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3 years ago

Explain how Cavalieri’s principle can be used to find the volume of any solid.

Mathematics

1 answer:

Kruka [31]3 years ago

8 0

Answer:

Cavalier's principle can be used to find the volume of any solid.

Step-by-step explanation:

Cavalier's Principle:

Cavalier introduced parallel planes and area to describe the relationship between solids.
Cavalier stated if two solids have the same height and equal areas of the base everywhere along the height then the solids have the same volume.

Suppose two regions are included between two parallel planes.
If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
The formula for the volume of a prism is the area of the base times the height.

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Graph shows the solution to the following inequality 40 - 6 is less than 18

Veseljchak [2.6K]

Step 1) Add 6 to both sides
Step 2) Divide both sides by 4

Following those steps above, you'll have this
4d - 6 < 18
4d - 6 + 6 < 18 + 6 .... applying step 1
4d + 0 < 24
4d < 24
4d/4 < 24/4 .... applying step 2
d < 6

So d can be any number that is less than 6. To graph this, we draw a number line, plot an open circle at 6 and shade to the left of the open circle. The open circle indicates to exclude the endpoint. The graph I'm describing is choice D

Answer: Choice D

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3 years ago

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Fantom [35]

Answer:

8.5

Step-by-step explanation:

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3 years ago

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When you add numbers with a common factor of 2, will the answer have a common factor of 2

zhannawk [14.2K]

Answer:

yes

Step-by-step explanation:

adding together even numbers will give an even result

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3 years ago

A set of city temperatures in April are normally distributed with a mean of 19.7 degrees Celsius and a standard deviation of 2 d

Sati [7]

Answer:

19.77% of average city temperatures are higher than that of Cairo

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 19.7, \sigma = 2$

What percentage of average city temperatures are higher than that of Cairo?

This is 1 subtracted by the pvalue of Z when X = 21.4.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21.4 - 19.7}{2}$

$Z = 0.85$

$Z = 0.85$ has a pvalue of 0.8023

1 - 0.8023 = 0.1977

19.77% of average city temperatures are higher than that of Cairo

6 0

3 years ago

The circle below has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters. A c

frez [133]

Answer:

31/40

Step-by-step explanation:

The question is incomplete. Here is the complete question with appropriate diagram.

The circle below has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters.

What is the probability that a point chosen at random is in the blue region?

Given the area of the circle to be 314cm², we need to get the diameter of the circle first since the diameter of the circle is equivalent to length of the side of the square inscribed in it.

Using the formula Area of a circle = πr²

314 = 3.14r²

r² = 314/3.14

r² = 100

r = 10 cm

Diameter of the circle = 2*10 = 20 cm

Area of a square = Length * length

Area of the outer square = 20*20 = 400cm²

Area of the inner square with side length 2cm = 2*2 =4cm²

Area of the shaded region = Area of the square - Area of the inner square

= 314-4 = 310cm²

The probability that a point chosen at random is in the blue region = Area of the shaded region/total area of the outer square

= 310/400

= 31/40

3 0

4 years ago