An open box is to be constructed so that the length of the base is 3 times larger than the width of the base. If the cost to construct the base is 4 dollars per square foot and the cost to construct the four sides is 1 dollars per square foot, determine the dimensions for a box to have volume

Answers

Answer 1

Answer:

Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

[tex]L = 3w --- (1)volume = l \times w \times h \\ \\ 88 = (3w) \times w \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\[/tex]

The construction cost now is:

[tex]C = 4(l \times w) + 2 ( w \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}[/tex]

Now, to determine the minimum cost:

[tex]\dfrac{dC}{dw}= 0 \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}[/tex]

[tex]w = \dfrac{88}{3(3)}^{1/3} \ feet[/tex]

Now;

[tex]length = 3 ( \dfrac{88}{3(3)})^{1/3} \ feet[/tex]

[tex]height = ( 88})^{1/3} (3)^{1/3} \ feet[/tex]


Related Questions

Factor 7/10 out of 7/10z+21.

7/10z+21=

Answers

Answer:

1/100 (1471 z + 2100)

0.01 (1471 z + 2100) the result I got

and the Factorization over the splitting field:

14.71 z + 21

If x = 2 and y = 4, what is 6x - 5y?

Answers

Answer:

-8

Step-by-step explanation:

6(2) = 12

5(4) = 20

12-20

-8

Answer:

44

Step-by-step explanation:

(6x4)+(5x4)= 44

Solve

(Perimeter)

Rectangle

Side- 10

Side- 5

Answers

the perimeter is 30

10*2=20
5*2=10
20+10=30

asap
Five students, Jeremiah, Claire, Alyssa, Brody, and Hudson, line up one behind the
other. How many different ways can they stand in line?

Answers

Answer:

25 dfferent ways

Step-by-step explanation:

The answer is 25 different ways because since there are students and thy line up behind each other you  would do 5 times 5 which equals to 25.

Which two integers is -√21 between?

Answers

Answer:

-5 and -4

Step-by-step explanation:

-√21  =  -4.58

Please help with these two problems don't rip me off I'm being generous.

Answers

Answer:

8 is $230

Step-by-step explanation:because there is a fee of $55 and $25 a week, the $55 is a one time charge and then $25 times 7 weeks is $175 then $55+$75 is $230

Find the lateral area of this cone.
Leave your answer in terms of a.
12cm
5cm
LA = [ ?]

Answers

The answer is
A=65pi cm2

Determine the value of x so that the numbers a1 = In(x + 2). a2 = In(x + 3).
a3 = In(4x + 8) form three consecutive members of an arithmetic sequence.
Select one:
a. Such x does not exist.
b. x = -+1
c. There are two possible solutions.
d. x = -1
e. None of the remaining possibilities is correct.

Answers

Answer:

Step-by-step explanation:

hello :

the numbers a1 , a2 ,a3

form three consecutive members of an arithmetic sequence means : 2a2 = a1+,a3

2 In(x + 3) = In(x + 2)+In(4x + 8)....(*)

now solve this equation use this note :

ln a^n = alna and : lna+lnb =lnab lna =lnb means : a=b ...a , b positif numbers

(*) equivaut : In(x + 3)² = In(x + 2)(4x + 8) and : x + 2 ,x + 3 , 4x + 8

are positifs numbers

(x + 3)² = (x + 2)(4x + 8)

x²+6x+9 = 4x²+16x+16

3x²+10x+7 =0

delta =10²-4(3)(7) 100 -84 = 4²

x1 = (-10-4)/6 = -7/3 reused

x 2 = (-10+4)/6 = -1 reused

conclusion : a. Such x does not exist.

Let X and Y be the following sets:
X = {5, 10, 15}
Y = {3, 6, 9, 12, 15}
Which of the following is the set
XUY?

Answers

Answer:

XuY = { 3,5,6,9,10,12,15}

Help me please please

Answers

9514 1404 393

Answer:

  A: 8 ft²

  B: draw diagonal AC; 4 ft²

Step-by-step explanation:

Part A: The area is given by the formula ...

