Let S be the set of all integers k such that, if k is in S, then
"TexFormula1" title="\frac{17k}{66}" alt="\frac{17k}{66}" align="absmiddle" class="latex-formula"> and 
are terminating decimals. What is the smallest integer in S that is greater than 2010?
1 answer:
Answer:
2079
Step-by-step explanation:
In order for the decimal equivalents to be terminating, the only factors that can remain in the denominators are 2 and 5.
Here, the given denominators are
66 = 2·3·11
105 = 5·3·7
So, the values of k must be multiples of 3, 7, and 11. The least common multiple of these numbers is 3·7·11 = 231, so ...
S = {0, ±231, ±462, ±693, ...}
The smallest member of S that is greater than 2010 is ...
ceiling(2010/231)·231 = 9·231 = 2079
_____
For k=2079, the terminating decimals are ...
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Step-by-step explanation:
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= 0.25 x
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Answer:
The height of the flag pole will be = 18.96 ft.
Step-by-step explanation:
See the attached diagram.
AB is the flag pole and the length of the shadow is AC.
Now, Δ ABC is a right triangle and has AB = 3x ft., BC = 20 ft. and AC = x ft.
So, applying Pythagoras theorem ,
AB² + AC² = BC²
⇒ (3x)² + x² = 20²
⇒ 10x² = 400
⇒ x² = 40
⇒ x = 6.32 ft. (Approx.)
So, the height of the flag pole will be = 3x = 3 × 6.32 = 18.96 ft. (Answer)
