What’s the cosine of

Mathematics

1 answer:

Vsevolod [243]3 years ago

4 0

Answer:

√23/√45 or √23/3√5

Step-by-step explanation:

Cosine is adjacent over hypotenuse. Angle W has an adjacent side of WU(√23) and WV .You know the adjacent but not the hypotenuse, so you will use the formula a^2+b^2=c^2 to find the hypotenuse. Plug in the sides for A and B -> (√23)^2+(√22)^2=c^2. Simplify it --> 23+22=c^2 --> 45=c^2. Solve for C alone (not c^2). √45=c. Then use the cosine formula (adjacent/hypotenuse) to plug in the numbers.

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Imagine a pond. In it sits one lilypad, which reproduces once a day. Each of its offspring also reproduces once a day, doubling

sergeinik [125]

Answer: On the 29th day

Step-by-step explanation:

According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.

On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.

The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are $2^{30}$ lilypads on the 30th, and $2^{29}$ lilypads on the 29th. This can be deduced multiplying succesively by 2.