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Sergio [31]
4 years ago
6

Chloe has two pyramid shaped paperweights that have the same height and cross-sectional area. which of the following best descri

bes the relationship between the paperweights according to Cavalieri's principle?
Mathematics
1 answer:
Ira Lisetskai [31]4 years ago
7 0
According to Cavalieri's principle, if two solids have the same height an the same cross-sectional area at every level, then they have the same volume. So the statement that would best describe the relationship between the paperweights according to Cavalieri's principle is that, t<span>he volumes of the paperweights are the same. Hope this helps.</span>
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Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3
Irina18 [472]

Answer:

Step-by-step explanation:

Let the ends of the given segment are A and B.

Coordinates of A → (8, 6)

Coordinates of B → (12, 12)

If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,

(x, y) → (kx, ky)

If k = \frac{2}{3}

(x, y) → (\frac{2}{3}x, \frac{2}{3}y)

By this rule coordinates of the image points of A and B will be,

A(8, 6) → A'(\frac{2\times 8}{3},\frac{2\times 6}{3})

           → A'(5.3, 4)

B(12, 12) → B'(\frac{12\times 2}{3}, \frac{12\times 2}{3})

             → B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of \frac{2}{3}.

5 0
3 years ago
If a stone tower is 15 meters tall and casts a shadow 8 meters long, then how long of a
goldenfox [79]

Answer:

32 meters long (please double-check! sometimes ppl make mistakes)

Step-by-step explanation:

the ratio of height to shadow length is 15:8, as established in the first sentence. if both sides of the ratio are multiplied by 4 then the ratio becomes 60:32.

more in depth:

if you think of it as fractions (which ratios can be written as) multiplying both the numerator and denominator by four is the equivalent of multiplying by 4/4 aka 1 so the value still stays the same (one times something is the same thing). since the ratio of height to shadow length is constant we needed to solve for the ratio in which the height is 60, so multiply each side by 4 (aka 60 divided by 15) to find the new ratio, 15(4):8(4) or 60:32. the ratio 60:32 describes height to shadow, so while the height is 60 (said in the problem) then the shadow length is 32. adding units, the answer would be 32 meters.

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