Hello from MrBillDoesMath!
Answer:
The first choice, Pi + (-Pi) = 0
Discussion:
Pi is an irrational number. Saying the irrational numbers <u>are</u> closed under addition means if we add two irrational numbers we will get another irrational number. In our case, Pi + (-Pi) = 0, which is correct, BUT 0 is a <u>rational </u>number. This shows the set of irrational numbers is NOT closed under addition.
Thank you,
MrB
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
<h3>How to derive a sinusoidal expression</h3>
In this problem we need to find a <em>sinusoidal</em> expression that models the curve seen in the picture. The most typical <em>sinusoidal</em> model is described below:
f(x) = a · sin (b · x + c) + d (1)
Where:
- a - Amplitude
- b - Angular frequency
- c - Angular phase
- d - Vertical midpoint
Now we proceed to find the value of each variable:
Amplitude
a = - 2 - (-6.5)
a = 4.5
Angular frequency
b = 2π / T, where T is the period.
0.25 · T = 4 - 3
T = 4
b = 2π / 4
b = π / 2
Midpoint
d = - 6.5
Angular phase
- 2 = 4.5 · sin (π · 4/2 + c) - 6.5
4.5 = 4.5 · sin (π · 4/2 + c)
1 = sin (2π + c)
π = 2π + c
c = - π
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
To learn more on trigonometric functions: brainly.com/question/15706158
#SPJ1
Answer:
It'd be easist if one of the variables was by itself
Step-by-step explanation:
I.E: y=2x+4 and 2y+x=23
Y=mx+b
slope: 3/2
y-intercept: -5
