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2 years ago

7

Tiana would like to buy cone-shaped hats for her birthday party. She wants hats with the largest volume, since they look bigger.

Which of the following brands of hat should she buy?

2 answers:

Alexus [3.1K]2 years ago

7 0

Probably the ones that are big..

pantera1 [17]2 years ago

6 0

This question seems to be incomplete, maybe there are diagrams which different cone shaped hat types. In that case, find the volume of each cone. The largest volume will be the answer. To solve for volume of a cone: V=πr2h/3 . So, it’s Pi times RAdius squared times height all divided by 3

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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

2 years ago

Determine the domain and range of the following graph

ipn [44]

Answer:

<u>As per the graph we see:</u>

Domain is:

x = [0, 1]

Range is:

y = [-4, -3]

7 0

2 years ago

Read 2 more answers

A calculator is required to obtain the final answer on this question. A solid metal sphere at room temperature 20oC is dropped i

yKpoI14uk [10]

Answer:

T = 47.1875°C

Step-by-step explanation:

Given:

Surrounding temp, Ts = 100°C

Initial Temperature ,T0= 20°C

Increase in temperature = 15°C

Final temperature, T = 20 + 15 = 35°C

Time, t = 9 seconds

Let's take Newton's law of cooling:

$T - Ts = (T_0 - Ts)e^k^t$

We'll solve for k

$35 - 100 = (20 - 100)e^9^k$

$-65 = (-80)e^9^k$

Divide both sides by -5

$13 = (16)e^9^k$

$9k = ln (\frac{13}{16})$

$k = \frac{1}{9} ln (\frac{13}{16})$

$k = -0.02307104053$

Let's now find the temperature of the ball after 18 seconds in boiling water.

Use the Newton's equation again:

$T - Ts = (T_0 - Ts)e^k^t$

$T - 100 = (20 - 100)e^-0.0^2^3^0^7^1^0^4^0^5^3^*^1^8$

$T - 100 = (-80)e^-0.0^2^3^0^7^1^0^4^0^5^3^*^1^8$

$T - 100= -52.8125$

$T = 100 - 52.8125$

T = 47.1875°C

Temperature of the ball after 18 seconds in boiling water is 47.1875°C

5 0

3 years ago

3c+6=18 how do you work this problem?

Bogdan [553]

Answer:

c = 4

Step-by-step explanation:

Simplifying

3c + 6 = 18

Reorder the terms:

6 + 3c = 18

Solving

6 + 3c = 18

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + 3c = 18 + -6

Combine like terms: 6 + -6 = 0

0 + 3c = 18 + -6

3c = 18 + -6

Combine like terms: 18 + -6 = 12

3c = 12

Divide each side by '3'.

c = 4

Simplifying

c = 4

4 0

2 years ago

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The “new look” of the cereal boxes has a length that is three more than two times the width, x, and a height that is one more th

jok3333 [9.3K]

The first option is correct. For the following question, the simplified expression for the volume is 8x3 + 14x2 + 3x.

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2 years ago

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