Answer:
The equation will be altered by doubling the angular velocity of motion, resulting in d(s) = 7·sin(720s)
Step-by-step explanation:
The current equation of the pendulum-like motion of the pocket watch is d(s) = 7sin(360s)
The formula for simple harmonic motion is x = A·sin(ω₁t + ∅)
By comparing, we find;
x = d(s)
A = 7
ω₁t = 360
∅ = 0
The period of oscillation is the duration needed for a complete cycle, calculated as 2·π/ω₁.
Thus;
ω₁ = 2·π/T₁
When the frequency of the swing doubles, the time taken to complete one cycle is halved, hence, the new period is T₂ = T₁/2.
Consequently, ω₂ = 2·π/T₂ = 2·π/(T₁/2) = 4·π/T₁ = 2ω₁.
The revised equation becomes:
x = A·sin(ω₂t) = A·sin(2ω₁t) leading to;
d(s) = 7·sin(2 × 360s) = 7·sin(720s).
This illustrates the modification due to an increase in the angular frequency of motion.
The correct answer is perpendicular based on the concept of Parallel and Perpendicular lines from Khan Academy.
Answer:
Rob's total debt to his father is calculated as: -$15 - $3 = -$18
Step-by-step explanation:
Initially, Rob borrows $15.
Then, he borrows an additional $3.
Expressing this with negative integers gives us
-15 - 3 = -18
Answer:
15.7 inches
Step-by-step breakdown:
A slice of a round pie is a sector of a circle.
The perimeter of a slice equals the arc length s plus two times the radius r.
P = s + 2r
s = rθ = r(16/360) = r/22.5. Therefore,
16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5
16 × 22.5 = 46r
360 = 46r
r = 7.826
D = 2r = 2 × 7.826 = 15.7 inches
Thus, the diameter of the cake should be 15.7 inches.
Verification:
It is accurate.
