A container manufacturer plans to make rectangular boxes whose bottom and top measure 4x by 3x. The container must contain 48in.3 The top and the bottom will cost $1.80 per square inch, while the four sides will cost $3.70 per square inch.

What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.

Answers

Answer 1

The height of the container that will be able to minimize the cost will be 3.08cm.

How to calculate the height?

The volume of the box will be:

= (3x)(4x)h

= 12x²h

From the information given, we are told that the container must contain 48in³. Therefore,

48 = 12x²h

h = 4/x²

The function cost will be:

= 3.50(2)(12x²) + 4.40(14x)h

= 84x² + 61.6x(4/x²)

= 84x² + 246.4/x

We'll use the first derivative. This will be:

dC/dx = 168x - 246.4/x²

x = 1.14.

Therefore, the height will be:

h = 4/x² = 4/1.14² = 3.08cm

In conclusion, the height is 3.08cm.

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Related Questions

investigue sobre 6sistemas diferentes​

Answers

Answer:

this is broken english

Step-by-step explanation:

ok ok

Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
Answer correctly you get brainliest.

Answers

Answer:

Step-by-step explanation:

44/8

= 5 whole 4 by 8

= 5 4/8

Answer:

5/2 = 2.5

Step-by-step explanation:

what is the 41st term of 8,17,26

Answers

Answer:

368

Step-by-step explanation:

We can see that 9 is being added to each term.

Thus, we obtain the following rule:

8 + 9(x - 1)

To make this easier, let's simplify the rule.

⇒ 8 + 9(x - 1)⇒ 8 + 9x - 9⇒ 9(x) - 1

Substitute 41 as "x" to obtain the 41st term:

⇒ 9(41) - 1⇒ 368

The value of 41st term of sequence 8, 17, 26 is,

⇒ 368

What is Arithmetic sequence?

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

Given that;

The sequence is,

⇒ 8, 17, 26.

Now, The common difference is,

⇒ d = 17 - 8 = 9

⇒ d = 26 - 17 = 9

Thus, The sequence is in arithmetic.

Hence, The value of 41st term of sequence 8, 17, 26 is,

⇒ a + (n - 1)d

⇒ 8 + (41 - 1) 9

⇒ 8 + 369 - 9

⇒ 8 + 360

⇒ 368

Thus, The value of 41st term of sequence 8, 17, 26 is,

⇒ 368

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Mr. Ketchum collets Pokémon cards. He purchases a rare charizard Pokémon card for $525. Research shows this card value will increase by 3.5% each year. Write an equation that determines the value,v,of the card t years after purchase

Answers

Answer:

18.37500

Step-by-step explanation:

Here You Go! Hope It Helps Bud

answer the question below. Type your response in the space provided What is the height of the cylinder in the diagram? Round your answer to the nearest whole V = 904.78 cm³ 6cm​

Answers

Answer:

For this question, we use the formula for the volume of a cylinder.

(formula for vol. of cylinder)

V = π[tex]r^{2}[/tex]h

Where 'π' represents pi(22/7 or 3.14), 'r' represents the radius which is being squared, and 'h' stands for the height.

We utilize the information that we know:

Radius = 6cmVolume = 904.78

Which we then plug into our equation(volume of cylinder formula):

V = π[tex]r^{2}[/tex]h

904.78 = 3.14(6^2) · h

Next solve for the h(height).

904.78 = 3.14(36) · h

904.78 = 113.04 · h

904.78 = 113.04h

/113.04     /113.04

8.00406935598 = h, which we round to 8.

8 centimetres is the height of this cylinder.

9-18.
Thui wrote the following inequalities for a problem that she was solving: 2n-1<5 or 2n-1 > -5. Which of the following statements is
true? Homework Help
a. n >-3 or n <3
b. n 2-2 or n <3
C. > -3 or n <3
d. n > -2 or n <3

Answers

Answer:

D is the correct answer

Step-by-step explanation:

2n-1<5= n<3

2n-1>-5= n>-2

I am having trouble with this problem

Answers

Answer:

b=330.90 and c=314.97

Step-by-step explanation:

b=245×sin71.2/sin44.5. c=245×sin64.3/sin44.5. you get the 64.3 by subtracting 180_(71.2+44.5)

Solve the following:

one and two fourths plus three and three fourths

Answers

Answer:

5 and 1/4 is the answer to your problem

Step-by-step explanation:

Answer:

[tex]\frac{21}{4}[/tex] or  [tex]5 \frac{1}{4}[/tex]

Step-by-step explanation:

[tex]1 \frac{2}{4} + 3 \frac{3}{4}\\[/tex]

First, I would convert them into improper fractions. To convert [tex]1 \frac{2}{4}[/tex], I would do 1 x 4 = 4, then + 2 = 6

To convert [tex]3 \frac{3}{4}\\[/tex] , I would do the same: 3 x 4 = 12 + 3 = 15

That leaves us with [tex]\frac{6}{4}[/tex] + [tex]\frac{15}{4}[/tex]

All we have to do is add the numerators (top numbers) so

6 + 15 = 21

Answer = [tex]\frac{21}{4}[/tex]

or, as a mixed number, [tex]5 \frac{1}{4}[/tex]

Hope this makes sense. If you require any further explanation, feel free to ask..

