1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zolol [24]
3 years ago
12

A storage box with a square base must have a volume of 90 cubic centimeters. the top and bottom cost $0.60 per square centimeter

and the sides cost $0.30 per square centimeter. find the dimensions that will minimize cost. (let x represent the length of the sides of the square base and let y represent the height.
Mathematics
2 answers:
Assoli18 [71]3 years ago
8 0

Answer:

side length of 3.56 cm and height of 7.10 cm

Step-by-step explanation:

Paul [167]3 years ago
4 0

<u>Answer-</u>

<em>For </em><em>side length of 3.56 cm</em><em> and </em><em>height of 7.10 cm</em><em> the cost will be minimum.</em>

<u>Solution-</u>

Let us assume that,

x represents the length of the sides of the square base,

y represent the height.

Given the volume of the box is 90 cm³, so

\Rightarrow V=90\\\\\Rightarrow x^2\times y=90\\\\\Rightarrow y=\dfrac{90}{x^2}

As the top and bottom cost $0.60 per cm² and the sides cost $0.30 per cm². Total cost C will be,

C=\text{cost for top and bottom}+\text{cost for rest 4 sides}\\\\=(2x^2\times 0.6)+(4xy\times 0.3)\\\\=(2x^2\times 0.6)+(4x\times \frac{90}{x^2}\times 0.3)\\\\=1.2x^2+ \dfrac{108}{x}

Then,

C'=\dfrac{d}{dx}(1.2x^2+ \dfrac{108}{x})=2.4x-\dfrac{108}\\\\C''=\dfrac{d^2}{dx^2}(1.2x^2+ \dfrac{108}{x})=2.4+\dfrac{216}{x^3}

As C'' has all positive terms  so, for every positive value of x (as length can't be negative), C'' is positive.

So, for minima C' = 0

\Rightarrow 2.4x-\dfrac{108}{x^2}=0\\\\\Rightarrow 2.4x=\dfrac{108}{x^2}\\\\\Rightarrow x^3=\dfrac{108}{2.4}=45\\\\\Rightarrow x=3.56

Then,

y=\dfrac{90}{x^2}

y=\dfrac{90}{3.56^2}

y=7.10

Therefore, for side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

You might be interested in
A textbook store sold a combined total of 274 psychology and biology textbooks in a week. The number of psychology textbooks sol
Shalnov [3]

Answer:176 psychology textbooks and 98 Biology textbooks were sold.

Step-by-step explanation:

Let x represent the number of psychology textbooks that were sold.

Let y represent the number of biology textbooks that were sold.

textbook store sold a combined total of 274 psychology and biology textbooks in a week. This means that

x + y = 274 - - - - - - - - - - -1

The number of psychology textbooks sold was 78 more than the number of biology textbooks sold. This means that

x = y + 78

Substituting x = y + 78 into equation 1, it becomes

y + 78 + y = 274

2y = 274 - 78

2y = 196

y = 98

x = y + 78 = 98 + 78

x = 176

6 0
3 years ago
Read 2 more answers
How many times can 9 go into 65
Rashid [163]
I think the answer is 7. 
8 0
3 years ago
Read 2 more answers
The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan
Crank

Answer:

<h3>2x + 5y = –15.</h3>

Step-by-step explanation:

We are given coordinates of the line passed through (–5, –1) and (10, –7) .

Applying slope formula,

Slope=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:-7\right)

Therefore,

m=\frac{-7-\left(-1\right)}{10-\left(-5\right)}

m=-\frac{2}{5}

Therefore, slope is m=-\frac{2}{5}.

Applying point-slope form y-y_1=m(x-x_1), we get

y+7 = -\frac{2}{5}(x-10)

y+7=-\frac{2}{5}(x-10)

On multiplying both sides by 5, we get

5(y+7)=5\times-\frac{2}{5}(x+1)

5y+35=-2(x-10)

5y+35=-2x+20

Adding 2x on both sides, we get

5y+25+2x=-2x+20+2x

2x+5y+35=20

Subtracting 35 from both sides, we get

2x+5y+35-35=20-35

2x+5y=-15.

Therefore, required equation is :

<h3>2x + 5y = –15.</h3>
6 0
3 years ago
What is the range of the following set? (-2,4), (0,3), (1,6), (-1,2)
Snowcat [4.5K]

Answer:

  d.  (4,3,6,2)

Step-by-step explanation:

The list of <em>second numbers</em> of the ordered pairs is the <em>range</em>.

___

The second number of the first pair is 4; the second number of the second pair is 3. The only 4-number answer choice containing these two numbers is (d). You don't even have to work the whole problem to make the proper choice.

8 0
3 years ago
How do you solve 4•(4y/3-2) + 3y = 17
Hunter-Best [27]
Us photo math , it show u even the steps of how was it solve
6 0
3 years ago
Other questions:
  • Can someone please answer my question please answer it correctly please show work please I need please help
    6·1 answer
  • “One third of a number is 12 less than the <br> number itself”
    15·1 answer
  • Help please! (Explanations are preferred, since I have to know how to do this for a test)
    5·1 answer
  • The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 com
    15·1 answer
  • Describe the steps required to determine the equation of a quadratic function given its zeros and a point.
    9·1 answer
  • Explain how many cupcakes Jasmine can make if she had 5 1/4 cups of frosting but needs 3/8 cups for each cupcake
    12·1 answer
  • Help ill give extra poihts
    13·1 answer
  • What is a positive integer? what is a negative integer?.
    10·2 answers
  • I need help with a assignment on McGrawhill pls help its due soon
    12·2 answers
  • Claire tried to evaluate an expression step by step.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!