<span>Using processing software (Excel) or even a decent scientific calculator. You input the values and generate the best fit cubic equation.
For number 1, the equation is
y = 8x10</span>⁻⁵ x³ - 0.0097 x² + 0.374 x + 1.083
where x is the number of years since 1900
y is the pounds cheese consumed
For number 2, the equation is
y = -3x10⁻⁵ x³ + 0.0028 x² + 0.2155 x + 1.7736
For number 3
P(-1) = 18
20x^2+50 = -40x^2+110x [ Taking x as the unknown positive integer ]
Answer:
580
Step-by-step explanation:
4*100=400
4*40=160
4*5=20
add them all up, you get 580
Answer: q = -13
Step-by-step explanation:
(q+5)/4 = -2 first you multiply 4 to remove denominators
(q+5) = -8 then subtract 5
q = -13
First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.
We have
130 = 2 • 5 • 13
231 = 3 • 7 • 11
so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.
To verify the claim, we try to solve the system of congruences

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:
130 = 7 • 17 + 11
17 = 1 • 11 + 6
11 = 1 • 6 + 5
6 = 1 • 5 + 1
⇒ 1 = 23 • 17 - 3 • 130
Then
23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)
so that x = 23.
Repeat for 231 and 17:
231 = 13 • 17 + 10
17 = 1 • 10 + 7
10 = 1 • 7 + 3
7 = 2 • 3 + 1
⇒ 1 = 68 • 17 - 5 • 231
Then
68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)
so that y = 68.