Answer:
Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.
The base case is n=2. P(2) is true because 2 is prime.
Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that
p1*p2*...*pj = a
pj+1*pj+2*...*pl = b
As a result
n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl
Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.
Label your sides= hypotenuse(h),opposite(o),adjacent(a)
hypotenuse=longest(opposite the right angle)
opposite= opposite the other angle
adjacent= the other side
see which sides are involved
in this case it is adjacent and hypotenuse
so A and H
we have to use the SOHCAHTOA rule
Sin=o/h Cos=a/h Tan=o/a
we use cos because a and h are involved
Cos(15°)=62/x
rearrange the equation to find x
x= 62/cos(15)
put this in your calculator
x= 64.12
Answer:
3.50378787879
Step-by-step explanation:
Answer:
3600 ways
Step-by-step explanation:
person A has 7 places to choose from :
→ He has 2 places ,one to the extreme left of the line ,the other to the extreme right of the line
If he chose one of those two ,person B will have 5 choices and the other 5 persons will have 5! Choices.
⇒ number of arrangements = 2×5×5! = 1 200
→ But Person A also , can choose one of the 5 places in between the two extremes .
If he chose one of those 5 ,person B will have 4 choices and the other 5 persons wil have 5! Choices.
⇒ number of arrangements = 5×4×5! = 2 400
In Total they can be arranged in :
1200 + 2400 = 3600 ways
I think it is 3 good luck me saying this then u getting the wrong answer
