MATHEMATICS MIDDLE SCHOOL

Monte performs an experiment using 2 identical graduated cylinders with a radius of 2 cm. The volume of the liquid in the first graduated cylinder is 188.4 cm3. The volume of the liquid in the second graduated cylinder is 314 cm3.What is the difference in the height of the liquid in the two cylinders?

Use 3.14 to approximate pi.

Answers

Answer 1

Answer:

Answer:

The difference of height is 10 cm

Step-by-step explanation:

Monte performs an experiment using 2 identical graduated cylinders with a radius of 2 cm.

The volume of the liquid in the first graduated cylinder is 188.4 cm³

The volume of the liquid in the second graduated cylinder is 314 cm³

Let height of first graduated cylinder be h₁ and radius (r) = 2 cm

Let height of second graduated cylinder be h₂ and radius (r) = 2 cm

Formula:

$\text{Volume of cylinder}=\pi r^2h$

$\text{Volume of 1st cylinder}=\pi\cdot 2^2h_1$

$188.4=3.14\cdot 2^2\cdot h_1$

$h_1=15$ cm

$\text{Volume of 2nd cylinder}=\pi\cdot 2^2h_2$

$314=3.14\cdot 2^2\cdot h_2$

$h_2=25$ cm

The difference in the height of the liquid in two cylinder,

$\Rightarrow h_2-h_1$

$\Rightarrow 25-15$

$\Rightarrow 10$ cm

Hence, The difference of height is 10 cm

Answer 2

Answer: Volume of a cylinder of radius r, height h : $V=\pi*r^2*h$

hence the height of the liquid in the first cylinder is $h1=(188.4)/(2^2\pi)=15$ cm, and in the second cylinder $h2=(314)/(2^2\pi)=25$ cm

Hence the difference is h2-h1=25-15=10 cm

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When 33 is added to a number the result is 13 more than 5 times the number.What is the number?

Answers

x - the number

$x+33=5x+13 \nx-5x=13-33 \n-4x=-20 \nx=(-20)/(-4) \nx=5$

The number is 5.

When 33 is added to a number, x+33
the result is 13 more than 5 times the number:
x+33=5x+13

THE ANSWER IS IN THE PICTURE DOWN BELOW.

I WROTE IT SOMEWHERE ELSE JUST TO SEE WHAT TO DO BUT I WAS TOO LAZY TO REWRITE IT ALL HERE SO I JUST TOOK A SCREENSHOT. BUT ANYWAYS HOPE THIS HELPS!!!!!!! :)

!= Question HelpLast month you spent $50 on clothing. This month you spent 120% of what you spent last month. Set
up a proportion to model this situation. How much did you spend this month?
Set up a proportion to model this situation. Choose the correct answer below

Answers

Answer:

This month you spent $60

50 x

__ = __

1 1.2

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5x + 10 = −4x − 17 what is x

Answers

5x + 10 = -4x - 17
+4x +4x

5x + 4x = 9x

9x + 10 = -17
-10 -10

-27

9x = -27 9x/9 = -27/9

x = -3

this is how you solve for x;

5x + 10 = -4x -17

5x + 4x + 10 = -4x +4x -17 (add 4x on both sides)

9x + 10 = -17

9x +10-10 = -17 -10 (subtract 10 on both sides)

9x = - 27 (next do the inverse operation of x)

x = -27 ÷ 9

x = -3

What total length of ribbon is needed to Line the two long sides of the hat?

Answers

Answer:

Total length of ribbon to line the long sides will be 22 in

Step-by-step explanation:

In the given figure of kite if we draw a line "h" vertically will form two right angle triangles.

Then by applying Pythagoras theorem in both the triangles.

h²= (3x + 5)² + (2x + 1)² ------(1)

h²= (5x + 1)² + 5² ------(2)

By equating both the equations

(3x + 5)² + (2x + 1)² = (5x + 1)² + 25

9x² + 25 + 30x + 4x² + 4x + 1 = 25x² + 10x + 1 + 25

13x² + 34x + 26 = 25x² + 10x + 26

13x² - 25x² + 34x - 10x + 26 - 26 = 0

- 12x² + 24x = 0

12x² - 24x = 0

x² - 2x = 0

x(x - 2) = 0

x = 2

Now we will put x = 2 in the measure of sides of the kite.

Side 1 = (3x + 5)

= 3×2 + 5

= 11

Side 2 = (5x + 1)

= 5×2 + 1

= 11

Side 3 = (2x + 1)

= 2×2 + 1

= 5

Therefore, Total length of ribbon to line the long sides will be = 11 + 11

= 22 in.

Your answer will be D-22.

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Answers

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