Which shows a correct order to solve this story problem?

A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th

Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

A square base and no top
It needs to be made using 300 ft² of material
It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ $y=\frac{75}{x}-\frac{1}{4}x$

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ $V=x^{2}(\frac{75}{x}-\frac{1}{4}x)$

∴ $V=75x-\frac{1}{4}x^{3}$

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ $\frac{dV}{dx}=75-\frac{3}{4}x^{2}$

∵ $\frac{dV}{dx}=0$ ⇒ greatest volume

∴ $75-\frac{3}{4}x^{2}=0$

- Subtract 75 from both sides

∴ $-\frac{3}{4}x^{2}=-75$

- Divide both sides by $-\frac{3}{4}$

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ $y=\frac{75}{10}-\frac{1}{4}(10)$

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ $V=75x-\frac{1}{4}x^{3}$

∵ x = 10

∴ $V=75(10)-\frac{1}{4}(10)^{3}$

∴ $V=750-\frac{1}{4}(1000)$

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0

3 years ago

What is the measure of angle X? Enter your answer as a decimal in the box. Round only your answer to the nearest hundredth. ° tr

klemol [59]

I have attached a diagram of the triangle described.

We can use any of the trigonometric functions to find angle x. Remember, SOH CAH TOA. And since we're finding the angle, we'll need to use an inverse trigonometric function. For this problem, I'll be using the sine function.

sin(x) = 84 / 85

x = sin^-1(84/85)

x = 81.2026 degrees (feel free to round to however many places you need)

Hope this helps!! :)

8 0

4 years ago

What is the hypothesis in this conditional statement?

nexus9112 [7]

The answer is
A.
Hope This Helps

8 0

3 years ago

What Numbers Go Into The Venn Diagram

antiseptic1488 [7]

Answer:

(a)The total number of outcomes where the sum is 9 or

greater than 9 is 10

(b)Total number of outcomes where the sum is odd = 18

(c)Total number of outcomes where the sum greater or equal to 9 and is

also odd = 6

Step-by-step explanation:

Here, Sample Space = { Sum of the two digits when two dices are thrown together}

or, S = {2,3,4,5,6,7,8,9,10,11,12}

(a) The number of ordered pairs where sum is 9 or greater than 9

= { sum is 9 , Sum is 10 , Sum is 11, Sum is 12}

= {(6,3)(3,6),(4,5)(5,4) , (5,5), (6,4),(4,6) , (6,5)(5,6), (6,6)}

Hence the total number of outcomes where the sum is 9 or

greater than 9 is 10

(b) The number of ordered pairs where sum is odd.

= { Sum is 3 , Sum is 5, Sum is 7, Sum is 9, Sum is 11}

= {(1,2)(2,1), (4,1)(1,4),(2,3)(3,2) , (6,1), (1,6),(5,2),(2,5),(4,3)(3,4) ,

(6,3)(3,6), (4,5)(5,4), (6,5),(5,6)} = 18

Hence total number of outcomes where the sum is odd = 18

(c) Intersection point refers the outcomes which have sum greater or equal to 9 and is odd

Here, the possible outcomes are = { Sum is 9 , Sum is 11}

={ (6,3)(3,6), (4,5)(5,4), (6,5),(5,6)} = 6

Hence total number of outcomes where the sum greater or equal to 9 and is also odd = 6

6 0

3 years ago

Isabel will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an a

zaharov [31]

The missing part of the question is "For what amount of driving do the two plans cost the same"

The amount of driving that do the two plans cost the same is 450 miles

Step-by-step explanation:

Isabel will rent a car for the weekend. She can choose one of two plans

The first plan has an initial fee of $46 and costs an additional $0.13 per mile driven
The second plan has an initial fee of $55 and costs an additional $0.11 per mile driven

We need to find for what amount of driving do the two plans cost the same

Assume that she will drive for d miles

The first plan:

∵ The initial fee is $46

∵ The additional cost is 0.13 per mile

∵ She will drive for d miles

- The cost of her trip is the sum of $46 and the product of

0.13 and d

∴ The cost = 46 + 0.13 d ⇒ (1)

The second plan:

∵ The initial fee is $55

∵ The additional cost is 0.11 per mile

∵ She will drive for d miles

- The cost of her trip is the sum of $55 and the product of

0.11 and d

∴ The cost = 55 + 0.11 d ⇒ (2)

∵ The cost of the two plans is the same

- Equate (1) and (2) to find d

∴ 46 + 0.13 d = 55 + 0.11 d

- Subtract 46 from both sides

∴ 0.13 d = 0.11 d + 9

- Subtract 0.11 d from both sides

∴ 0.02 d = 9

- Divide both sides by 0.02

∴ d = 450

The amount of driving that do the two plans cost the same is 450 miles

Learn more:

You can learn more about the word problems in brainly.com/question/3950386

#LearnwithBrainly

5 0

4 years ago