The tangent ratio is
tan(38°) = opposite/adjacent = (height of cliff)/(distance to base)
Multiplying the equation by the denominator gives
height of cliff = (80 ft)*tan(38°) ≈ 62.5 ft
Answer:
The fourth image, or D.
Why?
If you had a ruler and placed it on the grid vertically and moved the ruler left to right, pictures A, B, and C, all have two points that lay on the same X point.
Picture D is the only one that has no points that lay on the same X point, thus making it the right answer.
Thank you for reading into this.
(Hope this helps you! ^^)
The rows add up to
, respectively. (Notice they're all powers of 2)
The sum of the numbers in row
is
.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When
,
so the base case holds. Assume the claim holds for
, so that
Use this to show that it holds for
.
Notice that
So you can write the expansion for
as
and since
, you have
and so the claim holds for
, thus proving the claim overall that
Setting
gives
which agrees with the result obtained for part (c).
Answer:
Yes a number with 3 digits is usually bigger than a number with 2 digits but sometimes if it is a decimal than the decimal can be bigger
