Answers

Answer: Easy Answer: 41.679

Step-by-step explanation:

PLSSSSS HELP!!!!!!!!!!

Answers

Answer:

3x-26=2x(because they are vertical angle)

or,3x-2x=26

therefore x=26

Answer:

Step-by-step explanation:

2x + (3x-26) = 90

5x = 90+26

5x = 116

x = 116/5

x = 23.2

Evaluate the expression 53 ÷ (13 − 8) × 2.

Numerical Answers Expected!

Answers

53 ÷(13-8)x2
53 ÷5x2
10.6x2
21.2
Hope this helps

Answer:

21.2

Step-by-step explanation:

BODMAS : First bracket, then Division then multiplication.

[tex]53 \div (13-8) \times 2\\53 \div 5 \times 2\\10.6 \times 2\\21.2[/tex]

Find the value of x.

Answers

Answer:

[tex]4/12=x/18[/tex]

[tex]x=4*18/12[/tex]

[tex]x=6[/tex]

--------------------------

hope it helps...

have a great day!!

I need help anyone?

Answers

Answer:

0

Step-by-step explanation:

When you substitute x=1 for f(1),

you get f(1)=0

and the absolute value of 0 is 0.

hope I answered it correct.

please give brainliest, thanks!

Find the diameter of each
circle below. If there is not
enough information, write
"cannot tell."
Find the radius of each
circle below. If there is not
enough information, write
"cannot tell."

Answers

5. 4inch
6. 6cm
7. Cannot tell
8. 50mm
9. Cannot tell
10. 1.5cm

y= 2x + 1
y = -3x +6

Solve the solution to this system of linear equations

(Please help)

Answers

Answer:

yeahh, i'm proud of you

Step-by-step explanation:

I need help with this

Answers

Answer:

Step-by-step explanation:

It was confusing

Can y’all help me on question 24?!

Answers

Answer:

C

Step-by-step explanation:

:) glad I could help! Give Brainiest answer if you can! It doesn't cost you and it would make my day! :D

Answer:

b

helpful answer to your question

Use the correct function to find the missing angle y measurement to the
nearest whole degree. Then using the checkboxes, select the function you
used, and the answer you found rounded to the nearest degree. (SELECT
2 ANSWERS - READ CAREFULLY) Work points are build into the results. *
18 in
yo
20 in.
Cos
Tan
64 degrees
Sin
42 degrees
26 degrees

Answers

Answer:

Cos;

26 degrees

Step-by-step explanation:

Recall: SOH CAH TOA

Reference angle = y°

Adjacent side = 18 in.

Hypotenuse = 20 in.

We would apply the trigonometric function CAH since we are dealing with the Adjacent side (A) and the Hypotenuse (H). Thus:

Cos y° = Adj/Hyp

Cos y° = 18/20

Cos y° = 0.9

y° = cos^{-1}(0.9)

y = 25.8419328° ≈ 26 degrees (nearest whole degree)

The answers are:

Cos and 26 degrees

2b(to the power of 2)= 2.83

Answers

Step-by-step explanation:

2b²=2.83

b²=1.415

b=1.18953

What’s the distance ?

Answers

Answer:

[tex]3[/tex]

Step-by-step explanation:

This problem asks one to find the length of the given line. Another way to think about this problem is to believe that the problem asks one to find the distance from one point to another. The endpoints on this line are the following,

[tex](4,2), (5, 5)[/tex]

The formula to find the distance between two points on a 2-dimensional coordinate plane is as follows,

[tex]D=\sqrt{(x_1-x_2)^2*(y_1-y_2)^2}[/tex]

Substitute the endpoints of the line into the formula and solve for the distance between the points,

[tex]D=\sqrt{(4-5)^2*(2-5)^2}[/tex]

Simplify, solve for the distance between the two points,

[tex]D=\sqrt{(4-5)^2*(2-5)^2}[/tex]

[tex]D=\sqrt{(-1)^2*(-3)^2}\\\\D=\sqrt{1*9}\\\\D=\sqrt{9}\\\\D=3[/tex]

A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the second row, 23 in thethird row. How many seats are there in total? Show explain all work.

