Regina owns a drum that has a diameter of 14 inches and a height of 5.5 inches, as shown below. She wants to design a new drum b
y dilating the dimensions of the original drum by a scale factor of 1.4. 14 in. 5.5 in. What will be the diameter, d, and the height, h, of the new drum? F. d 19.6 in. and h 7.7 in. G. d 15.4 in. and h 6.9 in. H. d 12.5 in. and h 4 in. J. d 22.5 in. and h 14 in.
1 answer:
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Ah, this is an infinite sum question, or a sum of geometric sequence
when will the sum reach 1cm of the edge or about 1.99m
so
2m=200cm
within 1cm means at least 1.99m
so
we will use m and not cm for consitancy
sum of geometric sequence is
a1=first term=initial jjump=1
r=common ratio=1/2
n=?, we ar solving for that
so
we want it to equal 1.99 so
divide both sides by 2
times -1
add 1 or 2/2 to both sides
take the ln of both sides
divide both sides by ln(1/2)
use your calculatro to find that n≈7.64386
so on 7th jump, it is not yet at 1cm to the edge but at 8th jump, it is past
so 8th jump
when will the sum reach 1cm of the edge or about 1.99m
so
2m=200cm
within 1cm means at least 1.99m
so
we will use m and not cm for consitancy
sum of geometric sequence is
a1=first term=initial jjump=1
r=common ratio=1/2
n=?, we ar solving for that
so
we want it to equal 1.99 so
divide both sides by 2
times -1
add 1 or 2/2 to both sides
take the ln of both sides
divide both sides by ln(1/2)
use your calculatro to find that n≈7.64386
so on 7th jump, it is not yet at 1cm to the edge but at 8th jump, it is past
so 8th jump