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3 years ago

12

A spherical ball of wax with a radius of 5 inches is melted and poured into a container shaped like a rectangular prism with a 1

2 inch x 10 inch base. What is the height of the melted wax in the new shape?

2 answers:

Novosadov [1.4K]3 years ago

7 0

Answer:

4.36 in

Step-by-step explanation:

To solve this problem we first find the volume of the sphere using the volume formula, after this we set this volume equal to the volume container which is a rectangular prism. After this we simple solve for the height by dividing the volume of the sphere by 12*10 to get the height

So the steps should look like

(4/3)*π*5³=523.599 in³

523.599 in³=12*10*Height

(523.599/(12*10))=4.36 in

Sati [7]3 years ago

7 0

Answer:

4.4

Step-by-step explanation:

Took the test and got it right.

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Choices A, C and F work. This is because when in radical form, you may dive or subtract as long as you keep the sign. The square root of 9 is 3 and the square root of 4 is 2. When you solve it, the answer is 6. Hope this helped!

7 0

3 years ago

Read 2 more answers

Equilateral triangle ABC has an area of \sqrt{3}√ 3 . If the shaded region has an area of \piπK − \sqrt{3}√ 3 , what

Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ $(2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)$

∴ $4=r^{2}+r^{2}-2(r)(r)(-0.5)$

∴ $4=r^{2}+r^{2}-(-r^{2})$

∴ $4=r^{2}+r^{2}+r^{2}$

∴ $4=3r^{2}$

- Divide both sides by 3

∴ $r^{2}=\frac{4}{3}$

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

7 0

3 years ago

I need help please!!

mina [271]

Step-by-step explanation:

11

$\frac{ - 1}{5} \times \frac{4}{7}$

$\: \: \: \: \: \frac{ - 4}{35}$

12

$\frac{ - 1}{2} \times \frac{4}{5}$

$\frac{ - 2}{5}$

13

$\frac{ - 3}{2} \times \frac{7}{ - 10}$

$\frac{21}{20}$

14

$\frac{1}{2} \times \frac{7}{8}$

$\frac{7}{16}$

15

$\frac{ - 9}{5} \times \frac{1}{2}$

$\frac{ - 9}{10}$

16

$\frac{ - 32}{9} \times \frac{1}{3}$

$\frac{ - 32}{27}$

17

$\frac{ - 2}{1} \div \frac{ - 19}{5}$

$\: \: \: \: \: \: \frac{ - 2}{1} \times \frac{5}{ - 19}$

$\: \: \: \: \frac{ - 10}{19}$

18

$\frac{1}{9} \div \frac{ - 4}{3}$

$\frac{1}{9} \times \frac{3}{ - 4}$

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19

$\frac{13}{7} \div \frac{23}{4}$

$\frac{13}{7} \times \frac{4}{23}$

$\frac{52}{161}$

20

$\frac{ - 37}{10} \div \frac{9}{4}$

$\frac{ - 37}{10} \times \frac{4}{9}$

$\frac{ - 74}{45}$

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3 years ago

Read 2 more answers

Pls help i need it.

stepan [7]

Answer:

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3 years ago

Clara created the poster shown below:

lana66690 [7]

Answer:

$length=4\ cm\\width=6\ cm$

Step-by-step explanation:

Given the rectangular poster shown in the picture, you know that its dimensions (its width and its lenght) are:

$w_1=24\ cm\\l_1=16\ cm$

In order to calculate the dimensions of the rectangular at $\frac{1}{4}$ times its current size, you need to multiply the original lenght by $\frac{1}{4}$ and multiply the original width by $\frac{1}{4}$ .

Knowing this, you get:

$w_2=w_1\frac{1}{4}\\\\w_2=(24\ cm)(\frac{1}{4})\\\\w_2=6\ cm\\\\\\l_2=l_1\frac{1}{4}\\\\l_2=(16\ cm)(\frac{1}{4})\\\\l_2=4\ cm$

6 0

3 years ago