  A = bh . . . . . . . the product of base and height dimensions

  A = (9 ft)(8/9 ft) = 8 ft² . . . . area of the parallelogram

__

Part B:

Either diagonal (AC or BD) will divide the parallelogram into two congruent triangles, each with the same base and height as the parallelogram. It is no surprise, then, that the area of either of those triangles is ...

  A = 1/2bh

  A = 1/2(9 ft)(8/9 ft) = 4 ft² . . . . . . area of triangular half of parallelogram

__

AC divides the figure into congruent acute triangles; BD divides it into congruent obtuse triangles.

PLEASE HELP PLEASE! I AM SO STUCK!

Answers

f(x) = |7m + 4| = 1

First equation by taking positive modules

7m + 4 = 1

7m = -3

m = -3/7 . Ans.

Second equation by taking negative modules

-7m - 4 = 1

-7m = 5

m = -5/7 . Ans.

∴ m = [ -5/7 U -3/7 ] Ans .

Complete the table for all the lengths and widths that are missing for
Claire's garden.
*This is only some of the table from the problem.


Answers

Answer:

Step-by-step explanation:

x is 1,2,3,4,5

y is 14,13,12,11,10

If the discount is 27%, then what percentage of the original price do you pay? Please give an explanation as well if you can! Thank you in advance.


Whoever answers correctly will get Brainliest. Stay happy and have a blessed rest of your day. :)

Answers

100-27=73
Therefore you paid 73% of the original price. That’s the remaining percentage

Find the solution set for this inequality:
-4(3x - 5) < 2(3x + 4)

A. x > -(1)/2
B. x < -(1)/2
C. x > 2/3
D. x < 2/3

PLS ANSWER ASAP!! WILL MARK AS BRAINLYIST!!!!
time left (3:23)!!

Answers

Answer is c I believe, so sorry if I’m wrong

Find the percent of change from 32 feet to 79 feet. Round to the nearest tenth, if necessary. Then state whether the percent of change is percent of increase or percent of decrease.

Answers

Answer:

71 1/4%

Step-by-step explanation:

I think the change is percentage increase. the method of finding percentage iincrease is increase over percentage increase x 100%

Please help

Look at picture

Answers

Answer:

1/3

Step-by-step explanation:

Please help meeeeeeeeeeeeeeeee please

Answers

9514 1404 393

Answer:

  2.1 ft³

Step-by-step explanation:

Put the given radius and height into the volume formula and do the arithmetic.

  V = 1/3πr²h

  V = 1/3(3.14159)(1 ft)²(2 ft) ≈ 2.094 ft³

Rounded to tenths, this is 2.1 cubic feet.

__

The picture cuts off your rounding requirements. If it is hundredths, you need to use 2.09 ft³. If it is thousandths, your answer will depend on the value of pi you are asked to use.

Determine the solution

Answers

Answer:

:/

Step-by-step explanation:

:/

A public opinion survey investigated whether a majority (more than 50%) of adults supported a tax increase to help fund the local school system. A random sample of 200 adults showed that 113 of those sampled supported the tax increase.
Researchers used these results to test H0​:p=0.5 versus Ha​:p>0.5, where p is the true proportion of adults that support the tax increase. They calculated a test statistic of z≈1.84 and a corresponding P-value of approximately 0.033.
Assuming the conditions for inference were met, which of these is an appropriate conclusion?
A. At the α=0.01 significance level, they should conclude that more than 50% of adults support the tax increase.
B. At the α=0.01 significance level, they should conclude that less than 50% of adults support the tax increase.
C. At the α=0.05 significance level, they should conclude that more than 50% of adults support the tax increase.
D. At the α=0.05 significance level, they should conclude that less than 50% of adults support the tax increase.

Answers

Answer: C. At the α=0.05 significance level, they should conclude that more than 50% of adults support the tax increase.

