Is your question written correctly? Just making sure.
Answer:
The quadratic mean of 2 real positive numbers is greater than or equal to the arithmetic mean.
Step-by-step explanation:
x and y Quadratic Mean Arithmetic mean
3 and 3 3 3
2 and 3 2.55 2.5
3 and 6 4.74 4.5
2 and 5 3.8 3.5
2 and 17 12.1 9.5
18 and 28 23.5 23
10 and 48 34.7 29
The quadratic mean is always greater than the arithmetic mean except when x and y are the same.
When the difference between the pairs is small the difference in the means is also small. As that difference increases the difference in the means also increases.
So we conjecture that the quadratic mean is always greater than or equal to the arithmetic mean.
Proof.
Suppose it is true then:
√(x^2 + y^2) / 2) ≥ (x + y)/2 Squaring both sides:
(x ^2 + y^2) / 2 ≥ (x + y)^2 / 4 Multiply through by 4:
2x^2 +2y^2 ≥ (x + y)^2
2x^2 +2y^2 >= x^2 + 2xy + y^2
x^2 + y^2 >= 2xy.
x^2 - 2xy + y^2 ≥ 0
(x - y)^2 ≥ 0
This is true because the square of any real number is positive so the original inequality must also be true.
1 notebook costs $3.45
let's turn this into 2 equations, n being notebook price, and b being binder price ->
mandy -> 3n + b = 5.85
jordan -> 2n + b = 4.65
we need to take one equation, simplify for b, and plug it into the other equation, let's take jordan's equation for this ->
b = 4.65 - 2n
plug it into mandy's equation
3n + (4.65 - 2n) = 5.85
simpify until you get n = 1.20
take this and plug it back into jordan's equation ->
2(1.20) + b = 4.65
simplify until you get b = 2.25
plus this value into mnady's equation ->
3n + (2.25) = 5.85
simplify until you get that n = 2.25
Answer:
$3600
Step-by-step explanation:
she saves $300 a month for 12 months.
300×12=3600
hope this helps!
