Answer:
p = 5 and q = -3
Step-by-step explanation:
nth term = pn^2 + qn where n is the sequence number.
first term = p + q = 2.....................(1)
2nd term = p(2)^2 + 2n = 14
4p + 2q = 14
2p + q = 7 .......................(2)
Subtract equations (2) -(1) :-
p = 7 - 2 = 5
and q = 2 - 5 = -3
Answer:
The tree was 40 in tall when planted
The tree's growth rate is 10in per year
Ten years after Planting, it is 140 inches tall
Step-by-step explanation:
original(slope intercept form) : y = 10x + 40
y = 10(10) + 40
y = 100 + 40
y = 40
1) 50000
2) 770000
because you look at the place value before the 10,000 place and if it's above 4, then you round up. if it's below 5, you round down.
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.
A. you plug in to a calculator, which will give 1840.986 so you need to round up to 1840.99. if you truncate it to .98 then he won't reach 2000 in 3 years
b. for this one if you look at the equation given to find the principle it is principle = result (1+rate) ^ -time
if you re arrange this you get result=principle (1+rate)^time
so result = 1840.99(1.028)^5
= 2113.57