- profparis

If I helped you, I would appreciate a brainliest :D

A student’s height was 61 inches at the beginning of the year. At the end of the year it was 64 inches. What was his percent increase? Round to the nearest tenth of a percent.

Answers

Answer:

4.9% increase

Step-by-step explanation:

Starts at 61 inches

Ends at 64 inches

64 - 61 = 3 inches increase

percent of 3 to 61

3 / 61

≈ 0.49

= 4.9%

The table below gives the height h=f(t) in feet of a weight on a spring where t is time in seconds.
t (sec) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
h (feet) 4.8 6.6 7.6 7.8 7.6 6.6 4.8 3 2 1.8 2 3 4.8 6.6 7.6 7.8
what is the period

Answers

Using it's concept, it is found that the period of the function is of 20 seconds.

What is the period of a function?

The period of a function is given by the distance between it's repetitions.

In this problem, the function starts at 0s, with 4.8 ft, then in intervals of 2s, the heights are of 6.6 ft, 7.6 ft, 7.8 ft and so on. The same pattern starts again after 20 seconds.

Hence, the period of the function is of 20 seconds.

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4. Find the surface area of the triangular prism:
5 ft
5 ft
3 ft
14 ft
8 ft
Shows work please

Answers

Answer:

  276 ft²

Step-by-step explanation:

The total surface area of a prism is the sum of its lateral area and the area of its bases. Here, the bases are two triangles, and the area of the sides is that of three rectangles.

base area

The area of a triangle is given by the formula ...

  A = 1/2bh . . . . where b is the base of the triangle, h is its height

We have two identical triangles, so their total area will be ...

  A = 2(1/2bh) = bh = (8 ft)(3 ft) = 24 ft²

lateral area

The sides of the prism are rectangles, all with the same length: 14 ft. Their total area will be that length multiplied by the total of the rectangle widths. That total is the same as the perimeter of the triangular base:

  P = 5 ft + 5 ft + 8 ft = 18 ft

Then the lateral area is ...

  lateral area = Ph = (18 ft)(14 ft) = 252 ft²

total area

The sum of the base area and lateral area is ...

  (24 ft²) +(252 ft²) = 276 ft² . . . . area of the triangular prism

can i have some help? subject is stretching and reflecting quadratic functions

Answers

Answer:

(5,5)

(-3,-15)

(6,-12)

(-2,8)

Step-by-step explanation:

Multiply the value of "a" with the coordinates.

#1

(1,1) and a=5

y=ax²

y=5(1)²y=5

Coordinates (1,5)

#2

(5,25) and a=-0.6

So

y=-0.6(5)²y=-0.6(25)y=-15

Coordinates (5,-15)

#3

(-2,4) and a=-3

So

y=-3(-2)²y=-3(4)y=-12

Coordinates (-2,-12)

#4

(-4,16) and a=1/2

So

y=1/2(-4)²y=16/2y=8

Coordinates (-4,8)

Find the area of the parallelogram 9.9in 5.5in

Answers

Answer:

54.45 in²

Step-by-step explanation:

Let the base and height be 9.9 inches and 5.5 inches respectively.

Formula;

Area of parallelogram = Base × Height

Substitute the base and the height in the formula:

⇒ Area of parallelogram = Base × Height⇒ Area of parallelogram = 9.9 × 5.5

Evaluate the area of the parallelogram:

⇒ Area of parallelogram = 9.9 in × 5.5 in⇒ Area of parallelogram = 54.45 in²

Answer:

54.45 in²

Step-by-step explanation:

Formula

Area of a parallelogram = base × height

If you turn the parallelogram so that the sides that measure 9.9in are the base, you will see that 5.5in is the height (refer to the attached diagram).  Therefore, we can use the formula with these values to calculate the area.

Given:

base = 9.9 inheight - 5.5 in

⇒ area = 9.9 × 5.5 = 54.45 in²

find the values of the expression below when x = -4 and y= 2 -3x^2y+ 4x

Answers

Answer:

20720

Step-by-step explanation:

-3x^2y +4x

-3(-4)^2*2 + 4(-4)

= 12^4 -16

20736 - 16

= 20720

I hope this helped!

Answer:

When x = -4 and y = 2, -3x^(2y) + 4x is -784.

Step-by-step explanation:

-3x^(2y) + 4x

Substitute given variables.

-3(-4)^(2(2)) + 4(-4)

Multiply 2 and 2.

-3(-4)^4 + 4(-4)

Multiply -3 and -4.

Raise -4 to the 4th power.

-3(256) + 4(-4)
Multiply -3 and 256.

-768 + 4(-4)

Multiply 4 and -4

-768 + (-16)

Add -768 and -16.

