Answer:
we can draw the graph of cosine with amplitude 2.
Step-by-step explanation:
In the given function g(x) = 2cosx we know the following parameters which are helpful to draw the graph.
Its a cosine graph given in the form of y = acos(Bx + c) + d
Here a is amplitude, period = 
, c = phase shift, d = vertical shift
We know a = 2, B = 
, c = 0, d = 0.
Answer:
11
Step-by-step explanation:
a + 4 = ? you cannot solve this
but then they give you a help they tell you that a is equal to 7, so you can basically write 7 instead of a
7+4 = 11
Answer:
Step-by-step explanation:
2-6+9=5
Using the Pythagorean theorem we get:
Simplifying the above result we get:
Subtracting 64 from the above equation we get:
Therefore:
Answer:
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.
