Answer:
Debbie runs 9 feet per second: 9 ft/s
Jessica runs 1 mile in 440 seconds: 414/50 ft/s = 207/25 ft/s = 8 7/25 ft/s
jesssica runs 131 feet in 10 seconds: since 1 mile = 5280 ft we have 1/470 mi/s = 5280/470 ft/s = 528/47 ft/s = 11 11/47 ft/s
ron runs 603 feet in 1 minute: 547 ft/min = 603/60 ft/s = 201/20 ft/s = 10 1/20 ft/s
Since:
11 11/47 > 10 1/20 > 9 > 8 7/25
Emily runs the fastest.
Find the equation of 2 of the line segment, then find the perpendicular lines to them, then solve for x by making the perpendicular equations equal
Answer:
φ ≈ 1.19029 radians (≈ 68.2°)
Step-by-step explanation:
There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.
We want to compare ...
y(t) = Asin(ωt +φ)
to
y(t) = Psin(ωt) +Qcos(ωt)
Using trig identities to expand the first equation, we have ...
y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Matching coefficients with the second equation, we have ...
P = Acos(φ)
Q = Asin(φ)
The ratio of these eliminates A and gives a relation for φ:
Q/P = sin(φ)/cos(φ)
Q/P = tan(φ)
φ = arctan(Q/P) . . . . taking quadrant into account
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We can also use our equations for P and Q to find A:
P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²
A = √(P² +Q²)
_____
Here, we want φ.
φ = arctan(Q/P) = arctan(5/2)
φ ≈ 1.19029 . . . radians
I would think it to be A because 8/12 can be simplified into 3/4