-784

What is the surface area of the square pyramid? 30 m 18 m ות 36​

Answers

Answer:

the answer is 5100 im pretty sure.

Step-by-step explanation:

yes

If two cars hit head on at 50 mph what is the force of the impact?

Answers

Answer:

100mph

Step-by-step explanation:

PLEASE HELP PLEASE HELP PLEASE

Answers

Awnser: B is your awnser

Reason: you start at 1 and go to 5 15:16 and then you can just minus 5 15:16 by 1 making it 4 15:16

Answer:

D

Step-by-step explanation:

Well, the right edge is 1 line away from 6 so it is 5 15/16 inches.

There are 16 lines for each 1 line. so it is 5 inches and 15 lines out of 16

what digit 7 sits in this number 714,583​

Answers

Answer:

The hundred thousands place

Step-by-step explanation:

Answer:

The hundred thoudsands place; (700,000)

Step-by-step explanation:

The places of the number are listed below:

Hundred Thousands - 700,000
Ten Thousands - 10000
Thousands - 4000
Hundreds - 500
Tens - 80
Ones - 3

The digit 7 is in the hundred thoudsands place.

hope this helps!

HELP!! ASAPP!! (NO LINKS) WILL MARK BRAINLIEST

Identify the trinomial that is NOT a perfect square.


A. 121x^2 + 100x + 25

B. 100x^2 + 60x + 9

C. 25x^2 + 70x + 49

D. 64x^2 + 48x + 9

Answers

ANSWER: C. 25x^2 + 70x + 49

Hope for help po

What is the value of x?

Answers

Answer:

x=20

Step-by-step explanation:

These vertically opposite angles are equal

3x+50=6x-10

50+10=6x-3x

3x=60

x=20

Step-by-step explanation:

3x+50=6x-10(vertically opp angles)

3x-6x=-10-50

-3x=-60

Divide both side by - 3

X=20

Which type of function best models the data in the
table?
Sound Waves
Wavelength, *
© linear
exponential
o quadratic
inverse variation
Frequenc
(waves
680
0.5
1
340
227
15
DONE
2
170
25
136

Answers

Answer:

inverse variation

Step-by-step explanation:

$300 today is worth MORE than $300 tomorrow.
False or true?

Answers

false if the prices increase tomorrow or true if the prices decrease.

so basically it's always uphill so false

hope it helps...!!!

ANSWER:

false

EXPLANATION:

pls help me rn pleaseeeeeeeeeeeeeeee

Answers

I believe it’s negative, positive, zero

Box A contains only 20-cent coins and Box B contains only 50-cent coins. The number of coins in Box A is twice the number of coins in Box B. The amount of money in Box B is $1.60 more than the amount of money in Box A. How many 20-cent coins are there in Box A?​

Answers

Answer:

There should be 16, 20 cent coins in the box

Step-by-step explanation:

First we have to do 1.60 x 2 which equals 3.2

Then we divided by 0.20 because the equals the 20 cent coins

We get 16

We can check our work by 0.20 x 16 and that gives us 3.2

I hope this helps!

Pls helpppp thankssss

Answers

Answer:

D

Step-by-step explanation:

y=5x-2 since the formula is. y=mx+c

What is the value of x in the triangle?
45°
4
х
45°
OA. 4
B. 2
OC. 412
OD. 212

Answers

Answer:

D

Step-by-step explanation:

use the sine or cosine ratio in the right triangle.

using the sine ratio and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 4[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = 2[tex]\sqrt{2}[/tex]

The value of x is 2√2.

Hence the correct option is D.

Given that a right triangle with acute angles 45° each, and hypotenuse is 4 units,

we need to find the length of the perpendicular,

In a right triangle, the length of the perpendicular (also known as the altitude) can be found using trigonometric ratios.

In this case, since we have an angle of 45°, we can use the sine or cosine function.

Let's use the sine function to find the length of the perpendicular:

sin(45°) = opposite / hypotenuse

sin(45°) = perpendicular / 4

1/√2 = perpendicular / 4

perpendicular = 4/√2

perpendicular = 2√2

Hence the value of x is 2√2.

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anyone? giving brainliest

Answers

The answer is A I’m sure of it because 180-77-58 is 45

find the value of each variable in the given parallelogram

Answers

Answer:

x=16, y=26, z=13

Step-by-step explanation:

opposite angles are congruent so (3x+30)=(4x+14)

Solve for x

x=16

adjacent sides are supplementary so insert x in both equations just to make sure it is correct and you get 78

so 3y=78 and 6z=78

solve for y and z

y=26, z=13



Which algebraic rule describes the translation of ΔDEF to ΔD'E'F'?

Answers

Since the entire triangle is translated we can only refer to one point on the triangle, for example take point F(-1,3)

After Translation:F'(-5,-4)

we subtracted 4 from the x value

we subtracted 7 from the y value

Answer:

(x,y) => (x-4,y-7)

- Classify the quadrilateral in as many ways as possible.




.

Answers

rombus Rectangle sqare

Step-by-step explanation:

all have 4 Sides

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