Valeria drives 500 meters up a hill that makes an angle of 15 degrees with the horizontal. To the nearest tenth of a meter, what
horizontal distance has she covered?
1 answer:
Answer:
Approximately 485 meters
Step-by-step explanation:
We can first construct a right triangle, using the 500 m length of hill as our hypotenuse. Using the fact that the cosine of an angle is the ratio of the adjacent side to the hypotenuse, we see that
where x is the horizontal distance covered. Solving for x, we find this horizontal distance to be
so our answer is approximately 485 m.
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Answer:
Yes, he will have enough 3 over 8 ft pieces for his class.
Step-by-step explanation:
Given:
Number of wood required = 22
Length of each wood,
Total length of the board,
Therefore, the number of woods that can be made using the given board is given as:
So, he can make 24 woods of length using the 9 ft board. But he has to make only 22 pieces.
Therefore, he has enough of the wood to make the required number of pieces.
By induction:
It's true for
, since 
clearly contains a factor of 3.
Suppose it's true for
, that 
is divisible by 3. Then
where
is an integer. This reduces to
and both terms are clearly multiples of 3. We know that
is an integer since we had set 
previously, which implies is a multiple of 
. So the statement is true.
It's true for
Suppose it's true for
where
and both terms are clearly multiples of 3. We know that