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2 years ago

Solve for the balloon volume using the equation below

Mathematics

1 answer:

valentinak56 [21]2 years ago

3 0

The volume of the balloon is 1441.64cm³.

<h3>How to calculate the volume?</h3>

The radius of the balloon is given as 7cm. Also, the equation to calculate the volume is given as c³/6π²

The circumference c will be:

= 2πr = 2 × 22/7 × 7

= 44

The volume will be:

= c³/6π²

= 44³/(6 × 3.14²)

= 85284/(59.1576)

= 1441.64

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Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new hou

Musya8 [376]

The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;

(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

(2) The longest installable sprinkler system is approximately 172.4 feet

<h3>How can the points where the line crosses the farmland be found?</h3>

1. The slope of the sewer line is found as follows;

m = (6 - 3)/(12 - 2) = 3/10 = 0.3

The equation of the sewer line can be expressed in point and slope form as follows;

(y - 3) = 0.3×(x - 2)

y = 0.3•x - 0.6 + 3

y = 0.3•x + 2.4

The equation of the circumference of the sprinkler can be expressed as follows;

(x - 8)² + (y - 3)² = 2²

Therefore;

(x - 8)² + (0.3•x + 2.4 - 3)² = 2²

Solving gives;

x= 6.53, or x = 8.48

y = 0.3×6.53 + 2.4 = 4.36

y = 0.3×8.48 + 2.4 = 4.9

Therefore;

The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

2. When the farmland does not cross the sewer line, we have;

sewer line is tangent to circumference of farmland

Slope of radial line from center of the land is therefore;

m1 = -1/0.3

Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;

y - 3 = (-1/0.3)×(x - 8)

Which gives;

y = (-1/0.3)×(x - 8) + 3

The x-coordinate is therefore;

0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3

x ≈ 7.5

y = 0.3 × 7.5 + 2.4 ≈ 4.65

The longest sprinkler system is therefore;

d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724

Which gives;

The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.

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3 0

2 years ago

Which of the following mathematical symbols represents “the opposite of”?what do they mean

Lunna [17]

The negative sign show the change in direction, that is the opposite side of the value.

In the number line, 1 is the opposite of -1, that is the digit from the left side is the opposite value of the right side.

Consider an object P is moving in positive x direction than on moving the object into its opposite direction, it will move along the negative x axis.

Answer : A) -

5 0

1 year ago

GEOMETRY If one point is located at (–6, 2) and another point is located at (6, –3), find the distance between the points.

notka56 [123]

Answer:

It should be 13 units.

Step-by-step explanation:

In the picture shown, the two red dots are the coordinates (-6, 2) and (6, -3). The smaller light blue dots is the distance from one red dot to the other red dot. I counted 17 units between the two and using a ruler, I estimated 12 units. In conclusion, it should be roughly 13 units. I hope this helps! If this is not the right answer, I would love to recieve some feedback of what I did wrong! Thank you!

7 0

3 years ago

Can you guys help me I’d really appreciate it!

KatRina [158]

Answer:

A. Part to whole

You are comparing the vanilla ice cream (part of the whole) to the total number of ice cream cups (the whole), so therefore you have a part to whole comparison.

I hope I could help :)

8 0

3 years ago

Find the value of L. Perimeter = 22. Width is 3. So what is L? On a rectangular

yanalaym [24]

Perimeter of rectangle =2 X( L + w)
width=3
perimeter=22
length =?

2(L+3) =22
=>2L+6 =22
=>2L = 22-6
=>2L =16
=>L = 16/2
=>L=8 ..

Hope it helps !!!

8 0

2 years ago