Answers

Answer:

There are 54 in total because if you add them all it gets you 54

A cylindrical container has a diameter of 14 cm and a height of 10 cm, as
shown in the diagram. What is the volume of this container to the nearest
tenth of a cubic centimeter?*
14cm
10cm
1539.4
6157.5
490.0
219.9

Answers

Answer:

1539.4

Step-by-step explanation:

Steps:

Volume of a cylinder= πr²h

radius= diameter/2

         = 14/2

         = 7 cm

Volume= π x 7² x 10

            = 1539.38

            = 1539.4 cm³

Answer:

1539.4

Step-by-step explanation:

to find the area of a cylinder, you solve pi x radius²

3.14 x 7² = 153.94

then you multiply times the height

153.94 x 10 = 1549.4

What is a polygon?
a. A closed plane figure made up of line segments
b. An open plane figure made up of line segments
c. A closed plane figure made up of rays
d. An open plane figure made up of rays​

Answers

Answer:

A. A closed plane figure made up of line segments

Step-by-step explanation:

Answer:

A closed plane figure made up of line segments

What is the area of this???

Answers

9.09(m2)??
I think so

Dave wants to build a rectangular screened-in porch that is 20 feet long, and it will extend 6 feet out from the backside of his house.


Dave sketches a scale drawing of the porch. Choose a reasonable size and scale for Dave’s drawing of the porch. How should Dave label the dimensions of the model?

Answers

Answer:

Scale of the drawing would be 20/12 inch and 0.6 (6/12) inch

Step-by-step explanation:

For most of the residential buildings an scale of 1 inch = 12 feet can be used to draw the residential units.

In that case the scale of the drawing would be 20/12 inch and 0.6 (6/12) inch

Dave should label the dimensions in inches

pls plz anyone i’ll pass the class

Answers

Answer:

what's the question???

Answer:

x = 3.721

Step-by-step explanation:

Since, the triangle is right triangle, we can use trignometery equations ;

In this case, we need to use tangent equation in perpendicular :

tan θ = opposite side / adjacent side

Where , we've

opposite side = xθ , angle = 28 °Adjacent side = 7

tan 28 ° = x / 7

7 × tan 28 ° = 7 × x / 7 ..( Multiply each side by 7 )

7 × tan28° = x

Rewrite

x = 7 tan ×28°

multiply to get

x = 7 × 0.531709432

x = 3.72196602

In circle K, How would i solve this?

Answers

Hope this help!!!

Have a nice day!!!

Find the values of a through e that make these two relations inverses of each other.

Answers

Answer:

-1.4 1,0,-0.2 so this is the solution for this problem

The maximum load that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. A 9 meter column 2 meters in a diameter will support 64 metric tons. How many metric tons can be supported by a column 13 meters high and 5 meters in diameter? Round to the nearest whole metric ton

Answers

Answer:

2396

Step-by-step explanation:

Let the diameter = d

Let the height = h

Formula

Metric Tons = k * d^4 / h^2

Solution

Metric Tons = 64

d = 2

h = 9

k = ?

(You can't do the second part by not using a ratio unless you  put k in and solve for it)

64 = 2^4 k / 9^2

64 = 8 *k / 81

64 * 81 / 8 = k

5184 / 8 = k

k = 648

Solve for the second example

Metric Tons = d^4 * k / h^2

Metric Tons = ?

d = 5

h = 13

k = 648

Metric Tons = 5^4 * 648 / 13^2

Metric Tons = 625 * 648 / 169

Metric Tons = 2396 rounded.

A poll is given, showing 60% are in favor of a new building project.

If 7 people are chosen at random, what is the probability that exactly 5 of them favor the new building project?

Answers

Answer:  0.2612736

Round this value however you need to.

==================================================

Explanation:

n = 7 = sample sizep = 0.60 = probability of someone being in favork = 5 = number of people in favor

We use the binomial distribution here. The formula for that is

P(k) = (n C k)*(p)^k*(1-p)^(n-k)

where the n C k refers to the nCr combination formula

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

simply replace r with k.

------------------------------

So,

P(k) = (n C k)*(p)^k*(1-p)^(n-k)

P(5) = (7 C 5)*(0.6)^5*(1-0.6)^(7-5)

P(5) = 21*(0.6)^5*(0.4)^(2)

P(5) = 21*0.07776*0.16

P(5) = 0.2612736

This decimal value is exact (meaning there aren't any other digits after that last '6'). Round this value however you need to.

There's roughly a 26.1% chance of getting exactly 5 people to be in favor of the project.

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