Answer:
Addition Property of Equality
Step-by-step explanation:
You are adding 3/4 to both sides to isolate the <em>x</em>.
The length of the line segment here is 13.
Distance Formula:
√((x₂ - x₁)² + (y₂ - y₁))
√((5 - 0)² + (0 - 12)²) = 13
I used my calculator and got x=1 y=3
solve for y to put them in your calculator
2.1x+4.2y=14.7
y = (14.7 -2.1x)/4.2
−5.7x−1.9y=−11.4
y=(-11.4 +5.7x)/(-1.9)
then using the ploting tool I plotted them and found where they intersected
Answer:
A = √29
Step-by-step explanation:
The short of it is that ...
A² = 2² + 5² = 29
A = √29
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<u>Amplitude</u>
If you expand the second form using the sum-of-angles formula, you get ...
Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Comparing this to the first form, you find ...
c₂ = 2 = Acos(φ)
c₁ = 5 = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
(Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²
In terms of c₁ and c₂, this is ...
(c₁)² +(c₂)² = A²
A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude
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<u>Phase Shift</u>
We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...
φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*
φ = arctan(5/2) ≈ 1.19029 radians
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* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.
