Two similar cones have radii in the ratio n:m. What is the ratio of their slant heights?

Mathematics

1 answer:

denis-greek [22]3 years ago

8 0

Answer:

The ratio of the slant heights of the two cones will also be n : m.

Step-by-step explanation:

See the attached diagram.

If we take the vertical sections along any diameter of the base circle of the cones A and B then the triangular sections as we get will be similar.

Now, ratio of the base of the triangles A and B i.e. the ratio of the diameters of the cones A and B will be 2n : 2m = n : m and this will be the same as the ratios of other two sides of the triangles A and B.

Therefore, the ratio of the slant heights of the two cones will also be n : m. (Answer)

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The average of six positive integers starting with a is equal to b. What is the average of five consecutive integers ending with

kvasek [131]

The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.

<h3>What is the average of five consecutive integers ending with b?</h3>

First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;

(a+a+2+a+4+a+6+a+8+a+10)/6 = b

6b=6a+30

b=a+5

Also, let the average of the consecutive intergers ending with b be denoted by; x.

(b+b-1+b-2+b-3+b-4)/5 = x

=(5b-10)/5

=b–2

The average, x=b – 2 (where b = a-5)

Ultimately, the value of the required average is; = a+5-2 = a+3.

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