Answer:
The prove is as given below
Step-by-step explanation:
Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.
Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.
Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.
So this indicates that there are infinite prime numbers of the form 4k+3.
Answer:
Step-by-step explanation:
3x2x2=12
5x7x3=105
We have trapezoid with congruent legs.
30x + 11y = 2x + 3
28x +11y = 3
Also we have
30x + 11y = 12
We got 2 equations:
30x + 11y = 12
28x +11y = 3 (*-1) -----> -28x -11y = -3
30x + 11y = 12
<u> -28x -11y = -3</u>
2x = 9
x=9/2
30x + 11y = 12 ------> 30*9/2 +11y =12 ------> 135+11y =12, ---> 11y = - 123,
y= - 123/11
Answer: 13 . 99 seconds
Step-by-step explanation:
The formula to find how long it will take an object to rotate through 6.9 revolutions at an angular velocity is given as :
t = 2π x number of revolutions / angular velocity
Therefore :
t = 2π x 6.9 / 3.1
t = 2 x 3.142 x 6.9 / 3.1
t = 43.3596/3.1
t = 13. 98696774194
to the nearest tenth
t = 13. 99s