Step-by-step explanation:

Given: Null hypothesis: [tex]H_0:p=0.5[/tex]

Alternative hypothesis: [tex]H_a: p>0.5[/tex]

p-value = 0.033

If the p-value is greater than alpha (p > . 05), then we fail to reject the null hypothesis.

If α=0.01 , then p-value > α i.e. we fail to reject the null hypothesis.

Conclusion: Exactly 50% of adults support the tax increase.

If α=0.05 then p-value < α i.e. we reject the null hypothesis.

Conclusion: more than 50% of adults support the tax increase.

Thus, Correct option: C .

Answer: At the a = 0.05 significance level, they should conclude that more than 50% of adults support the tax increase.

Step-by-step explanation:

how many millitres of curry poweder are needed​

Answers

Answer:

3 kfjdasidutiriqkvjcksot

Answer:

2 Tbsp

Step-by-step explanation:

Our simple homemade curry powder is an easy way to have instant access to curry powder, using spices that you probably already have in your pantry. (We have found that 2 Tbsp (6 tsp) of curry powder is typically enough to season one recipe of curry for 4 people.)

Hope it helps you. please give me brainliest if it is correct

evaluate the intergral2x(xsquared+3)exponent 4​

Answers

Answer:

Step-by-step explanation:

I hope it helped you

At his birthday party, Aiden collected 15% of the candy that fell out of the pinata. If Aiden collected 6 pieces of candy, how many pieces of candy fell out of the pinata?

pls help its today

Answers

Answer:

40 pieces

Step-by-step explanation:

To make it easier I divided each number (15, 6) by 3 and then multiplied by 2.

10% of candy = 4 pieces

Multiply by 10

100% of candy = 40 pieces

Solve for f(-7)

f(x)=5-x

f(-7)= ?

Answers

Answer:

7 f + 5 ??

Step-by-step explanation:

Which lists the fractions and in order from least to greatest?
9/5,13/8,1 3/4

Answers

Answer:

A

Step-by-step explanation:

13/8, 1 3/4, 9/5

Answer: Hi! Your Answer Is A: 13/8, 1 3/4, 9/5! Please Mark The Person Above Me Brainliest Don't Forget Thank You! :D

Step-by-step explanation: Hi! Your answer is A but please Mark The Person Above Me  Brainliest ! :D

Solve for x in the equation x2 - 12x+ 36 = 90

Answers

Answer:

6 + 3[tex]\sqrt{10\\}[/tex] or 6 - 3[tex]\sqrt{10\\}[/tex]

Step-by-step explanation:

x^2 - 12x + 36 = 90

x^2 - 12x - 54 = 0

x = [tex]\frac{-b +/- \sqrt{b^{2} + 4ac }}{2a}[/tex]

a = 1, b= -12, c= -54

6 + 3[tex]\sqrt{10\\}[/tex] or 6 - 3[tex]\sqrt{10\\}[/tex]

Find the range of the data.
67, 63, 72, 62, 64, 81, 74, 66
The range is
WILL GET BRAINLEST

Answers

Answer: Range is 19

HOPE THIS HELP!

helppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

A

Step-by-step explanation:

Pi r^2 is the equation to solve any circle. R=5 in this case, so A is your answer.

Pretty sure the answer is A

Please help.. You can answer one if you want but whoever answers both get brainliest

Answers

Answer:

l

Step-by-step explanation:

l

each group of students receives a bag that has 4 red cubes, 9 green cubes and 7 blue cubes if if each group makes 200 pulls and replaces the cube after each pull, how many times would you expect them to draw a green cube?

Answers

There are 20 cubes total. Green cubes make up 9/20 of the cubes. So if you make 20 pulls with replacement you would expect to get 9 green cubes. Therefore, you would expect to pull a green cube 90 times after pulling 200 cubes.

pls help me understand this pls show how u got it​

Answers

Answer:

25 inches

Step-by-step explanation:

Area is given as 75 in^2

Area of a triangle = 1/2 * base * height

             75            = 1/2 (6) * height

             75 / (1/2 * 6) = height

                     25 inches = height

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