Answer:
annually compounded interest at 7. 5% for three years will pay more by $22.97
Explanation:
Simple interest
A = P (1+ rt)
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
A = 10000(1+0.08x3) = $12,400
Annual compound interest
A = P (1+ r/n)^nt
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
A = 10000(1+0.075/1)^(1x3) = $12,422.97
$12,422.97 - $12,400 = $22.97
Using sum and difference identities from trigonometric identities shows that; Asin(ωt)cos(φ) +Acos(ωt)sin(φ) = Asin(ωt + φ)
<h3>How to prove Trigonometric Identities?</h3>
We know from sum and difference identities that;
sin (α + β) = sin(α)cos(β) + cos(α)sin(β)
sin (α - β) = sin(α)cos(β) - cos(α)sin(β)
c₂ = Acos(φ)
c₁ = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
c₁² + c₂² =
(Asin(φ))² + (Acos(φ))²
= A²(sin(φ)² +cos(φ)²)
= A² * 1
= A²
Using common factor as shown in the trigonometric identity above for Asin(ωt)cos(φ) +Acos(ωt)sin(φ) gives us; Asin(ωt + φ)
Complete Question is;
y(t) = distance of weight from equilibrium position
ω = Angular Frequency (measured in radians per second)
A = Amplitude
φ = Phase shift
c₂ = Acos(φ)
c₁ = Asin(φ)
Use the information above and the trigonometric identities to prove that
Asin(ωt + φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Read more about Trigonometric Identities at; brainly.com/question/7331447
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Answer:
Forgiveness can and should exist within the criminal justice system.
Explanation: I hope this helps
